‘Should I stay or should I go?‘ refers not only to an iconic 1980s punk anthem but also the fundamental dilemma all animals face in uncertain or unstable environments. Should someone buy coffee from the cafe that serves their favorite roast or try the new cafe that opened down the street? If their favorite drink is bitter one day, is that a sign to switch to a new blend or is one subpar experience inadequate to prompt a switch? Ultimately, these decisions converge to a single predicament: whether we choose an action that we believe is likely to produce desirable results (i.e. exploit) or risk choosing another action that is less certain, on the chance that it will produce a more positive outcome (i.e. explore) (O’Reilly, 2013). Ultimately, this is the problem of knowing when to change your mind.

The shift of a decision policy from exploratory to exploitative states is driven by environmental context. To illustrate this, Figure 1A shows what happens when a simple reinforcement learning (RL) agent tries to maximize reward in a dynamic variant of the two-armed bandit task (Sutton and Barto, 1998; see Materials and methods). Here, the relative difference in reward probability for the two actions (conflict) and the frequency of a change in the optimal action (volatility) were independently manipulated. For each level of conflict and volatility, a set of tabular Q-learning (Sutton and Barto, 1998) agents played the task with learning rate held constant while the degree of randomness of the selection policy ($\beta$ in a Softmax function) varied. The agent that returned the most rewards was identified as the agent with the best exploration-exploitation balance. Increasing either form of uncertainty led to selecting agents with more random or exploratory selection policies (Figure 1A). As the value of the optimal choice decreases relative to the value of a suboptimal choice (conflict increases), the learner exploits what she already knows. Action values grow unstable (volatility increases) when the clarity of the optimal choice is constant (constant conflict), and the learner is biased toward exploration (Bland and Schaefer, 2012). As these two forms of uncertainty change together, the gradient of action selection strategy also changes.

Figure 1

Download asset Open asset

Knowing how decision policies shift in the face of dynamic environments requires looking at the algorithmic properties of the policy itself. One popular set of algorithms for describing the dynamics of decision making are accumulation-to-bound processes like the drift-diffusion model (DDM; Ratcliff, 1978). The normative form of the DDM proposes that a decision between two choices is described by a noisy accumulation process that drifts toward one of two decision boundaries at a specific rate (Figure 1B). Two parameters of this model are critical in determining the degree of randomness of a selection policy: the rate of evidence accumulation (drift rate; $v$) and the amount of information required to make a decision (boundary height; $a$). For example, decreasing the drift rate and increasing the boundary height leads to more random decisions (Figure 1C), with the speed of these decisions depending on the ratio of the two parameters (Figure 1D). Thus, exploratory policies can result in either fast or slow decisions, depending on the relative configuration of drift rate and boundary height.

Are the parameters that govern accumulation of evidence for decision making modifiable? Previous modeling work has shown that the parameters of a DDM process can be modulated by feedback signals and choice history (Pedersen et al., 2017; Ratcliff and Frank, 2012; Dunovan and Verstynen, 2019; Dunovan et al., 2019; Mendonça et al., 2020; Urai et al., 2018) with different mechanisms for adapting the drift rate and the boundary height. In value-based decision-making tasks where the statistics of sensory signals are equivalent for all actions, drift rate fluctuations appear to track the relative value of an action or the value difference between actions (Dunovan et al., 2019; Mikhael and Bogacz, 2016; Bariselli et al., 2019; Rubin et al., 2021). In contrast to value estimation, selection errors in this context have been linked to changes in the boundary height (Forstmann et al., 2008; Forstmann et al., 2010; Bogacz et al., 2010; Herz et al., 2016; Herz et al., 2017; Dunovan et al., 2019; Dunovan and Verstynen, 2019) and internal estimates of environmental change (Nassar et al., 2010; Wilson and Niv, 2011; Nassar et al., 2012; Behrens et al., 2007).

Given the adaptive sensitivity of the drift rate and the boundary height to value estimation and selection, respectively, these decision parameters define unique states on a surface of fast or slow and exploratory or exploitative decision policies. These policies, in turn, adaptively reconfigure based on current environmental feedback signals by modulating value estimation and the rate of selection errors (Figure 1E). Agents can move along the surface of decision policies, from exploitative states (bright colors, Figure 1E) to different types of exploratory states (darker colors, Figure 1E), as they commit a greater number of selection errors prompted by change in action-outcome contingencies. As the system relearns properties of the environment, the decision policy migrates along the surface to return to an exploitative state until a change occurs again.

One plausible neural mechanism for this migration along the surface of selection policies is the locus coereleus norepinephrine (LC-NE) system, which has been linked to adaptive behavioral variability in response to uncertainty (Urai et al., 2017; Dayan and Yu, 2006; Bouret and Sara, 2005). The LC-NE system has two distinct modes (Aston-Jones and Bloom, 1981) that map onto distinct decision states (Aston-Jones and Cohen, 2005). In the phasic mode, a burst of LC activity results in a global, temporally precise release of NE. This increases the gain on cortical processing and encourages exploitation. In the tonic mode, NE is released without the temporal precision of the phasic mode, increasing baseline NE (Aston-Jones and Bloom, 1981). This encourages disengagement from the current task and facilitates exploration. The dynamic fluctuation of these two modes is thought to optimize the trade-off between the exploitation of stable sources of reward and the exploration of potentially better options (Aston-Jones and Cohen, 2005). Thus the LC-NE system, which can be indirectly measured by fluctuations in pupil diameter (Aston-Jones and Cohen, 2005; Jepma and Nieuwenhuis, 2011), may be a central mechanism for modulating selection policies.

We investigated the malleability of decision policies as the environment necessitates a change of mind as to what constitutes the ‘best’ decision. To control environmental uncertainty, we manipulated the volatility of changes in action-outcome contingencies (i.e. which of two targets returns the most rewards), as well as ambiguity in optimal choice (conflict), while human participants performed a dynamic variant of the two-armed bandit task (Sutton and Barto, 2018). We predicted that, in response to suspected changes in action-outcome contingencies, humans would exhibit a stereotyped adjustment in the drift rate and boundary height that pushes decisions from certain, exploitative states to uncertain, exploratory states and back again (Figure 1E). In addition, using pupillary data, we explored whether the LC-NE system covaries with shifts of the boundary height in response to a change in action outcomes to facilitate exploration, consistent with prior studies (Keung et al., 2019; Murphy et al., 2014; Cavanagh et al., 2014).

Across two experiments, we used a dynamic two-armed bandit task with equivalent sensory reliability across arms to independently manipulate the reward conflict and the volatility of action outcomes in order to measure how underlying decision processes respond to changes in action-outcome contingencies (see Stimuli and Procedure). Both of these experiments shared a common feedback structure. Participants were asked to select either the left or right target presented on the screen using the corresponding key on a response box. Rewards were probabilistically determined for each target and, if a reward was delivered, it was sampled from a Gaussian distribution. The optimally rewarding target delivered reward with a predetermined probability ($P(optimal)$) and the suboptimal target gave reward with the inverse probability ($1-P(optimal)$). After a delay determined by the rate parameter of a Poisson distribution ($\lambda$), the reward probabilities for the optimal and suboptimal targets would switch.

In Experiment 1, 24 participants completed four sessions (high and low conflict; high and low volatility) each composed of 600 trials. During each session, they were asked to select one of two coin boxes (Exp. 1: Figure 2A). The levels of conflict and volatility for all four conditions in Experiment 1 are shown as gray dots in Figure 2C. Experiment 2 was a replication of Experiment 1 with more extensive within-subject sampling of conflict and volatility, as well as the inclusion of pupilometry as a proxy for measuring LC-NE dynamics. In Experiment 2, participants were asked to choose between one of two Greebles (one male, one female). Each Greeble probabilistically delivered a monetary reward (Exp. 2: Figure 2B). Participants were trained to discriminate between male and female Greebles prior to testing to prevent errors in perceptual discrimination from interfering with selection on the basis of value estimation. Four participants completed nine sessions composed of 400 trials each, generating 3600 trials in total per subject. The levels of conflict and volatility for all nine conditions in Experiment 2 are shown as black dots in Figure 2C. Importantly, Experiment 2 manipulated the same forms of uncertainty as Experiment 1, but had different perceptual features and more expansively sampled the space of conflict and volatility. Given the similarity in design, the behavioral results for both of these experiments are presented together below.

Figure 2

Download asset Open asset

The influence of ambiguity and instability on speed and accuracy

We first looked at overall speed and accuracy effects in both Experiments 1 and 2. In Experiment 1, accuracy (i.e. optimal choice selection) suffered as the optimal choice grew more ambiguous, with accuracy in the low conflict condition being 1.2 times higher than what is observed in the high conflict condition (Figure 3A; $\beta =1.213$, 95% CI: 1.192, 1.235, z = 21.36, p < 2e-16). In contrast, increasing conflict had no observable impact on overall reaction times (Figure 3A; $\beta =-6.902e^{-}5$, 95% CI: –0.002, 0.002, t = −0.06, p = 0.951). As expected, participants also became less accurate as the instability of action outcomes (i.e. volatility) grew (Figure 3B; $\beta =0.092$, 95% CI: 0.077, 0.111, z = 10.36, p < 2e-16). Under volatile conditions, participants also took slightly longer to make a decision ($\beta =-0.012$, 95% CI: –0.015,–.010, t = −10.80, p < 2e-16); however, while this effect on reaction times was statistically reliable, the impact of volatility on reaction times was weak (increasing volatility increased reaction time by ∼13 ms on average; Figure 3B).

Figure 3

Download asset Open asset

Experiment 2 served as a high powered test of whether the effects we observed in Experiment 1 were replicable at the within-subject level. Because Experiment 2 independently manipulated conflict and volatility, we were able to test whether conflict and volatility interacted to affect behavior. We found similar effects of conflict and volatility on accuracy as we observed in Experiment 1 (Figure 3C). Accuracy increased as conflict decreased (i.e. as the probability of reward increased; $\beta$=0.223, 95% CI = 0.189,0.256, z = 12.757, p<2e-16). As the environment grew less volatile, accuracy increased ($\beta$ = 0.101, 95% CI = 0.066,0.14, z = 5.828, p = 5.6e-09). We did not observe an interaction of conflict and volatility on accuracy ($\beta$ = 0.024, 95% CI = −0.013, 0.058, z = 1.364, p = 0.173).

However, we did find that conflict and volatility interacted to affect reaction time (RT; $\beta$=−0.002, 95% CI = −0.004, –0.001, t = −3.084, p = 0.002), with a linear increase in reaction time as the environment grew less volatile and conflict was highest (when $p(r)=0.65\overline{RT}=0.472,0.480,0.493$ as a function of $\lambda$; see Figure 3D for RT distributions). When conflict was moderate (${\displaystyle p(r)=0.75}$) or low ($p(r)=0.85$), volatility had a nonlinear effect on RTs. Here, reaction times decreased when volatility was moderate ($\overline{RT}=0.483$ when $\lambda$=20 and ${\displaystyle p(r)=0.75}$ when $\lambda$=20 and $p(r)=0.85$). Reaction times increased to approximately the same extent within moderate or low conflict conditions when volatility was high ($\overline{RT}=0.499$ when $\lambda$=10 and ${\displaystyle p(r)=75}$ when $\lambda$=10 and $p(r)=0.85$) and when volatility was low ($\overline{RT}=0.506$ when $\lambda =30$ and ${\displaystyle p(r)=0.75}$ when $\lambda =30$ and ${\displaystyle p(r)=0.85}$), with an increase in baseline reaction times when conflict was low relative to moderate ($\overline{RT}=0.527$ when ${\displaystyle p(r)=0.85}$ when $p(r)=0.75$; see Appendix 1—figure 1 for interaction visualization).

At the gross level, over all trials within an experimental condition, increasing the ambiguity of the optimal choice (conflict) and increasing the instability of action outcomes (volatility) decreases the probability of selecting the optimal choice. Reaction time effects were inconsistent, with a negligible effect of volatility in Experiment 1. Experiment two revealed that volatility and conflict interact to influence reaction times in complex ways. However, because trials where action-outcome contingencies change are so infrequent, even under high volatility conditions, these overall effects on speed and accuracy may be masking more subtle behavioral dynamics in response to feedback changes. We adopt a more focal, model-based analysis in the next section to clarify these peri-change point dynamics.

Tracking estimates of action value and environmental volatility

We calculated trial-by-trial estimates of two ideal observer parameters of environmental states (see Cognitive model for calculation details; Nassar et al., 2010; Vaghi et al., 2017). Belief in the value difference ($\mathrm{\Delta }B$) reflects the difference between the learned values of the optimal and suboptimal targets. For ease of interpretation, we refer to the converse of belief as doubt, such that when belief decreases doubt increases. $\mathrm{\Delta }B$ thus reflects a local estimate of uncertainty regarding the choices themselves. To capture the estimated probability of fundamental shifts in action values, we calculated how often the same action gave a different reward (change point probability; $\mathrm{\Omega }$). Here, $\mathrm{\Omega }$ reflects a global estimate of uncertainty in the environment, specifically the uncertainty in response contingencies. We used the data from Experiment 1 to assess how well these learning estimates captured our imposed manipulations, and observed similar results in Experiment 2 (Appendix 1—figure 4).

In Experiment 1, we observed a sharp decrease in $\mathrm{\Delta }B$ after a switch in action outcomes and a gradual return to asymptotic values (Figure 4A) with a decreased difference in reward probability resulting in increased doubt (Figure 4B; $\beta =0.216$, 95% CI:0.206, 0.224, t = 46.24, p < 2e-16). As expected, less volatile conditions allowed the learner to more fully update her belief in the value of the optimal choice over all trials ($\beta =0.058$, 95% CI:0.050, 0.068, t = 12.32, p < 2e-16), though to a smaller degree than low conflict conditions allowed (see Figure 4B). Increasing volatility resulted in a sharp increase in the estimate of $\mathrm{\Omega }$ at the onset of a change point with a quick return to a baseline estimate of change (Figure 4C). Notably, this estimate of $\mathrm{\Omega }$ was more sensitive to change points when conditions were relatively volatile, with a more pronounced peak in response to a change under high volatility conditions than under low volatility conditions (Figure 4C). Correspondingly, over all trials, $\mathrm{\Omega }$ was higher under more volatile conditions (Figure 4D, $\beta =-0.022$, 95% CI:−0.023,–0.020, t = −30.74, p < 2e-16) indicating sensitivity to the increased frequency of action outcome switches in the reward schedule.

Figure 4

Download asset Open asset

When the identity of the optimal choice was clear (i.e. when conflict was low), the estimate of $\mathrm{\Omega }$ was more sensitive to the presence of a true change point than when the optimal choice was ambiguous (i.e. when conflict was high) (Figure 4C and D). This observation is consistent with the idea that increasing the difficulty of value estimation and, thereby, the assignment of value to a given choice also impairs change point sensitivity. Interestingly, increasing conflict nevertheless resulted in a net increase in $\mathrm{\Omega }$ calculated over all trials (Figure 4D; $\beta$=−0.006, 95 %CI:−0.007,–0.004, t = −8.64, p < 2e-16), likely because higher conflict conditions increased the baseline estimate of change instead of enhancing sensitivity to true change points (see change point response and relative baseline values for the high conflict condition in Figure 4C). Here, the system conservatively over-estimates the volatility of action outcomes, assuming a slightly greater frequency of changes in the probability of reward for the optimal choice than we imposed (actual proportion of change points for high conflict condition: ${\displaystyle 0.041\pm 0.004}$; estimated ${\displaystyle \mathrm{\Omega }}$).

Reassuringly, net change point probability was much greater when change points were more frequent (see increased $\mathrm{\Omega }$ estimates for high volatility conditions over high conflict conditions in Figure 4D). These results suggest that our formulation of these ideal observer estimates adequately captures our manipulation of volatility and conflict at a continuous level.

Thus, these ideal observer parameters show a reliable response to a change in action-outcome contingencies. The difference in value belief decreases, or doubt increases, when a change point occurs and slowly recovers over the course of six to eight trials as participants learn new action-outcome contingencies. The initial drop in belief difference is deeper and the recovery time after a change point is slower in conditions with greater overall uncertainty (i.e. under high conflict and high volatility). In contrast, internal estimates that a change has occurred briefly spike at a change point, indicating that participants can reliably detect that something has changed, and quickly settle after a few trials. Interestingly, net change point probability estimates are higher in the conditions with higher uncertainty (high conflict, high volatility), likely reflecting increased vigilance for changes in those conditions. In the next section, we explore how the underlying parameters of the decision process itself respond to local changes in action-outcome contingencies.

Different forms of uncertainty impact distinct decision processes

Our next goal was to test which decision parameters were sensitive to a change point. To this end, we estimated the change point evoked response of the boundary height $a$, drift rate $v$, non-decision time $t$, starting bias $z$, and drift criterion $dc$ for each trial surrounding the change point. To detect changes in the change-point-evoked distributions for each decision parameter, we evaluated whether the sequential distributions evoked by each trial were significantly different, beginning with the trial preceding the change point and ending three trials after the change point. For example, if the 95% CI of the $z$ distribution evoked on the trial prior to the change point overlapped with the 95% CI of the distribution evoked on the change point and so on for all successive trials considered, then we would conclude that $z$ failed to show change point sensitivity (see Hierarchical drift diffusion modeling for details). To select the model that best accounted for the data, we compared the deviance information criterion (DIC) scores (Spiegelhalter et al., 2002) for these models. DIC scores provide a measure of model fit adjusted for model complexity and quantify information loss. A lower DIC score indicates a model that loses less information. Here, a difference of ≤ two points from the lowest-scoring model cannot rule out the higher scoring model; a difference of 3–7 points suggests that the higher scoring model has considerably less support; and a difference of 10 points suggests essentially no support for the higher scoring model (Spiegelhalter et al., 2002; Burnham and Anderson, 1998).

Under this analysis, we found that only the boundary height and drift rate showed change point sensitivity as defined above. The drift rate showed a clear, persistent separation between trial-specific distributions, with a rapid decrease at the onset of the change point ($t_{-1}$ 95% CI = 1.021, 1.218; $t_0$=−0.972, –0.779) and a return to baseline values thereafter ($t_1$ = −0.656,,–0.46; $t_2$=0.039, 0.241; $t_3$=0.411, 0.616; Figure 5A). The boundary height showed a transient response to the change point, spiking ($t_{-1}$ 95% CI = 0.792, 0.819; $t_0$=0.820, 0.847) and then dropping to baseline levels ($t_1$ = 0.789, 0.815; $t_2$=0.783, 0.811; $t_3$=0.780, 0.808; Figure 5B).

Figure 5

Download asset Open asset

The remainder of the decision parameters showed no change point sensitivity. Non-decision time showed no clear response ($t_{-1}$ 95% CI = 0.183, 0.188; $t_0$=0.183, 0.186; $t_1$=0.184, 0.191; $t_2$=0.181, 0.186; $t_3$=0.183, 0.186; Figure 5C) along with the starting bias ($t_{-1}$ 95% CI = −0.112,,–0.01; $t_0$=−0.098, 0.002; $t_1$=−0.090, 0.008; $t_2$=−0.069, 0.032; $t_3$=−0.055, 0.045; Figure 5D) and the drift criterion ($t_{-1}$ 95% CI = 0.229, 0.439; $t_0$=0.175, 0.374; $t_1$=0.223, 0.435; $t_2$=0.245, 0.458; $t_3$=0.244, 0.464; Figure 5E).

Further, models fitting drift rate and boundary height lost the least null-model-adjusted information relative to models of the change-point-evoked response for the other parameters, showing that a change-point-evoked decrease in drift rate and spike in the boundary height best accounted for our observational data in comparison to all alternatives ($\mathrm{\Delta }DI{C}_{null}$ for $v$ = –978 and $\mathrm{\Delta }DI{C}_{null}$ for $a$ = –13.7; see Figure 5F).

Given that only the drift rate and boundary height showed change point sensitivity, we next focused on how those two parameters related to internal estimates of change and conflict in both experiments. Recall that we used the ideal observer parameters $\mathrm{\Delta }B$ and $\mathrm{\Omega }$ as proxies for internal estimates of belief in the difference in learned target values and change point probability, respectively. This provided a continuous quantification of our manipulation of conflict and volatility (see Tracking estimates of action value and environmental volatility). Experiment 2 provided an intensively sampled within-subject test of the change-point-evoked mapping between decision processes and these ideal observer estimates.

In order to determine the nature of the mapping between the ideal observer parameters and the change-point sensitive decision parameters, we estimated single and dual-parameter models mapping $\mathrm{\Delta }B$ and $\mathrm{\Omega }$ and the change-point-sensitive decision parameters, drift rate and boundary height, and examined the fit of these models to our data. We found that the model mapping $\mathrm{\Delta }B$ to drift rate and $\mathrm{\Omega }$ to boundary height provided the best fit in Experiment 1 ($\mathrm{\Delta }DI{C}_{null}=-2698.0$; left panel of Table 1).

Table 1

Experiment 1
	${\displaystyle \mathrm{\Delta }B}$	${\displaystyle \mathrm{\Omega }}$	DIC	${\displaystyle \mathrm{\Delta }{\text{DIC}}_{\text{null}}}$	${\displaystyle \mathrm{\Delta }DI{C}_{best}}$
*I	$v$	$a$	–18643.9	–2698.0	0.0
II	$a$	$v$	–16265.6	–319.7	2378.3
III	–	$v$	–16180.5	–234.7	2463.3
IV	$v$	–	–18630.8	–2684.9	13.1
V	–	$a$	–15949.20	–3.4	2694.7
VI	$a$	–	–16032.8	–87.0	2611.1
VII	–	–	–15945.8	0.0	2698.0
Experiment 2
	$\mathrm{\Delta }B$	$\mathrm{\Omega }$	$\mathrm{\Delta }{\text{DIC}}_{\text{null}}$	$\mathrm{\Delta }{\text{DIC}}_{\text{best}}$
*∼I	$v$	$a$	–90.3 ± 71.7	1.0 ± 0.8
II	$a$	$v$	–7.6 ± 13.1	83.8 ± 60.5
III	–	$v$	–8.5 ± 13.1	82.9 ± 61.4
*∼IV	$v$	–	–90.8 ± 71.0	0.5 ± 1.1
V	–	$a$	0.3 ± 2.5	91.6 ± 70.6
VI	$a$	–	0.95 ± 1.4	92.3 ± 70.9
VII	–	–	0 ± 0	91.3 ± 71.5

To test whether this mapping was preserved in an independent data set, we performed the same model comparison procedure for Experiment 2. Because Experiment 2 followed a replication-based design, we fit a separate model to each subject to assess the replicability of the best fitting model from Experiment 1. While we found support for the model mapping $\mathrm{\Delta }B$ to drift rate and $\mathrm{\Omega }$ to boundary height, we also found that the DIC scores for the single-parameter model mapping $\mathrm{\Delta }B$ to $v$ alone fit the data equally well (see bottom panel of Table 1 for summary statistics and Appendix 3—table 1). Altogether, this suggests that we have strong evidentiary support for a mapping between value-driven belief and drift rate (Figure 6A, blue). However, the support for a mapping between change point probability and boundary height (Figure 6A, red), while robustly present in Experiment 1, fails to appear when tested in an independent data set.

Figure 6

Download asset Open asset

For a more granular assessment of how drift rate and boundary height respond to a change point, we quantified the change-point-evoked effect of $\mathrm{\Delta }B$ and $\mathrm{\Omega }$ on drift rate and boundary height, respectively, for both experiments (see Hierarchical drift diffusion modeling for details). In Experiment 1, we found that the rate of evidence accumulation, $v$, increased with the belief in the value of the optimal choice relative to a change point (${\beta }_{v\sim \mathrm{\Delta }B}=0.576$, 95% CI: 0.544, 0.609, empirical $p=0.000$; Figure 6B, left panel). The boundary height increased with change point probability (${\beta }_{a\sim \mathrm{\Omega }}=0.046$, 95% CI: 0.005, 0.088, empirical $p=0.001$; Figure 6B, right panel).

Experiment two showed similar, but attenuated, results, with drift rate increasing with $\mathrm{\Delta }B$ (${\beta }_{v\sim \mathrm{\Delta }B}=0.112$, 95% CI: 0.016, 0.227, empirical $p=0.004$; Figure 6B, inset panel on left) and an unreliable effect of $\mathrm{\Omega }$ on boundary height (${\beta }_{a\sim \mathrm{\Omega }}=-0.036$, 95% CI: –0.155, 0.097, empirical $p=0.282$; Figure 6B, inset panel on right). Therefore, as the belief in the value of the optimal choice approaches the reward value for the optimal choice, the rate of information accumulation increases. An internal estimate of change point probability weakly increases the amount of information required to make a decision, although this latter effect is less reliable.

Altogether, these results suggest a drift rate mechanism for adaptation to change that may also combine with boundary height dynamics (Figure 6A). However, the strength of the drift rate response weakened and the boundary height response was statistically unreliable in Experiment 2 (Figure 6B inset panels). When a change point is detected and the threshold for committing to a choice (a) responds, it shows a weak, transient increase. At the same time, the drift rate approaches zero, allowing time for the decision process to diffuse and encouraging a random selection. As the learner accrues information about the new optimal choice, the rate of information accumulation slowly recovers to asymptotic levels, with the decision process assuming a more directed path toward the choice that has accrued evidence for reward. Together, the changes in these underlying decision processes, largely driven by drift rate dynamics, point to a mechanism for gathering information in a relatively slow, unbiased manner shortly after the learner suspects she should update her valuation. We now explore these dynamics in more detail in the next section.

Environmental instability prompts a stereotyped decision trajectory

So far, we have established that both the drift rate and the boundary height can be independently manipulated by two different estimates of environmental uncertainty with different temporal dynamics, although this effect reduces to drift rate dynamics in Experiment 2. This suggests that a change in action-outcome contingencies prompts a unique trajectory through the space of possible decision policies (Figure 1E).

To visualize this trajectory, we plot the temporal relationship between drift rate and boundary height beginning with the trial prior to the change point and ending three trials after the change point (Figure 7A). To clearly visualize the distribution of the change-point driven response in the relationship between drift rate and boundary height over time, we also represent the trialwise shift in these two decision variables as vectors. The trial-by-trial estimates of drift rate and boundary height were taken from the best model of the fitted change-point-evoked response and z-scored (see Different forms of uncertainty impact distinct decision processes for model selection). Then the difference between each sequential set of boundary height and drift rate coordinates, $(a,v)$, was calculated to produce a vector length. The arc tangent between these differenced values was computed to yield an angle in radians between sequential decision vectors, concisely representing the overall decision dynamics ($\theta$, Figure 7B; see Decision vector representation for methodological details).

Figure 7

Download asset Open asset

For Experiment 1, following a shift in response contingencies, the navigation of this decision surface follows a stereotyped pattern. The boundary height spikes and drift rate decreases rapidly, gradually recovering and stabilizing over time (see the trial prior to the change point in Figure 7A). This decision trajectory is robust in Experiment 1 (Figure 7B, top panel).

Here, we find that the distribution of $\theta$ prior to a change point averages to ∼300°, sharply changes in response to the observation of a change point (∼165°) and steadily returns to values prior to the onset of a change (main panels in Figure 7B). One trial after the change point, drift rate sharply decreases and boundary height spikes, after which boundary height quickly recovers and drift rate steadily progresses toward its baseline value.

However, this trajectory is substantially more variable in Experiment 2, with most of the response restricted to the drift rate dimension and inconsistent trajectories along the boundary height dimension (Figure 7B, lower panel). Here, the distribution of $\theta$ prior to a change point averages to ∼270° and shifts to ∼90° with the observation of a change. In both experiments, we find that the decision trajectory quickly responds to a shift in action outcomes and also quickly recovers and stabilizes.

Having characterized the change-point-evoked trajectory through the range of decision policies, we next asked whether conditions of increased volatility and increased conflict might modify its path. To this end, we conducted a comparison of a null model with models specifying the change-point evoked response alone and this evoked response as a function of conflict and volatility. To estimate this relationship between drift rate and boundary height, we used Bayesian circular regression (Mulder and Klugkist, 2017). First, we tested the null hypothesis that the decision dynamics (the relationship between drift rate and boundary height; $\theta$) were solely a function of the intercept, or the average of the decision dynamics $\theta$:

$\theta ={\beta }_0$

We call this the null model.

To test the hypothesis that decision dynamics varied solely as a function of time after a switch in action-outcome contingencies, we estimated the change in $(a,v)$ coordinates ($\theta$) relative to a change point, with the time scale of consideration determined by the results of a stability analysis from Experiment 1 (see Model proposals and evaluation; Appendix 1—figure 5):

$\theta ={\beta }_0+{\beta }_{\mathrm{\Delta }{t}_{i:3}}$

We call this the evoked response model.

Our model comparison logic was as follows. We first evaluated whether the posterior probability of the evoked response model was greater than that for the null model. This would suggest that time relative to a change point alone is a better predictor of decision dynamics than the average response. If the posterior probability of the evoked response model reliably exceeded the posterior probability of the null model, we then quantified the evidence for alternative models relative to the evoked response model. The sole effect of time relative to a change point was then framed as the new null hypothesis.

We used Bayes Factors to quantify the ratio of evidence for two competing hypotheses. If the ratio is close to 1, then the evidence is equivocal. As the ratio grows more positive, there is greater evidence for the model specified in the numerator, and if the ratio is less than 1, then there is evidence for the model specified in the denominator (Jeffreys, 1998). Evidence for the null hypothesis is denoted $B{F}_{01}$ and evidence for the alternative hypothesis is denoted $B{F}_{10}$. Because Experiment 2 took a within-subject approach, a separate model was fit for each participant for all proposed models.

To determine whether volatility and conflict affected these peri-change decision dynamics, we modeled changes in decision policy on the drift rate and boundary height surface as a function of $\lambda$ and $p$, where $\lambda$ corresponds to the average period of stability and $p$ corresponds to the mean probability of reward for the optimal choice (see Figure 8 for the full set of models considered). We explored the potential influence of volatility and conflict on the relationship between drift rate and boundary height by examining the posterior probability for each hypothesized model given the set of alternative hypotheses (Model proposals and evaluation; Figure 8A). We found that the evoked response model describing the relationship between shifts in decision parameters and time relative to a change point was more probable than the null model (see Figure 8A).

Figure 8

Download asset Open asset

We also present the evidence for the null model against each alternative model as a Bayes Factor ($B{F}_{01}$) (Figure 8B). The 95% confidence interval for the $BF01$ comparing the ratio of evidence for the null model and the evoked response model specifying time-dependent effects of volatility included 1, suggesting inconclusive evidence for either of these models. Likewise, the 95% confidence interval for the $B{F}_{01}$ comparing the evidence for the null model against the model specifying change-point-evoked effects of conflict included 1, suggesting no substantive difference between them. Given the equivocal evidence for these two models we excluded them from further comparison with the evoked response model.

The remainder of the models had substantially negative $B{F}_{01}$ values (Figure 8B), suggesting that they better fit the data than the null model and allowing them to survive to the next stage of analysis. To evaluate the hypothesis that time alone best accounted for the data, we computed the $B{F}_{01}$ for the evoked response model against the surviving models from the null model analysis. We find that, for all the remaining models, the $B{F}_{01}$ is substantially positive (Figure 8C), indicating that the evoked response model best accounted for the data (posterior probability of evoked response model given the set of models considered: $0.76\pm 0.473$; posterior prob. for 3/4 participants > 0.99).

These analyses suggest that the relationship between the rate of evidence accumulation and the boundary height is only related to the change point itself. We find no evidence to suggest that changing the degree of volatility or changing the degree of conflict changes the path of the decision policy following a change point. Thus, the stereotyped response of the decision policy is solely dependent on the presence of a change point rather than either the history of change point frequency or the history of optimal choice ambiguity. Note that while the ideal observer estimates respond to our conditional manipulations of volatility and conflict, the decision dynamics $\theta$ we observe do not reflect these effects. This is due to the noisy, imperfect correspondence between the ideal observer signals and $a$ and $v$. This suggests that adaptation to environmental changes in action-outcome contingencies involves a rapid, coordinated increase in the relationship between the amount of information needed to make a decision and a decrease in the rate of information accumulation, with a stereotyped return to a stable baseline soon thereafter until another change occurs.

No evidence for locus-coeruleus norepinephrine (LC-NE) system contribution to the decision trajectory

The LC-NE system is known to modulate exploration states under uncertainty and pupil diameter shows a tight correspondence with LC neuron firing rate (Aston-Jones and Cohen, 2005; Rajkowski et al., 1994), with changes in pupil diameter indexing the explore-exploit decision state (Jepma and Nieuwenhuis, 2011). Similar to the classic Yerkes-Dodson curve relating arousal to performance (Yerkes and Dodson, 1908), performance is optimal when tonic LC activity is moderate and phasic LC activity increases following a goal-related stimulus (Aston-Jones et al., 1999, but see Joshi et al., 2016 for an exception). Because of this link between LC-NE and the regulation of behavioral variability in response to uncertainty, we expected that LC-NE system responses, as recorded by pupil diameter, would associate with environmental uncertainty and the trajectory through decision policy space following a change in action-contingencies. Specifically, if the LC-NE system were sensitive to a change in the optimal choice then we should observe a moderate spike in phasic activity following a change in action-outcome contingencies. Note that we do not observe previously established links between exploratory choice behavior and the pupillary response (Jepma and Nieuwenhuis, 2011; Murphy et al., 2011; van Kempen et al., 2019). We ask the reader to titrate their interpretation of these pupillary data accordingly.

We characterized the evoked pupillary response on each trial in Experiment 2 using seven metrics: the mean of the pupil data over each trial interval, the latency to the peak onset and offset, the latency to peak amplitude, the peak amplitude, and the area under the curve of the pupillary response (see Pupil data preprocessing; Figure 9A). From a computational perspective, reducing the dimensionality of this set of pupillary response metrics expands the set of models we can consider without taxing computational resources in a reasonable amount of time. Further, dimensionality reduction of the pupillary response allows us to capture separable sources of variance relating to timing and amplitude effects without restricting the data to a smaller set of metrics and possibly discarding information (e.g. timing effects may not be constrained to peak latency or onset latency; amplitude effects may not be constrained to peak dilation amplitude). Therefore, we submitted these metrics to principal component analysis to reduce their dimensionality while capturing maximum variance.

Figure 9

Download asset Open asset

Evoked response characterization and principal component analyses were conducted for each session and for each subject in Experiment 2. The 95% CI for the number of principal components needed to explain 95% of the variance in the data was calculated over subjects and sessions to determine the number of principal components to keep for further analysis. To aid in interpreting subsequent analysis using the selected principal components, the feature importance of each pupil metric was calculated for each principal component and aggregated across subjects as a mean and bootstrapped 95% CI (Figure 9). We found that the first two principal components explained 95% of the variance in the pupillary data. Peak onset, peak offset, and latency to peak amplitude had the greatest feature importance for the first principal component (Figure 9B, upper panel). Mean pupil diameter and peak amplitude had the greatest feature importance for the second principal component (Figure 9B, lower panel). Thus, for interpretability, we refer to the first and second principal components as timing and magnitude components, respectively (Figure 9B). Note that we also conduct this analysis using more conventional methods of pupillary analysis and continue to observe a null effect (see Pupil data preprocessing for details).

To test for the possibility that fluctuations in norepinephrine covaried with changes in the drift-rate and the boundary height, we evaluated a set of models exploring the relationship between the timing and magnitude components of the change-point-evoked pupillary response and shifts in $\theta$. As in our previous model comparison (Figure 8; see Environmental instability prompts a stereotyped decision trajectory), we found that the model describing the relationship between decision policy shift and time relative to a change point had the highest posterior probability given the set of models considered (Figure 10A). To further evaluate the extent of the evidence for the evoked response hypothesis, we present the evidence for the evoked response model against the original model set as $B{F}_{01}$ (Figure 10B). We find unambiguous evidence in favor of the evoked response model relative to the models specifying the modulation of $\theta$ via the timing and magnitude features of the change-point-evoked pupillary response (posterior probability of time-null model given the set of models considered: $0.997\pm 0.002$), with substantially positive $B{F}_{01}$ values. We find no evidence that the pupillary response associates with the dynamics of the decision policy changes in response to a change in action-outcome contingencies.

Figure 10

Download asset Open asset

We investigated how decision policies change when the rules of the environment change. In two separate experiments, we characterized how decision processes adapted in response to a change in action-outcome contingencies as a trajectory through the space of possible types of exploratory and exploitative decision policies. Our findings highlight how, in the context of two choice paradigms, when faced with a possible change in outcomes, humans rapidly shift to a slow exploratory strategy by reducing the drift rate and, sometimes, increasing the boundary height in a stereotyped manner. Using pupillary data, we were unable to detect a relationship between the LC-NE system and the dynamics of adaptive decision policies in unstable environments. Our findings show how the underlying decision algorithm adapts to different forms of uncertainty.

Exploration and exploitation states are not discrete, but exist along a continuum (Addicott et al., 2017). Instead of switching between binary states, humans manage environmental instability by adjusting the greediness of their decision policies (Sadeghiyeh et al., 2020; Prat-Carrabin et al., 2020; Feng et al., 2020; Wilson et al., 2014; Payzan-LeNestour and Bossaerts, 2011; Payzan-Lenestour and Bossaerts, 2012; Wilson et al., 2021). Depending on the relative configuration of parameters in the accumulation to bound process, this adjustment can manifest as either speeded or slowed decisions (Figure 1E; Alexandrowicz, 2020; Ratcliff, 1978). Our results suggest that, in the context of volatile two-choice decisions, humans adopt a mechanism that simultaneously changes the rate of evidence accumulation and, sometimes, the threshold of evidence needed to trigger a decision, so as to adapt to an environmental change (Figure 6A). As soon as a shift in action outcomes is suspected, an internal estimate of change point probability increases and an estimate of the belief in the value of the optimal target plummets (Figure 7A). The rapid increase in change point probability causes a rapid rise in the boundary height on the subsequent trial, thereby increasing the criterion for selecting a new action and allowing variability in the accumulation process to have a greater influence on choice (Figure 7B), although this latter effect is inconsistent across experiments. These changes lead to slow exploratory decisions that facilitate discovery of the new optimal action and result in a quick recovery of the original threshold value over the course of a few trials. In parallel, the rate of evidence accumulation for the optimal choice decreases, with an immediate drop that gradually returns to its asymptotic value as the belief in the value of the optimal choice stabilizes. These results show that when a learner confronts a change point, the decision policy becomes more exploratory by simultaneously increasing the amount of evidence needed to make a decision and slowing the integration of evidence over time. Together, these decision dynamics form a mechanism for gathering information in an unbiased manner that slows the decision at the decision process level but responds quickly relative to a suspected change in trial time.

Critically, our finding that underlying decision policies can reconfigure multiple underlying decision parameters closely parallels recent work in the domain of information-seeking. Information seeking has been decomposed into random and directed components (Wilson et al., 2014). Random exploration refers to inherent behavioral variability that leads us to explore other options, while directed exploration refers to the volitional pursuit of new information. Feng and colleagues recently found that random exploration is driven by changes in the drift rate and the boundary height, with drift rate changes dominating the policy shift (Feng et al., 2020). When environmental conditions encouraged exploration, the drift rate slowed, reducing the signal-to-noise ratio of the reward representation. This finding clearly aligns with our current observations showing that the drift rate sharply decreases in response to a change point and that this change in drift rate dominates the reconfiguration of decision processes, although our experiments were not designed to isolate the directed and random elements of exploration.

Our results are also broadly consistent with a growing body of research converging on the idea that decision policies are not static, but sensitive to changes in environmental dynamics (Dunovan and Verstynen, 2019; Urai et al., 2018). Previous work by our lab (Dunovan and Verstynen, 2019) has shown how, during a modified reactive inhibitory control task, different feedback signals target different parts of the accumulation-to-bound process. Specifically, errors in response timing drove rapid changes in the drift rate on subsequent trials, while selection errors (i.e. making a response on trials where the response should be inhibited) changed the boundary height. Further, there is new evidence that the drift rate adapts on the basis of previous choices, independent of the feedback given for those choices. Urai and colleagues have convincingly demonstrated that choice history signals sculpt the dynamics of the accumulation process by biasing the rate of evidence accumulation (Urai et al., 2018). Our current findings and these previous observations (Pedersen et al., 2017; Ratcliff and Frank, 2012) all highlight how sensitive the parameters of accumulation-to-bound processes are to immediate experience.

Previous literature has shown a conflict-induced spike in reaction time (e.g. Jahfari et al., 2019). However, our complex reaction time results depart from this. One reason for this departure may relate to the demands of the task we are asking participants to perform. While increased cognitive demand should increase reaction times across conditions, we observe a linear decrease in reaction time as a function of volatility when conflict is highest, and we also see that a net increase in conflict decreases reaction times (Figure 3D). We suspect that the presence of both conflict and volatility blurs the distinction between these two sources of uncertainty, especially under high volatility and high conflict conditions. We also see this effect in our formulation of change point probability (CPP), with a bias to overestimate CPP when conflict is high (Figure 4D). It is possible that participants also exhibit this bias to overestimate volatility when conflict is high, which could muddle the effect of conflict on reaction times. Future research should explore the interaction of change point and conflict estimation on the speed-accuracy trade-off.

We hypothesized that any shift in decision policy in response to a change in action-outcome contingencies would be linked to changes in phasic responses of the LC-NE pathways (Aston-Jones and Cohen, 2005). However, we failed to find any evidence of this link using pupillary responses as a proxy of LC-NE dynamics. It should be noted, however, that our experimental design cannot distinguish between pupillary dynamics driven by other catecholamines, such as dopamine, and those dynamics driven by the LC-NE system (Spiers and Calne, 1969; McClure et al., 2005; Gershman and Tzovaras, 2018; Gershman and Uchida, 2019), Thus it is possible that the LC-NE system may still be playing a role in shift of decision policies, and the pupil responses we collected were insensitive to the underlying dynamics. Nonetheless, this null association suggests that an alternative neural mechanism drives the adaptive changes that we observed behaviorally.

One possible alternative mechanism for resetting decision policies is is dopaminergic changes to the cortico-basal ganglia-thalamic (CBGT) pathways, or ‘loops’. Both recent experimental (Yartsev et al., 2018; Dunovan et al., 2015) and theoretical (Bogacz and Larsen, 2011; Caballero et al., 2018; Wei et al., 2015) studies have pointed to the CBGT loops as being a crucial pathway for accumulating evidence during decision making, with the wiring architecture of these pathways ideal for implementing the sequential probability ratio test (Bogacz and Gurney, 2007; Bogacz, 2007), the statistically optimal algorithm for evidence accumulation decisions and the basis for the DDM itself (Ratcliff, 1978). Further, multiple lines of theoretical work have suggested that, within the CBGT pathways, the difference in direct pathway activity between action channels covaries with the rate of evidence accumulation for individual decisions (Mikhael and Bogacz, 2016; Bariselli et al., 2019; Dunovan et al., 2019; Rubin et al., 2021), while the indirect pathways are linked to control of the boundary height (Wei et al., 2015; Herz et al., 2016; Bogacz, 2007; Ratcliff and Frank, 2012). This suggests that changes in the direct and indirect pathways, both within and between representations of different actions, may regulate shifts in decision policies.

Critically, the CBGT pathways are a target of the dopaminergic signaling that drives reinforcement learning (Schultz et al., 1992), suggesting that changes in relative action-value should drive trial-by-trial changes in the drift rate. Indeed, previous work relating dopaminergic circuitry to decision policy adaptation suggests that dopamine may play a critical role in modulating decision policies. Dopamine has substantial links to exploration (Kakade and Dayan, 2002) and recent pharmacological evidence suggests a role for dopaminergic regulation of exploration in humans (Chakroun et al., 2020). More explicitly, both directed and random exploration have been linked to variations in genes that affect dopamine levels in prefrontal cortex and striatum, respectively (Gershman and Tzovaras, 2018). Physiologically, previous work has found that a dopamine-controlled spike-timing-dependent plasticity rule alters the ratio of direct to indirect pathway efficacy in a simulated corticostriatal network (Vich et al., 2020), with overall indirect pathway activity (i.e. pre-decision firing rates) linked to the modulation of the boundary height in a DDM and the difference in direct pathway activation across action channels associating with changes in the drift rate (Dunovan et al., 2019; Rubin et al., 2021). Moreover, recent optogenetic work in mice suggests that activating the subthalamic nucleus, a key node in the indirect pathway, not only halts the motoric response but also interrupts cognitive processes related to action selection (Heston et al., 2020). Our current observations, combined with this previous work, suggests that the decision policy reconfiguration that we observe may associate with similar underlying corticostriatal dynamics, with belief-driven changes to drift rate varying with the difference in direct pathway firing rates across action channels (Dunovan et al., 2019), and change-point-probability-driven changes to the boundary height varying with overall indirect pathway activity (Dunovan et al., 2019; Vich et al., 2020). Future physiological studies should focus on validating this predicted relationship between decision policy reconfiguration and CBGT pathways.

The current study raises many more questions about the dynamics of adaptive decision policies than it answers. For example, we only sparsely sampled the space of possible states of value conflict and volatility. Future work would benefit from a more complete sampling of the conflict and volatility space. A psychophysical characterization of how decision states shift in response to varying forms of uncertainty will expose potential non-linear relationships between the decision policy and feedback uncertainty. Moreover, the decisions that we have modeled here are simple two choice decisions, constrained mostly by the normative form of the traditional DDM framework (Ratcliff, 1978). Scaling the complexity of the task will allow for a more complete assessment of how these relationships change with more complex decisions that better approximate the choices that we make outside the lab. This could be done by moving the cognitive model to frameworks that can fit processes for decisions involving more than two alternatives (e.g. Tajima et al., 2019). Finally, because our estimate of the relationship between our ideal observer estimates of uncertainty and human estimates of uncertainty were indirect, this work would benefit from online approximations of ideal observer estimates, as has been done previously (Wilson et al., 2010). Indeed, there can be substantive individual differences in the detection of of change points (Wilson et al., 2010). Thus, an approximation of how well the estimates of change point probability from our ideal observer correspond to estimates that human observers hold is needed. This approximation would validate the fidelity of the relationship between the ideal observer estimates of uncertainty and the decision parameters that we observed.

Together, our results suggest that when humans are forced to change their mind about the best action to take, the underlying decision policy adapts in a specific way. When a change in action-outcome contingency is suspected, the rate of evidence accumulation decreases and more evidence may briefly be required to commit to a response, allowing variability inherent to the decision process to play a greater role in response selection and resulting in a slow exploratory state. As the environment becomes stable, the system gradually adapts to an exploitative state. Importantly, we find no evidence that norepinephrine pathways associate with this response. This suggests that other pathways may be engaged in this adaptive reconfiguration of decision policies. These results reveal the multifaceted underlying decision processes that can adapt action selection policy under multiple forms of environmental uncertainty.

Behavioral data and their computational derivatives are available at https://github.com/kmbond/dynamic_decision_policy_reconfiguration (copy archived at swh:1:rev:0486705db0f004a5e1365759f5f5a391790771f8). Code used to generate figures can be found here. Raw pupillometry data (DOI: 10.1184/R1/13543133), the features of the task-evoked pupillometry response (DOI: 10.1184/R1/13543067.v1), and the principal components calculated from those features (DOI: 10.1184/R1/13543160.v1) are available here.

1. 1. Bond K

   (2021) KiltHub

   Raw pupillometry data.

   https://doi.org/10.1184/R1/13543133
2. 1. Bond K

   (2021) KiltHub

   Features of task-evoked pupillary response.

   https://doi.org/10.1184/R1/13543067.v1
3. 1. Bond K

   (2021) KiltHub

   Principal components of task-evoked pupillary response.

   https://doi.org/10.1184/R1/13543160.v1

1. 1. Addicott MA
   2. Pearson JM
   3. Sweitzer MM
   4. Barack DL
   5. Platt ML

   (2017) A primer on foraging and the explore/exploit trade-off for psychiatry research

   Neuropsychopharmacology: Official Publication of the American College of Neuropsychopharmacology 42:1931–1939.

   https://doi.org/10.1038/npp.2017.108

   • PubMed
   • Google Scholar
2. 1. Alexandrowicz RW

   (2020) The diffusion model visualizer: an interactive tool to understand the diffusion model parameters

   Psychological Research 84:1157–1165.

   https://doi.org/10.1007/s00426-018-1112-6

   • PubMed
   • Google Scholar
3. 1. Aston-Jones G
   2. Bloom FE

   (1981) Activity of norepinephrine-containing locus coeruleus neurons in behaving rats anticipates fluctuations in the sleep-waking cycle

   The Journal of Neuroscience 1:876–886.

   https://doi.org/10.1523/JNEUROSCI.01-08-00876.1981

   • PubMed
   • Google Scholar
4. 1. Aston-Jones G
   2. Rajkowski J
   3. Cohen J

   (1999) Role of locus coeruleus in attention and behavioral flexibility

   Biological Psychiatry 46:1309–1320.

   https://doi.org/10.1016/s0006-3223(99)00140-7

   • PubMed
   • Google Scholar
5. 1. Aston-Jones G
   2. Cohen JD

   (2005) An integrative theory of locus coeruleus-norepinephrine function: adaptive gain and optimal performance

   Annual Review of Neuroscience 28:403–450.

   https://doi.org/10.1146/annurev.neuro.28.061604.135709

   • PubMed
   • Google Scholar
6. 1. Bariselli S
   2. Fobbs WC
   3. Creed MC
   4. Kravitz AV

   (2019) A competitive model for striatal action selection

   Brain Research 1713:70–79.

   https://doi.org/10.1016/j.brainres.2018.10.009

   • PubMed
   • Google Scholar
7. 1. Beatty J

   (1982) Task-evoked pupillary responses, processing load, and the structure of processing resources

   Psychological Bulletin 91:276–292.

   https://doi.org/10.1037/0033-2909.91.2.276

   • PubMed
   • Google Scholar
8. 1. Behrens TEJ
   2. Woolrich MW
   3. Walton ME
   4. Rushworth MFS

   (2007) Learning the value of information in an uncertain world

   Nature Neuroscience 10:1214–1221.

   https://doi.org/10.1038/nn1954

   • PubMed
   • Google Scholar
9. 1. Bland AR
   2. Schaefer A

   (2012) Different varieties of uncertainty in human decision-making

   Frontiers in Neuroscience 6:85.

   https://doi.org/10.3389/fnins.2012.00085

   • PubMed
   • Google Scholar
10. 1. Bogacz R

    (2007) Optimal decision-making theories: linking neurobiology with behaviour

    Trends in Cognitive Sciences 11:118–125.

    https://doi.org/10.1016/j.tics.2006.12.006

    • PubMed
    • Google Scholar
11. 1. Bogacz R
    2. Gurney K

    (2007) The basal ganglia and cortex implement optimal decision making between alternative actions

    Neural Computation 19:442–477.

    https://doi.org/10.1162/neco.2007.19.2.442

    • PubMed
    • Google Scholar
12. 1. Bogacz R
    2. Wagenmakers EJ
    3. Forstmann BU
    4. Nieuwenhuis S

    (2010) The neural basis of the speed-accuracy tradeoff

    Trends in Neurosciences 33:10–16.

    https://doi.org/10.1016/j.tins.2009.09.002

    • PubMed
    • Google Scholar
13. 1. Bogacz R
    2. Larsen T

    (2011) Integration of reinforcement learning and optimal decision-making theories of the basal ganglia

    Neural Computation 23:817–851.

    https://doi.org/10.1162/NECO_a_00103

    • PubMed
    • Google Scholar
14. Book

    1. Bond K
    2. Dunovan K
    3. Verstynen TD

    (2018)

    The Influence of Volatility and Conflict on Adaptive Decision Making

    OSF.

    • Google Scholar
15. Software

    1. Bond K

    (2021) Dynamic decision policy reconfiguration under outcome uncertainty, version swh:1:rev:0486705db0f004a5e1365759f5f5a391790771f8

    Software Heritage.

    https://archive.softwareheritage.org/swh:1:dir:de31a380724a5954d16e67a0a6eda17431e11607;origin=https://github.com/kmbond/dynamic_decision_policy_reconfiguration;visit=swh:1:snp:561cc2fa2a2a7aa9aba3d43fe505a2d36b992b7d;anchor=swh:1:rev:0486705db0f004a5e1365759f5f5a391790771f8
16. 1. Bouret S
    2. Sara SJ

    (2005) Network reset: a simplified overarching theory of locus coeruleus noradrenaline function

    Trends in Neurosciences 28:574–582.

    https://doi.org/10.1016/j.tins.2005.09.002

    • PubMed
    • Google Scholar
17. Book

    1. Burnham KP
    2. Anderson DR

    (1998) Practical use of the information-theoretic approach

    In: Burnham KP, editors. Model Selection and Inference. New York, NY: Springer. pp. 75–117.

    https://doi.org/10.1007/978-1-4757-2917-7

    • Google Scholar
18. 1. Byrne JEM
    2. Hughes ME
    3. Rossell SL
    4. Johnson SL
    5. Murray G

    (2017) Time of day differences in neural reward functioning in healthy young men

    The Journal of Neuroscience 37:8895–8900.

    https://doi.org/10.1523/JNEUROSCI.0918-17.2017

    • PubMed
    • Google Scholar
19. 1. Caballero JA
    2. Humphries MD
    3. Gurney KN

    (2018) A probabilistic, distributed, recursive mechanism for decision-making in the brain

    PLOS Computational Biology 14:e1006033.

    https://doi.org/10.1371/journal.pcbi.1006033

    • PubMed
    • Google Scholar
20. 1. Cavanagh JF
    2. Wiecki TV
    3. Kochar A
    4. Frank MJ

    (2014) Eye tracking and pupillometry are indicators of dissociable latent decision processes

    Journal of Experimental Psychology. General 143:1476–1488.

    https://doi.org/10.1037/a0035813

    • PubMed
    • Google Scholar
21. 1. Chakroun K
    2. Mathar D
    3. Wiehler A
    4. Ganzer F
    5. Peters J

    (2020) Dopaminergic modulation of the exploration/exploitation trade-off in human decision-making

    eLife 9:e51260.

    https://doi.org/10.7554/eLife.51260

    • PubMed
    • Google Scholar
22. 1. Dayan P
    2. Yu AJ

    (2006) Phasic norepinephrine: a neural interrupt signal for unexpected events

    Network 17:335–350.

    https://doi.org/10.1080/09548980601004024

    • PubMed
    • Google Scholar
23. 1. Dunovan K
    2. Lynch B
    3. Molesworth T
    4. Verstynen T

    (2015) Competing basal ganglia pathways determine the difference between stopping and deciding not to go

    eLife 4:e08723.

    https://doi.org/10.7554/eLife.08723

    • PubMed
    • Google Scholar
24. 1. Dunovan K
    2. Verstynen T

    (2019) Errors in action timing and inhibition facilitate learning by tuning distinct mechanisms in the underlying decision process

    The Journal of Neuroscience 39:2251–2264.

    https://doi.org/10.1523/JNEUROSCI.1924-18.2019

    • PubMed
    • Google Scholar
25. 1. Dunovan K
    2. Vich C
    3. Clapp M
    4. Verstynen T
    5. Rubin J

    (2019) Reward-driven changes in striatal pathway competition shape evidence evaluation in decision-making

    PLOS Computational Biology 15:e1006998.

    https://doi.org/10.1371/journal.pcbi.1006998

    • PubMed
    • Google Scholar
26. Preprint

    1. Feng SF
    2. Wang S
    3. Zarnescu S
    4. Wilson RC

    (2020) The Dynamics of Explore-Exploit Decisions Reveal a Signal-to-Noise Mechanism for Random Exploration

    PsyArXiv.

    https://doi.org/10.31234/osf.io/uepr7

    • Google Scholar
27. 1. Forstmann BU
    2. Dutilh G
    3. Brown S
    4. Neumann J
    5. von Cramon DY
    6. Ridderinkhof KR
    7. Wagenmakers EJ

    (2008) Striatum and pre-SMA facilitate decision-making under time pressure

    PNAS 105:17538–17542.

    https://doi.org/10.1073/pnas.0805903105

    • PubMed
    • Google Scholar
28. 1. Forstmann BU
    2. Anwander A
    3. Schäfer A
    4. Neumann J
    5. Brown S
    6. Wagenmakers EJ
    7. Bogacz R
    8. Turner R

    (2010) Cortico-striatal connections predict control over speed and accuracy in perceptual decision making

    PNAS 107:15916–15920.

    https://doi.org/10.1073/pnas.1004932107

    • PubMed
    • Google Scholar
29. 1. Foster, MSLS ED
    2. Deardorff, MLIS A

    (2017) Open Science Framework (OSF)

    Journal of the Medical Library Association 105:88.

    https://doi.org/10.5195/JMLA.2017.88

    • Google Scholar
30. 1. Gauthier I
    2. Tarr MJ

    (1997) Becoming a “Greeble” expert: exploring mechanisms for face recognition

    Vision Research 37:1673–1682.

    https://doi.org/10.1016/s0042-6989(96)00286-6

    • PubMed
    • Google Scholar
31. 1. Gershman SJ
    2. Tzovaras BG

    (2018) Dopaminergic genes are associated with both directed and random exploration

    Neuropsychologia 120:97–104.

    https://doi.org/10.1016/j.neuropsychologia.2018.10.009

    • PubMed
    • Google Scholar
32. 1. Gershman SJ
    2. Uchida N

    (2019) Believing in dopamine

    Nature Reviews. Neuroscience 20:703–714.

    https://doi.org/10.1038/s41583-019-0220-7

    • PubMed
    • Google Scholar
33. 1. Gilzenrat MS
    2. Nieuwenhuis S
    3. Jepma M
    4. Cohen JD

    (2010) Pupil diameter tracks changes in control state predicted by the adaptive gain theory of locus coeruleus function

    Cognitive, Affective & Behavioral Neuroscience 10:252–269.

    https://doi.org/10.3758/CABN.10.2.252

    • PubMed
    • Google Scholar
34. 1. Herz DM
    2. Zavala BA
    3. Bogacz R
    4. Brown P

    (2016) Neural correlates of decision thresholds in the human subthalamic nucleus

    Current Biology 26:916–920.

    https://doi.org/10.1016/j.cub.2016.01.051

    • PubMed
    • Google Scholar
35. 1. Herz DM
    2. Tan H
    3. Brittain JS
    4. Fischer P
    5. Cheeran B
    6. Green AL
    7. FitzGerald J
    8. Aziz TZ
    9. Ashkan K
    10. Little S
    11. Foltynie T
    12. Limousin P
    13. Zrinzo L
    14. Bogacz R
    15. Brown P

    (2017) Distinct mechanisms mediate speed-accuracy adjustments in cortico-subthalamic networks

    eLife 6:e21481.

    https://doi.org/10.7554/eLife.21481

    • PubMed
    • Google Scholar
36. 1. Heston J
    2. Friedman A
    3. Baqai M
    4. Bavafa N
    5. Aron AR
    6. Hnasko TS

    (2020) Activation of subthalamic nucleus stop circuit disrupts cognitive performance

    ENeuro 7:ENEURO.0159-20.2020.

    https://doi.org/10.1523/ENEURO.0159-20.2020

    • PubMed
    • Google Scholar
37. 1. Hurwicz L

    (1972)

    On informationally decentralized systems

    Decision and Organization 1:320.

    • Google Scholar
38. 1. Jahfari S
    2. Ridderinkhof KR
    3. Collins AGE
    4. Knapen T
    5. Waldorp LJ
    6. Frank MJ

    (2019) Cross-task contributions of frontobasal ganglia circuitry in response inhibition and conflict-induced slowing

    Cerebral Cortex 29:1969–1983.

    https://doi.org/10.1093/cercor/bhy076

    • PubMed
    • Google Scholar
39. Book

    1. Jeffreys H

    (1998)

    The Theory of Probability

    OUP Oxford Press.

    • Google Scholar
40. 1. Jepma M
    2. Nieuwenhuis S

    (2011) Pupil diameter predicts changes in the exploration-exploitation trade-off: evidence for the adaptive gain theory

    Journal of Cognitive Neuroscience 23:1587–1596.

    https://doi.org/10.1162/jocn.2010.21548

    • PubMed
    • Google Scholar
41. 1. Joshi S
    2. Li Y
    3. Kalwani RM
    4. Gold JI

    (2016) Relationships between Pupil Diameter and Neuronal Activity in the Locus Coeruleus, Colliculi, and Cingulate Cortex

    Neuron 89:221–234.

    https://doi.org/10.1016/j.neuron.2015.11.028

    • PubMed
    • Google Scholar
42. 1. Kakade S
    2. Dayan P

    (2002) Dopamine: generalization and bonuses

    Neural Networks 15:549–559.

    https://doi.org/10.1016/s0893-6080(02)00048-5

    • PubMed
    • Google Scholar
43. 1. Keung W
    2. Hagen TA
    3. Wilson RC

    (2019) Regulation of evidence accumulation by pupil-linked arousal processes

    Nature Human Behaviour 3:636–645.

    https://doi.org/10.1038/s41562-019-0551-4

    • PubMed
    • Google Scholar
44. Book

    1. Kruschke JK
    2. Vanpaemel W

    (2015) Bayesian estimation in hierarchical models

    In: Busemeyer JR, Wang Z, Townsend JT, Eidels A, editors. The Oxford Handbook of Computational and Mathematical Psychology. Oxford University Press. pp. 279–299.

    https://doi.org/10.1093/oxfordhb/9780199957996.013.13

    • Google Scholar
45. Book

    1. Ledyard JO

    (1989) Incentive compatibility

    In: Eatwell J, Milgate M, Newman P, editors. Allocation, Information and Markets. Springer. pp. 1–2.

    https://doi.org/10.1007/978-1-349-20215-7

    • Google Scholar
46. 1. Luke SG

    (2017) Evaluating significance in linear mixed-effects models in R

    Behavior Research Methods 49:1494–1502.

    https://doi.org/10.3758/s13428-016-0809-y

    • PubMed
    • Google Scholar
47. Conference

    1. McClure SM
    2. Gilzenrat MS
    3. Cohen JD

    (2005)

    Advances in Neural Information Processing Systems

    An exploration-exploitation model based on norepinepherine and dopamine activity. pp. 867–874.

    • Google Scholar
48. 1. Mendonça AG
    2. Drugowitsch J
    3. Vicente MI
    4. DeWitt EEJ
    5. Pouget A
    6. Mainen ZF

    (2020) The impact of learning on perceptual decisions and its implication for speed-accuracy tradeoffs

    Nature Communications 11:1–15.

    https://doi.org/10.1038/s41467-020-16196-7

    • PubMed
    • Google Scholar
49. 1. Mikhael JG
    2. Bogacz R

    (2016) Learning Reward Uncertainty in the Basal Ganglia

    PLOS Computational Biology 12:e1005062.

    https://doi.org/10.1371/journal.pcbi.1005062

    • PubMed
    • Google Scholar
50. 1. Mulder K
    2. Klugkist I

    (2017) Bayesian estimation and hypothesis tests for a circular Generalized Linear Model

    Journal of Mathematical Psychology 80:4–14.

    https://doi.org/10.1016/j.jmp.2017.07.001

    • Google Scholar
51. 1. Murphy PR
    2. Robertson IH
    3. Balsters JH
    4. O’connell RG

    (2011) Pupillometry and P3 index the locus coeruleus-noradrenergic arousal function in humans

    Psychophysiology 48:1532–1543.

    https://doi.org/10.1111/j.1469-8986.2011.01226.x

    • PubMed
    • Google Scholar
52. 1. Murphy PR
    2. Vandekerckhove J
    3. Nieuwenhuis S

    (2014) Pupil-linked arousal determines variability in perceptual decision making

    PLOS Computational Biology 10:e1003854.

    https://doi.org/10.1371/journal.pcbi.1003854

    • PubMed
    • Google Scholar
53. 1. Murray G
    2. Nicholas CL
    3. Kleiman J
    4. Dwyer R
    5. Carrington MJ
    6. Allen NB
    7. Trinder J

    (2009) Nature’s clocks and human mood: the circadian system modulates reward motivation

    Emotion 9:705–716.

    https://doi.org/10.1037/a0017080

    • PubMed
    • Google Scholar
54. 1. Nassar MR
    2. Wilson RC
    3. Heasly B
    4. Gold JI

    (2010) An approximately Bayesian delta-rule model explains the dynamics of belief updating in a changing environment

    The Journal of Neuroscience 30:12366–12378.

    https://doi.org/10.1523/JNEUROSCI.0822-10.2010

    • PubMed
    • Google Scholar
55. 1. Nassar MR
    2. Rumsey KM
    3. Wilson RC
    4. Parikh K
    5. Heasly B
    6. Gold JI

    (2012) Rational regulation of learning dynamics by pupil-linked arousal systems

    Nature Neuroscience 15:1040–1046.

    https://doi.org/10.1038/nn.3130

    • PubMed
    • Google Scholar
56. 1. O’Reilly JX

    (2013) Making predictions in a changing world-inference, uncertainty, and learning

    Frontiers in Neuroscience 7:105.

    https://doi.org/10.3389/fnins.2013.00105

    • PubMed
    • Google Scholar
57. 1. Payzan-LeNestour E
    2. Bossaerts P

    (2011) Risk, unexpected uncertainty, and estimation uncertainty: Bayesian learning in unstable settings

    PLOS Computational Biology 7:e1001048.

    https://doi.org/10.1371/journal.pcbi.1001048

    • PubMed
    • Google Scholar
58. 1. Payzan-Lenestour E
    2. Bossaerts P

    (2012) Do not bet on the unknown versus try to find out more: Estimation uncertainty and “unexpected uncertainty” both modulate exploration

    Frontiers in Neuroscience 6:150.

    https://doi.org/10.3389/fnins.2012.00150

    • PubMed
    • Google Scholar
59. 1. Pedersen ML
    2. Frank MJ
    3. Biele G

    (2017) The drift diffusion model as the choice rule in reinforcement learning

    Psychonomic Bulletin & Review 24:1234–1251.

    https://doi.org/10.3758/s13423-016-1199-y

    • PubMed
    • Google Scholar
60. Preprint

    1. Prat-Carrabin A
    2. Wilson RC
    3. Cohen JD
    4. Da Silveira RA

    (2020) Human Inference in Changing Environments with Temporal Structure

    bioRxiv.

    https://doi.org/10.1101/720516

    • Google Scholar
61. 1. Rajkowski J
    2. Kubiak P
    3. Aston-Jones G

    (1994) Locus coeruleus activity in monkey: phasic and tonic changes are associated with altered vigilance

    Brain Research Bulletin 35:607–616.

    https://doi.org/10.1016/0361-9230(94)90175-9

    • PubMed
    • Google Scholar
62. 1. Ratcliff R

    (1978) A theory of memory retrieval

    Psychological Review 85:59–108.

    https://doi.org/10.1037/0033-295X.85.2.59

    • Google Scholar
63. 1. Ratcliff R
    2. Frank MJ

    (2012) Reinforcement-based decision making in corticostriatal circuits: mutual constraints by neurocomputational and diffusion models

    Neural Computation 24:1186–1229.

    https://doi.org/10.1162/NECO_a_00270

    • PubMed
    • Google Scholar
64. 1. Reimer J
    2. McGinley MJ
    3. Liu Y
    4. Rodenkirch C
    5. Wang Q
    6. McCormick DA
    7. Tolias AS

    (2016) Pupil fluctuations track rapid changes in adrenergic and cholinergic activity in cortex

    Nature Communications 7:1–7.

    https://doi.org/10.1038/ncomms13289

    • PubMed
    • Google Scholar
65. 1. Rubin JE
    2. Vich C
    3. Clapp M
    4. Noneman K
    5. Verstynen T

    (2021) The credit assignment problem in cortico-basal ganglia-thalamic networks: A review, a problem and a possible solution

    The European Journal of Neuroscience 53:2234–2253.

    https://doi.org/10.1111/ejn.14745

    • PubMed
    • Google Scholar
66. 1. Sadeghiyeh H
    2. Wang S
    3. Alberhasky MR
    4. Kyllo HM
    5. Shenhav A
    6. Wilson RC

    (2020) Temporal discounting correlates with directed exploration but not with random exploration

    Scientific Reports 10:1–10.

    https://doi.org/10.1038/s41598-020-60576-4

    • PubMed
    • Google Scholar
67. 1. Satterthwaite FE

    (1946) An approximate distribution of estimates of variance components

    Biometrics 2:110–114.

    https://doi.org/10.2307/3002019

    • PubMed
    • Google Scholar
68. 1. Schultz W
    2. Apicella P
    3. Scarnati E
    4. Ljungberg T

    (1992) Neuronal activity in monkey ventral striatum related to the expectation of reward

    The Journal of Neuroscience 12:4595–4610.

    https://doi.org/10.1523/JNEUROSCI.12-12-04595.1992

    • PubMed
    • Google Scholar
69. 1. Sirois S
    2. Brisson J

    (2014) Pupillometry

    Wiley Interdisciplinary Reviews. Cognitive Science 5:679–692.

    https://doi.org/10.1002/wcs.1323

    • PubMed
    • Google Scholar
70. 1. Spiegelhalter DJ
    2. Best NG
    3. Carlin BP
    4. van der Linde A

    (2002) Bayesian measures of model complexity and fit

    Journal of the Royal Statistical Society 64:583–639.

    https://doi.org/10.1111/1467-9868.00353

    • Google Scholar
71. 1. Spiers AS
    2. Calne DB

    (1969) Action of dopamine on the human iris

    British Medical Journal 4:333–335.

    https://doi.org/10.1136/bmj.4.5679.333

    • PubMed
    • Google Scholar
72. 1. Sutton RS
    2. Barto AG

    (1998) Reinforcement Learning: An Introduction

    IEEE Transactions on Neural Networks 9:1054.

    https://doi.org/10.1109/TNN.1998.712192

    • Google Scholar
73. Book

    1. Sutton RS
    2. Barto AG

    (2018)

    Reinforcement Learning: An Introduction

    MIT press.

    • Google Scholar
74. 1. Tajima S
    2. Drugowitsch J
    3. Patel N
    4. Pouget A

    (2019) Optimal policy for multi-alternative decisions

    Nature Neuroscience 22:1503–1511.

    https://doi.org/10.1038/s41593-019-0453-9

    • PubMed
    • Google Scholar
75. 1. Urai AE
    2. Braun A
    3. Donner TH

    (2017) Pupil-linked arousal is driven by decision uncertainty and alters serial choice bias

    Nature Communications 8:1–11.

    https://doi.org/10.1038/ncomms14637

    • PubMed
    • Google Scholar
76. Conference

    1. Urai A
    2. de Gee JW
    3. Tsetsos K
    4. Donner T

    (2018) 2018 Conference on Cognitive Computational Neuroscience

    Choice History Biases Subsequent Evidence Accumulation.

    https://doi.org/10.32470/CCN.2018.1192-0

    • Google Scholar
77. 1. Vaghi MM
    2. Luyckx F
    3. Sule A
    4. Fineberg NA
    5. Robbins TW
    6. De Martino B

    (2017) Compulsivity Reveals a Novel Dissociation between Action and Confidence

    Neuron 96:348–354.

    https://doi.org/10.1016/j.neuron.2017.09.006

    • PubMed
    • Google Scholar
78. 1. van Kempen J
    2. Loughnane GM
    3. Newman DP
    4. Kelly SP
    5. Thiele A
    6. O’Connell RG
    7. Bellgrove MA

    (2019) Behavioural and neural signatures of perceptual decision-making are modulated by pupil-linked arousal

    eLife 8:e42541.

    https://doi.org/10.7554/eLife.42541

    • PubMed
    • Google Scholar
79. 1. Vich C
    2. Dunovan K
    3. Verstynen T
    4. Rubin J

    (2020) Corticostriatal synaptic weight evolution in a two-alternative forced choice task: a computational study

    Communications in Nonlinear Science and Numerical Simulation 82:105048.

    https://doi.org/10.1016/j.cnsns.2019.105048

    • Google Scholar
80. 1. Wagenmakers EJ

    (2007) A practical solution to the pervasive problems of p values

    Psychonomic Bulletin & Review 14:779–804.

    https://doi.org/10.3758/bf03194105

    • PubMed
    • Google Scholar
81. 1. Wei W
    2. Rubin JE
    3. Wang XJ

    (2015) Role of the indirect pathway of the basal ganglia in perceptual decision making

    The Journal of Neuroscience 35:4052–4064.

    https://doi.org/10.1523/JNEUROSCI.3611-14.2015

    • PubMed
    • Google Scholar
82. 1. Wiecki TV
    2. Sofer I
    3. Frank MJ

    (2013) HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python

    Frontiers in Neuroinformatics 7:14.

    https://doi.org/10.3389/fninf.2013.00014

    • PubMed
    • Google Scholar
83. 1. Wilson RC
    2. Nassar MR
    3. Gold JI

    (2010) Bayesian online learning of the hazard rate in change-point problems

    Neural Computation 22:2452–2476.

    https://doi.org/10.1162/NECO_a_00007

    • PubMed
    • Google Scholar
84. 1. Wilson RC
    2. Niv Y

    (2011) Inferring relevance in a changing world

    Frontiers in Human Neuroscience 5:189.

    https://doi.org/10.3389/fnhum.2011.00189

    • PubMed
    • Google Scholar
85. 1. Wilson RC
    2. Geana A
    3. White JM
    4. Ludvig EA
    5. Cohen JD

    (2014) Humans use directed and random exploration to solve the explore-exploit dilemma

    Journal of Experimental Psychology. General 143:2074–2081.

    https://doi.org/10.1037/a0038199

    • PubMed
    • Google Scholar
86. 1. Wilson RC
    2. Bonawitz E
    3. Costa VD
    4. Ebitz RB

    (2021) Balancing exploration and exploitation with information and randomization

    Current Opinion in Behavioral Sciences 38:49–56.

    https://doi.org/10.1016/j.cobeha.2020.10.001

    • PubMed
    • Google Scholar
87. 1. Yartsev MM
    2. Hanks TD
    3. Yoon AM
    4. Brody CD

    (2018) Causal contribution and dynamical encoding in the striatum during evidence accumulation

    eLife 7:e34929.

    https://doi.org/10.7554/eLife.34929

    • PubMed
    • Google Scholar
88. 1. Yerkes RM
    2. Dodson JD

    (1908) The relation of strength of stimulus to rapidity of habit-formation

    Journal of Comparative Neurology and Psychology 18:459–482.

    https://doi.org/10.1002/cne.920180503

    • Google Scholar

Author details

1. Krista Bond

   1. Department of Psychology, Carnegie Mellon University, Pittsburgh, United States
   2. Center for the Neural Basis of Cognition, Pittsburgh, United States
   3. Carnegie Mellon Neuroscience Institute, Pittsburgh, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Visualization, Writing - original draft, Writing - review and editing

   For correspondence

   kbond@andrew.cmu.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1492-6798

2. Kyle Dunovan

   Department of Psychology, Carnegie Mellon University, Pittsburgh, United States

   Contribution

   Conceptualization, Methodology, Software, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7857-5133

3. Alexis Porter

   Department of Psychology, Northwestern University, Evanston, United States

   Contribution

   Data curation, Investigation, Project administration

   Competing interests

   No competing interests declared

4. Jonathan E Rubin

   1. Center for the Neural Basis of Cognition, Pittsburgh, United States
   2. Department of Mathematics, University of Pittsburgh, Pittsburgh, United States

   Contribution

   Conceptualization, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-1513-1551

5. Timothy Verstynen

   1. Department of Psychology, Carnegie Mellon University, Pittsburgh, United States
   2. Center for the Neural Basis of Cognition, Pittsburgh, United States
   3. Carnegie Mellon Neuroscience Institute, Pittsburgh, United States
   4. Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, United States

   Contribution

   Conceptualization, Formal analysis, Funding acquisition, Investigation, Project administration, Resources, Supervision, Validation, Writing - review and editing

   For correspondence

   timothyv@andrew.cmu.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4720-0336

• 952

  views

• 173

  downloads

• 7

  citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.