(A) The effective learning rate (red), defined by the average potentiation/depression rate weighted by the synaptic population on each state, changes depending on the volatility of the environment, consistent with key experimental findings in Behrens et al. (2007), Nassar et al. (2010). The learning rate gradually decreases over each stable condition, while it rapidly increases in response to a sudden change in environment. The grey vertical lines indicate the change points of contingencies. (B) The effective learning rate is self-tuned depending on the timescale of the environment. This contrasts the effective learning rate of our model (red line) to the harvesting efficiency if the model had a single-fixed rate of plasticity in a multi-armed bandit task with given block size (indicated by x-axis). The background colour shows the normalized harvesting efficiency of a single rate of plasticity model, which is defined by the amount of rewards that the model collected, divided by the maximum amount of rewards that the best model for each block size collected, so that the maximum is always equal to one. The median of the effective learning rate in each block is shown by the red trace, as the effective learning rate constantly changes over trials. The error bars indicate the 25th and 70th percentiles of the effective learning rates. (C) Our cascade model of metaplastic synapses can significantly outperform the model with fixed learning rates when the environment changes on multiple timescales. The harvest efficiency of our model of cascade synapses combined with surprise detection system (red) is significantly higher then the ones of the model with fixed learning rates, or the rates of plasticity (black). The task is a four-armed bandit task with blocks of 10 trials and 10,000 trials with the total reward rate . The total number of blocks is set to . In a given block, one of the targets has the reward probability of , while the others have . The network parameters are taken as , , , , , , , for (A), , ,, , for (B), , , , , for (C) , and and for the single timescale model in (B).