Time and memory costs jointly determine a speed-accuracy trade-off and set-size effects

Policies, the mappings from states to actions, require memory. The amount of memory is dictated by the mutual information between states and actions, or the policy complexity. High-complexity policies preserve state information and generally lead to greater reward compared to low-complexity policies, which require less memory by discarding state information and exploiting environmental regularities. Under this theory, high-complexity policies incur a time cost: they take longer to decode than low-complexity policies. This naturally gives rise to a speed-accuracy trade-off, in which acting quickly necessitates inaccuracy (via low-complexity policies) and acting accurately necessitates acting slowly (via high-complexity policies). Furthermore, the relationship between policy complexity and decoding speed accounts for set-size effects: response times grow as a function of the number of possible states because larger state sets encourage higher policy complexity. Across three experiments, we tested these predictions by manipulating inter-trial intervals, environmental regularities, and state set sizes. In all cases, we found that humans are sensitive to both time and memory costs when modulating policy complexity. Altogether, our theory suggests that policy complexity constraints may underlie some speed-accuracy trade-offs and set-size effects.