The complexity dividend: when sophisticated inference matters

Animals continuously infer latent properties of the world from noisy and changing observations. Complex approaches to this challenge such as Bayesian inference are accurate but cognitively demanding, requiring extensive working memory and adaptive learning. Simple strategies such as always using a prior bias or following the last observation are easy to implement but may be less accurate. What is the appropriate balance between complexity and accuracy? We construct a hierarchy of strategies that vary in complexity between these limits and find a power law of diminishing returns: increasing complexity gives progressively smaller gains in accuracy. Moreover, the rate at which the gain decrements depends systematically on the statistical uncertainty in the world, such that complex strategies do not provide substantial benefits over simple ones when uncertainty is too high or too low. In between, when the world is neither too predictable nor too unpredictable, there is a complexity dividend.