A vast space of compact strategies for effective decisions.

Inference-based decision-making, which underlies a broad range of behavioral tasks, is typically studied using a small number of handcrafted models. We instead enumerate a complete ensemble of strategies that could be used to effectively, but not necessarily optimally, solve a dynamic foraging task. Each strategy is expressed as a behavioral "program" that uses a limited number of internal states to specify actions conditioned on past observations. We show that the ensemble of strategies is enormous-comprising a quarter million programs with up to five internal states-but can nevertheless be understood in terms of algorithmic "mutations" that alter the structure of individual programs. We devise embedding algorithms that reveal how mutations away from a Bayesian-like strategy can diversify behavior while preserving performance, and we construct a compositional description to link low-dimensional changes in algorithmic structure with high-dimensional changes in behavior. Together, this work provides an alternative approach for understanding individual variability in behavior across animals and tasks.