Fig. 5.

Globally optimal and optimal even sample allocations share similar features and have similar performances. (A) Fraction of sampled options (compared to the maximum number of potentially accessible alternatives, equal to $C$) as a function of capacity $C$. The fraction is close to 1 for small values for all environments (flat, black line; rich, brown; and poor, blue). The fraction decays rapidly to zero from a critical value that depends on the prior. The jagged nature of the lines is due to the discrete nature of capacity. (B) Percentage increase (gain) in averaged reward by using globally optimal sample allocation compared to even allocation (see SI Appendix). Color code as in the previous panel. (C) Percentage loss in averaged reward by using triangular (gray), square root sampling law (black), random (orange), pure breadth (red), and pure depth (pink) heuristics compared to optimal allocation, in a flat environment. For the square root and triangular heuristics, we used pure breadth search when C ≤ 5.