A Note on the Bernoulli Two-Armed Bandit Problem

Suppose the arms of a two-armed bandit generate i.i.d. Bernoulli random variables with success probabilities ρ and λ respectively. It is desired to maximize the expected sum of N trials where N is fixed. If the prior distribution of (ρ, λ) is concentrated at two points $(a, b)$ and $(c, d)$ in the unit square, a characterization of the optimal policy is given. In terms of $a, b, c$, and d, necessary and sufficient conditions are given for the optimality of the myopic policy.