Finding minimax strategy and minimax risk in a random environment (the two‐armed bandit problem)

Minimax strategy and risk in a stationary random environment are found as Bayesian ones corresponding to the worst prior distribution. For environments with normally distributed incomes with unit variance and expectations that depend only on the alternative selected, this distribution can be chosen to be symmetric and asymptotically uniform. This lets one use numerical methods. The results can be used for systems with parallel data processing, in particular, for controlling environments with distributions other than normal.