Optimality of deterministic policies for certain stochastic control problems with multiple criteria and constraints

For single-criterion stochastic control and sequential decision problems, optimal policies, if they exist, are typically nonrandomized. For problems with multiple criteria and constraints, optimal nonrandomized policies may not exist and, if optimal policies exist, they are typically randomized. In this paper we discuss certain conditions that lead to optimality of nonrandomized policies. In the most interesting situations, these conditions do not impose convexity assumptions on the action sets and reward functions.