Risk-sensitive and minimax control of discrete-time, finite-state Markov decision processes

This paper analyzes a connection between risk-sensitive and minimax criteria for discrete-time, nite-states Markov Decision Processes (MDPs). We synthesize optimal policies with respect to both criteria, both for nite horizon and discounted in nite horizon problem. A generalized decision-making framework is introduced, which includes as special cases a number of approaches that have been considered in the literature. The framework allows for discounted risk-sensitive and minimax formulations leading to stationary optimal policies on the in nite horizon. We illustrate our results with a simple machine replacement problem.