Risk-Sensitive, Minimax, and Mixed Risk-Neutral / Minimax Control of Markov Decision Processes
Stefano P. Coraluppi, Steven I. Marcus · Birkhäuser Boston eBooks · 1999
This paper analyzes a connection between risk-sensitive and minimax criteria for discrete-time, finite-state Markov Decision Processes (MDPs). We synthesize optimal policies with respect to both criteria, both for finite horizon and discounted infinite horizon problems. A generalized decision-making framework is introduced, leading to stationary risk-sensitive and minimax optimal policies on the infinite horizon with discounted costs. We introduce the mixed risk-neutral/minimax objective, and utilize results from risk-neutral and minimax control to derive an information state process and dynamic programming equations for the value function. We synthesize optimal control laws both on the finite and infinite horizon, and establish the effectiveness of the controller as a tool to trade off risk-neutral and minimax objectives.