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Modified policy iteration (MPI) also known as optimistic policy iteration isat the core of many reinforcement learning algorithms. It works by combiningelements of policy iteration and value iteration. The convergence of MPI hasbeen well studied in the case of discounted and average-cost MDPs. In thiswork, we consider the exponential cost risk-sensitive MDP formulation, which isknown to provide some robustness to model parameters. Although policy iterationand value iteration have been well studied in the context of risk sensitiveMDPs, modified policy iteration is relatively unexplored. We provide the firstproof that MPI also converges for the risk-sensitive problem in the case offinite state and action spaces. Since the exponential cost formulation dealswith the multiplicative Bellman equation, our main contribution is aconvergence proof which is quite different than existing results for discountedand risk-neutral average-cost problems. The proof of approximate modifiedpolicy iteration for risk sensitive MDPs is also provided in the appendix.

Modified Policy Iteration for Exponential Cost Risk Sensitive MDPs