Semismooth Newton Methods for Risk-Averse Markov Decision Processes

TL;DR

This paper introduces a semismooth Newton-based framework for solving risk-averse Markov decision processes, providing convergence guarantees and demonstrating competitive empirical performance across various risk measures.

Contribution

It develops a versatile, convergence-guaranteed solution framework for risk-averse MDPs inspired by semismooth Newton methods, unifying and extending existing approaches.

Findings

Designed three solution methods with proven convergence

Validated methods on benchmark problems showing competitive performance

Linked risk-averse policy iteration to semismooth Newton's method

Abstract

Inspired by semismooth Newton methods, we propose a general framework for designing solution methods with convergence guarantees for risk-averse Markov decision processes. Our approach accommodates a wide variety of risk measures by leveraging the assumption of Markovian coherent risk measures. To demonstrate the versatility and effectiveness of this framework, we design three distinct solution methods, each with proven convergence guarantees and competitive empirical performance. Validation results on benchmark problems demonstrate the competitive performance of our methods. Furthermore, we establish that risk-averse policy iteration can be interpreted as an instance of semismooth Newton's method. This insight explains its superior convergence properties compared to risk-averse value iteration. The core contribution of our work, however, lies in developing an algorithmic framework inspired by semismooth Newton methods, rather than evaluating specific risk measures or advocating for risk-averse approaches over risk-neutral ones in particular applications.