Constrained Risk-Averse Markov Decision Processes

TL;DR

This paper develops an optimization framework for designing risk-averse policies in Markov decision processes with constraints, using difference convex programming to handle coherent risk measures like CVaR and EVaR.

Contribution

It introduces a novel method to synthesize Markovian policies for constrained risk-averse MDPs via DCPs, generalizing linear programming approaches.

Findings

Effective policy synthesis demonstrated on rover navigation with CVaR and EVaR.

The approach generalizes constrained MDP solutions to risk-averse settings.

Optimization problems are solvable using disciplined convex-concave programming.

Abstract

We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.