Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach

TL;DR

This paper introduces a CVaR-based approach to decision-making in MDPs that accounts for risk sensitivity and model errors, providing a new unified framework with an efficient solution algorithm and practical validation.

Contribution

It establishes CVaR as a unifying measure for risk-sensitive and robust decision-making, and develops the first error-guaranteed algorithm for CVaR MDPs.

Findings

The CVaR objective can be interpreted as worst-case expected cost.

The proposed algorithm converges with quantifiable error bounds.

Numerical results demonstrate the approach's practicality.

Abstract

In this paper we address the problem of decision making within a Markov decision process (MDP) framework where risk and modeling errors are taken into account. Our approach is to minimize a risk-sensitive conditional-value-at-risk (CVaR) objective, as opposed to a standard risk-neutral expectation. We refer to such problem as CVaR MDP. Our first contribution is to show that a CVaR objective, besides capturing risk sensitivity, has an alternative interpretation as expected cost under worst-case modeling errors, for a given error budget. This result, which is of independent interest, motivates CVaR MDPs as a unifying framework for risk-sensitive and robust decision making. Our second contribution is to present an approximate value-iteration algorithm for CVaR MDPs and analyze its convergence rate. To our knowledge, this is the first solution algorithm for CVaR MDPs that enjoys error guarantees. Finally, we present results from numerical experiments that corroborate our theoretical findings and show the practicality of our approach.