Policy Gradients for CVaR-Constrained MDPs

TL;DR

This paper introduces two algorithms for risk-constrained stochastic shortest path problems using CVaR, combining stochastic approximation, mini-batches, policy gradients, and importance sampling to achieve risk-aware optimal policies with proven convergence.

Contribution

The paper develops and analyzes two novel algorithms for CVaR-constrained MDPs, integrating importance sampling and gradient estimation techniques.

Findings

Both algorithms converge asymptotically.

Importance sampling reduces variance in CVaR estimation.

Algorithms effectively incorporate risk constraints into policy optimization.

Abstract

We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four tools: stochastic approximation, mini batches, policy gradients and importance sampling. Both the algorithms incorporate a CVaR estimation procedure, along the lines of Bardou et al. [2009], which in turn is based on Rockafellar-Uryasev's representation for CVaR and utilize the likelihood ratio principle for estimating the gradient of the sum of one cost function (objective of the SSP) and the gradient of the CVaR of the sum of another cost function (in the constraint of SSP). The algorithms differ in the manner in which they approximate the CVaR estimates/necessary gradients - the first algorithm uses stochastic approximation, while the second employ mini-batches in the spirit of Monte Carlo methods. We establish asymptotic convergence of both the algorithms. Further, since estimating CVaR is related to rare-event simulation, we incorporate an importance sampling based variance reduction scheme into our proposed algorithms.