Variance-Constrained Actor-Critic Algorithms for Discounted and Average Reward MDPs
This work addresses risk-sensitive optimization in MDPs for applications like finance and operations research, though it appears incremental as it builds on existing actor-critic methods with variance constraints.
The paper tackles the problem of managing risk in sequential decision-making by optimizing variance-constrained criteria in Markov decision processes (MDPs) for discounted and average reward settings, resulting in actor-critic algorithms that converge to locally risk-sensitive optimal policies and are demonstrated in a traffic signal control application.
In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common risk-sensitive criteria in finance and operations research. However, optimizing many such criteria is known to be a hard problem. In this paper, we consider both discounted and average reward Markov decision processes. For each formulation, we first define a measure of variability for a policy, which in turn gives us a set of risk-sensitive criteria to optimize. For each of these criteria, we derive a formula for computing its gradient. We then devise actor-critic algorithms that operate on three timescales - a TD critic on the fastest timescale, a policy gradient (actor) on the intermediate timescale, and a dual ascent for Lagrange multipliers on the slowest timescale. In the discounted setting, we point out the difficulty in estimating the gradient of the variance of the return and incorporate simultaneous perturbation approaches to alleviate this. The average setting, on the other hand, allows for an actor update using compatible features to estimate the gradient of the variance. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in a traffic signal control application.