A Finite-Sample Analysis of an Actor-Critic Algorithm for Mean-Variance Optimization in a Discounted MDP
This provides theoretical guarantees for risk-sensitive actor-critic methods, addressing variance as a risk measure, but it is incremental as it builds on existing TD and SPSA techniques.
The paper tackles mean-variance optimization in discounted MDPs for risk-sensitive reinforcement learning, deriving finite-sample bounds for a TD learning algorithm with linear function approximation and establishing an O(n^{-1/4}) convergence rate for an SPSA-based actor-critic method.
Motivated by applications in risk-sensitive reinforcement learning, we study mean-variance optimization in a discounted reward Markov Decision Process (MDP). Specifically, we analyze a Temporal Difference (TD) learning algorithm with linear function approximation (LFA) for policy evaluation. We derive finite-sample bounds that hold (i) in the mean-squared sense and (ii) with high probability under tail iterate averaging, both with and without regularization. Our bounds exhibit an exponentially decaying dependence on the initial error and a convergence rate of $O(1/t)$ after $t$ iterations. Moreover, for the regularized TD variant, our bound holds for a universal step size. Next, we integrate a Simultaneous Perturbation Stochastic Approximation (SPSA)-based actor update with an LFA critic and establish an $O(n^{-1/4})$ convergence guarantee, where $n$ denotes the iterations of the SPSA-based actor-critic algorithm. These results establish finite-sample theoretical guarantees for risk-sensitive actor-critic methods in reinforcement learning, with a focus on variance as a risk measure.