A Finite-Sample Analysis of an Actor-Critic Algorithm for Mean-Variance Optimization in a Discounted MDP

Tejaram Sangadi, Prashanth L. A., Krishna Jagannathan; 6:976−1024, 2025.

Presented at the Reinforcement Learning Conference (RLC), Edmonton, Alberta, Canada, August 5–9, 2025.

Abstract

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.

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BibTeX

@article{sangadi2025finite,
    title={A Finite-Sample Analysis of an Actor-Critic Algorithm for Mean-Variance Optimization in a Discounted {MDP}},
    author={Sangadi, Tejaram and A., Prashanth L. and Jagannathan, Krishna},
    journal={Reinforcement Learning Journal},
    volume={6},
    pages={976--1024},
    year={2025}
}