# Beyond Exponentially Fast Mixing in Average-Reward Reinforcement Learning via Multi-Level Monte Carlo Actor-Critic

arXiv: https://arxiv.org/abs/2301.12083 · HTML: https://mlsanity.com/paper/2301.12083/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 55 references that are in the map.
- First posted on arXiv 28 Jan 2023.

## Builds on (most cited first, 21 of 21)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [On the Global Convergence Rates of Softmax Policy Gradient Methods](https://mlsanity.com/paper/2005.06392/) (2020)
- [A Finite Time Analysis of Temporal Difference Learning With Linear Function Approximation](https://mlsanity.com/paper/1806.02450/) (2018)
- [On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shift](https://mlsanity.com/paper/1908.00261/) (2019)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [Global Optimality Guarantees For Policy Gradient Methods](https://mlsanity.com/paper/1906.01786/) (2019)
- [Global Convergence of Policy Gradient Methods to (Almost) Locally Optimal Policies](https://mlsanity.com/paper/1906.08383/) (2019)
- [A Finite Time Analysis of Two Time-Scale Actor Critic Methods](https://mlsanity.com/paper/2005.01350/) (2020)
- [Stochastic Variance-Reduced Policy Gradient](https://mlsanity.com/paper/1806.05618/) (2018)
- [Finite-Sample Analysis for SARSA with Linear Function Approximation](https://mlsanity.com/paper/1902.02234/) (2019)
- [An Improved Convergence Analysis of Stochastic Variance-Reduced Policy Gradient](https://mlsanity.com/paper/1905.12615/) (2019)
- [Least Squares Regression with Markovian Data: Fundamental Limits and Algorithms](https://mlsanity.com/paper/2006.08916/) (2020)
- [On the Sample Complexity of Actor-Critic Method for Reinforcement Learning with Function Approximation](https://mlsanity.com/paper/1910.08412/) (2019)
- [Federated Learning Meets Natural Language Processing: A Survey](https://mlsanity.com/paper/2107.12603/) (2021)
- [Adapting to Mixing Time in Stochastic Optimization with Markovian Data](https://mlsanity.com/paper/2202.04428/) (2022)
- [Finite-time analysis of single-timescale actor-critic](https://mlsanity.com/paper/2210.09921/) (2022)
- [Convergence of Policy Gradient for Entropy Regularized MDPs with Neural Network Approximation in the Mean-Field Regime](https://mlsanity.com/paper/2201.07296/) (2022)
- [Continual Learning In Environments With Polynomial Mixing Times](https://mlsanity.com/paper/2112.07066/) (2021)
- [On the Hidden Biases of Policy Mirror Ascent in Continuous Action Spaces](https://mlsanity.com/paper/2201.12332/) (2022)
- [Deep Portfolio Theory](https://mlsanity.com/paper/1605.07230/) (2016)

## Built on by (most cited first, 18 of 18)

- [Regret Analysis of Policy Gradient Algorithm for Infinite Horizon Average Reward Markov Decision Processes](https://mlsanity.com/paper/2309.01922/) (2023)
- [A Sharper Global Convergence Analysis for Average Reward Reinforcement Learning via an Actor-Critic Approach](https://mlsanity.com/paper/2407.18878/) (2024)
- [Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm](https://mlsanity.com/paper/2505.15138/) (2025)
- [Two-Timescale Critic-Actor for Average Reward MDPs with Function Approximation](https://mlsanity.com/paper/2402.01371/) (2024)
- [Regret Analysis of Average-Reward Unichain MDPs via an Actor-Critic Approach](https://mlsanity.com/paper/2505.19986/) (2025)
- [Towards Global Optimality for Practical Average Reward Reinforcement Learning without Mixing Time Oracles](https://mlsanity.com/paper/2403.11925/) (2024)
- [Dynamic Byzantine-Robust Learning: Adapting to Switching Byzantine Workers](https://mlsanity.com/paper/2402.02951/) (2024)
- [Sampling-based Safe Reinforcement Learning for Nonlinear Dynamical Systems](https://mlsanity.com/paper/2403.04007/) (2024)
- [Regret Analysis of Unichain Average Reward Constrained MDPs with General Parameterization](https://mlsanity.com/paper/2602.08000/) (2026)
- [Finite-Time Analysis of Three-Timescale Constrained Actor-Critic and Constrained Natural Actor-Critic Algorithms](https://mlsanity.com/paper/2310.16363/) (2023)
- [Policy Mirror Descent with Temporal Difference Learning: Sample Complexity under Online Markov Data](https://mlsanity.com/paper/2512.24056/) (2025)
- [Breaking the Bias Barrier in Concave Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2603.08518/) (2026)
- [Stabilizing Policy Gradient Methods via Reward Profiling](https://mlsanity.com/paper/2511.16629/) (2025)
- [Provably Efficient Algorithms for S- and Non-Rectangular Robust MDPs with General Parameterization](https://mlsanity.com/paper/2602.11387/) (2026)
- [Confidence-Controlled Exploration: Efficient Sparse-Reward Policy Learning for Robot Navigation](https://mlsanity.com/paper/2306.06192/) (2023)
- [Signal attenuation enables scalable decentralized multi-agent reinforcement learning over networks](https://mlsanity.com/paper/2505.11461/) (2025)
- [Finite Time Analysis of Constrained Natural Critic-Actor Algorithm with Improved Sample Complexity](https://mlsanity.com/paper/2510.04189/) (2025)
- [Bias-Controlled Primal-Dual Natural Actor-Critic: Optimal Rates for Constrained Multi-Objective Average-Reward RL](https://mlsanity.com/paper/2606.25012/) (2026)

## Abstract (arXiv)

Many existing reinforcement learning (RL) methods employ stochastic gradient iteration on the back end, whose stability hinges upon a hypothesis that the data-generating process mixes exponentially fast with a rate parameter that appears in the step-size selection. Unfortunately, this assumption is violated for large state spaces or settings with sparse rewards, and the mixing time is unknown, making the step size inoperable. In this work, we propose an RL methodology attuned to the mixing time by employing a multi-level Monte Carlo estimator for the critic, the actor, and the average reward embedded within an actor-critic (AC) algorithm. This method, which we call Multi-level Actor-Critic (MAC), is developed especially for infinite-horizon average-reward settings and neither relies on oracle knowledge of the mixing time in its parameter selection nor assumes its exponential decay; it, therefore, is readily applicable to applications with slower mixing times. Nonetheless, it achieves a convergence rate comparable to the state-of-the-art AC algorithms. We experimentally show that these alleviated restrictions on the technical conditions required for stability translate to superior performance in practice for RL problems with sparse rewards.