# Mirror descent actor-critic methods for entropy regularised MDPs in general spaces: stability and convergence

arXiv: https://arxiv.org/abs/2602.10838 · HTML: https://mlsanity.com/paper/2602.10838/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 20 of 20)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [On the Global Convergence Rates of Softmax Policy Gradient Methods](https://mlsanity.com/paper/2005.06392/) (2020)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classes](https://mlsanity.com/paper/2102.00135/) (2021)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [Mirror Descent Policy Optimization](https://mlsanity.com/paper/2005.09814/) (2020)
- [Frequentist Regret Bounds for Randomized Least-Squares Value Iteration](https://mlsanity.com/paper/1911.00567/) (2019)
- [Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EM](https://mlsanity.com/paper/2206.08873/) (2022)
- [Sample-Efficient Reinforcement Learning Is Feasible for Linearly Realizable MDPs with Limited Revisiting](https://mlsanity.com/paper/2105.08024/) (2021)
- [A Fisher-Rao gradient flow for entropy-regularised Markov decision processes in Polish spaces](https://mlsanity.com/paper/2310.02951/) (2023)
- [Convergence of Policy Gradient for Entropy Regularized MDPs with Neural Network Approximation in the Mean-Field Regime](https://mlsanity.com/paper/2201.07296/) (2022)
- [Finite-Time Analysis of Entropy-Regularized Neural Natural Actor-Critic Algorithm](https://mlsanity.com/paper/2206.00833/) (2022)
- [Linear Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximation](https://mlsanity.com/paper/2106.04096/) (2021)
- [Wasserstein Flow Meets Replicator Dynamics: A Mean-Field Analysis of Representation Learning in Actor-Critic](https://mlsanity.com/paper/2112.13530/) (2021)
- [Skill Transfer and Discovery for Sim-to-Real Learning: A Representation-Based Viewpoint](https://mlsanity.com/paper/2404.05051/) (2024)
- [Confident Natural Policy Gradient for Local Planning in qπ-realizable Constrained MDPs](https://mlsanity.com/paper/2406.18529/) (2024)

## Abstract (arXiv)

We provide theoretical guarantees for convergence of discrete-time policy mirror descent with inexact advantage functions updated using temporal difference (TD) learning for entropy regularised MDPs in Polish state and action spaces. We rigorously derive sufficient conditions under which the single-loop actor-critic scheme is stable and convergent. To weaken these conditions, we introduce a variant that performs multiple TD steps per policy update and derive an explicit lower bound on the number of TD steps required to ensure stability. Finally, we establish sub-linear convergence when the number of TD steps grows logarithmically with the number of policy updates, and linear convergence when it grows linearly under a concentrability assumption.