# Convergence of Policy Mirror Descent Beyond Compatible Function Approximation

arXiv: https://arxiv.org/abs/2502.11033 · HTML: https://mlsanity.com/paper/2502.11033/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 57 references that are in the map.
- First posted on arXiv 16 Feb 2025.

## Builds on (most cited first, 30 of 36)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [On the Global Convergence Rates of Softmax Policy Gradient Methods](https://mlsanity.com/paper/2005.06392/) (2020)
- [Learning Near Optimal Policies with Low Inherent Bellman Error](https://mlsanity.com/paper/2003.00153/) (2020)
- [Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization](https://mlsanity.com/paper/2007.06558/) (2020)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classes](https://mlsanity.com/paper/2102.00135/) (2021)
- [Global Optimality Guarantees For Policy Gradient Methods](https://mlsanity.com/paper/1906.01786/) (2019)
- [Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization](https://mlsanity.com/paper/1308.6594/) (2013)
- [Global Convergence of Policy Gradient Methods to (Almost) Locally Optimal Policies](https://mlsanity.com/paper/1906.08383/) (2019)
- [On the Convergence Rates of Policy Gradient Methods](https://mlsanity.com/paper/2201.07443/) (2022)
- [Adaptive Trust Region Policy Optimization: Global Convergence and Faster Rates for Regularized MDPs](https://mlsanity.com/paper/1909.02769/) (2019)
- [Relatively-Smooth Convex Optimization by First-Order Methods, and Applications](https://mlsanity.com/paper/1610.05708/) (2016)
- [Mirror Descent Policy Optimization](https://mlsanity.com/paper/2005.09814/) (2020)
- [Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergence](https://mlsanity.com/paper/2105.11066/) (2021)
- [A general sample complexity analysis of vanilla policy gradient](https://mlsanity.com/paper/2107.11433/) (2021)
- [An Improved Analysis of (Variance-Reduced) Policy Gradient and Natural Policy Gradient Methods](https://mlsanity.com/paper/2211.07937/) (2022)
- [On Linear Convergence of Policy Gradient Methods for Finite MDPs](https://mlsanity.com/paper/2007.11120/) (2020)
- [On the Linear convergence of Natural Policy Gradient Algorithm](https://mlsanity.com/paper/2105.01424/) (2021)
- [Linear Convergence of Natural Policy Gradient Methods with Log-Linear Policies](https://mlsanity.com/paper/2210.01400/) (2022)
- [Leveraging Non-uniformity in First-order Non-convex Optimization](https://mlsanity.com/paper/2105.06072/) (2021)
- [Mirror Learning: A Unifying Framework of Policy Optimisation](https://mlsanity.com/paper/2201.02373/) (2022)
- [A Novel Framework for Policy Mirror Descent with General Parameterization and Linear Convergence](https://mlsanity.com/paper/2301.13139/) (2023)
- [Policy Optimization over General State and Action Spaces](https://mlsanity.com/paper/2211.16715/) (2022)
- [A general class of surrogate functions for stable and efficient reinforcement learning](https://mlsanity.com/paper/2108.05828/) (2021)
- [Optimal Convergence Rate for Exact Policy Mirror Descent in Discounted Markov Decision Processes](https://mlsanity.com/paper/2302.11381/) (2023)
- [Linear Convergence for Natural Policy Gradient with Log-linear Policy Parametrization](https://mlsanity.com/paper/2209.15382/) (2022)

## Built on by (most cited first, 2 of 2)

- [Convergence and Sample Complexity of First-Order Methods for Agnostic Reinforcement Learning](https://mlsanity.com/paper/2507.04406/) (2025)
- [An analysis of Mirror-Descent Soft Actor-Critic](https://mlsanity.com/paper/2609.35466/) (2026)

## Abstract (arXiv)

Modern policy optimization methods roughly follow the policy mirror descent (PMD) algorithmic template, for which there are by now numerous theoretical convergence results. However, most of these either target tabular environments, or can be applied effectively only when the class of policies being optimized over satisfies strong closure conditions, which is typically not the case when working with parametric policy classes in large-scale environments. In this work, we develop a theoretical framework for PMD for general policy classes where we replace the closure conditions with a strictly weaker variational gradient dominance assumption, and obtain upper bounds on the rate of convergence to the best-in-class policy. Our main result leverages a novel notion of smoothness with respect to a local norm induced by the occupancy measure of the current policy, and casts PMD as a particular instance of smooth non-convex optimization in non-Euclidean space.