# Mirror Descent Actor Critic via Bounded Advantage Learning

arXiv: https://arxiv.org/abs/2502.03854 · HTML: https://mlsanity.com/paper/2502.03854/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 26 of its 48 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## 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, 26 of 26)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [dm_control: Software and Tasks for Continuous Control](https://mlsanity.com/paper/2006.12983/) (2020)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classes](https://mlsanity.com/paper/2102.00135/) (2021)
- [Extreme Q-Learning: MaxEnt RL without Entropy](https://mlsanity.com/paper/2301.02328/) (2023)
- [Mirror Descent Policy Optimization](https://mlsanity.com/paper/2005.09814/) (2020)
- [Munchausen Reinforcement Learning](https://mlsanity.com/paper/2007.14430/) (2020)
- [Increasing the Action Gap: New Operators for Reinforcement Learning](https://mlsanity.com/paper/1512.04860/) (2015)
- [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 with Stochastic Mirror Descent](https://mlsanity.com/paper/1906.10462/) (2019)
- [A general class of surrogate functions for stable and efficient reinforcement learning](https://mlsanity.com/paper/2108.05828/) (2021)
- [KL-Entropy-Regularized RL with a Generative Model is Minimax Optimal](https://mlsanity.com/paper/2205.14211/) (2022)
- [Implicitly Regularized RL with Implicit Q-Values](https://mlsanity.com/paper/2108.07041/) (2021)
- [Divergence-Augmented Policy Optimization](https://mlsanity.com/paper/2501.15034/) (2025)
- [Robust Action Gap Increasing with Clipped Advantage Learning](https://mlsanity.com/paper/2203.11677/) (2022)
- [Generalized Munchausen Reinforcement Learning using Tsallis KL Divergence](https://mlsanity.com/paper/2301.11476/) (2023)

## Built on by (most cited first, 1 of 1)

- [Policy as Data: Replay-Based Policy Dual Averaging via Advantage Regression](https://mlsanity.com/paper/2610.04638/) (2026)

## Abstract (arXiv)

Regularization is a core component of recent Reinforcement Learning (RL) algorithms. Mirror Descent Value Iteration (MDVI) uses both Kullback-Leibler divergence and entropy as regularizers in its value and policy updates. Despite its empirical success in discrete action domains and strong theoretical guarantees, the performance of KL-entropy-regularized methods does not surpass that of a strong entropy-only-regularized method in continuous action domains. In this study, we propose Mirror Descent Actor Critic (MDAC) as an actor-critic style instantiation of MDVI for continuous action domains, and show that its empirical performance is significantly boosted by bounding the actor's log-density terms in the critic's loss function, compared to a non-bounded naive instantiation. Further, we relate MDAC to Advantage Learning by recalling that the actor's log-probability is equal to the regularized advantage function in tabular cases, and theoretically discuss when and why bounding the advantage terms is validated and beneficial. We also empirically explore effective choices for the bounding functions, and show that MDAC performs better than strong non-regularized and entropy-only-regularized methods with an appropriate choice of the bounding functions.