# Revisiting Regularized Policy Optimization for Stable and Efficient Reinforcement Learning in Two-Player Games

arXiv: https://arxiv.org/abs/2602.10894 · HTML: https://mlsanity.com/paper/2602.10894/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 28 of its 54 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 28 of 28)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Deep Reinforcement Learning for Robotics: A Survey of Real-World Successes](https://mlsanity.com/paper/2408.03539/) (2024)
- [Soft Actor-Critic for Discrete Action Settings](https://mlsanity.com/paper/1910.07207/) (2019)
- [A Review of Robot Learning for Manipulation: Challenges, Representations, and Algorithms](https://mlsanity.com/paper/1907.03146/) (2019)
- [Mastering the Game of Stratego with Model-Free Multiagent Reinforcement Learning](https://mlsanity.com/paper/2206.15378/) (2022)
- [Online and Offline Reinforcement Learning by Planning with a Learned Model](https://mlsanity.com/paper/2104.06294/) (2021)
- [V-MPO: On-Policy Maximum a Posteriori Policy Optimization for Discrete and Continuous Control](https://mlsanity.com/paper/1909.12238/) (2019)
- [Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergence](https://mlsanity.com/paper/2105.11066/) (2021)
- [Learning and Planning in Complex Action Spaces](https://mlsanity.com/paper/2104.06303/) (2021)
- [Munchausen Reinforcement Learning](https://mlsanity.com/paper/2007.14430/) (2020)
- [A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Games](https://mlsanity.com/paper/2206.05825/) (2022)
- [Monte-Carlo Tree Search as Regularized Policy Optimization](https://mlsanity.com/paper/2007.12509/) (2020)
- [Suphx: Mastering Mahjong with Deep Reinforcement Learning](https://mlsanity.com/paper/2003.13590/) (2020)
- [Pgx: Hardware-Accelerated Parallel Game Simulators for Reinforcement Learning](https://mlsanity.com/paper/2303.17503/) (2023)
- [Vector Quantized Models for Planning](https://mlsanity.com/paper/2106.04615/) (2021)
- [Mastering the Game of No-Press Diplomacy via Human-Regularized Reinforcement Learning and Planning](https://mlsanity.com/paper/2210.05492/) (2022)
- [Re-evaluating Evaluation](https://mlsanity.com/paper/1806.02643/) (2018)
- [ELF OpenGo: An Analysis and Open Reimplementation of AlphaZero](https://mlsanity.com/paper/1902.04522/) (2019)
- [Accelerating and Improving AlphaZero Using Population Based Training](https://mlsanity.com/paper/2003.06212/) (2020)
- [Re-evaluating Open-ended Evaluation of Large Language Models](https://mlsanity.com/paper/2502.20170/) (2025)

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

- [Beyond Search-Imitation: Prior-Directed Exploration for Searchless Chess](https://mlsanity.com/paper/2608.27757/) (2026)

## Abstract (arXiv)

Two-player games such as board games have long been used as traditional benchmarks for reinforcement learning. This work revisits a policy optimization method with reverse Kullback-Leibler regularization and entropy regularization and analyzes this combination in two-player zero-sum settings from theoretical and empirical perspectives. From a theoretical perspective, we investigate the stability of the policy update rule in two theoretical settings: game-theoretic normal-form games and finite-length games. We provide novel convergence guarantees and verify our theoretical results through numerical experiments on synthetic games. From an empirical perspective, we derive a practical model-free reinforcement learning algorithm based on the regularized policy optimization. We validate the training efficiency of our algorithm through comprehensive experiments on five board games: Animal Shogi, Gardner Chess, Go, Hex, and Othello. Experimental results show that our agent learns more efficiently than existing methods across environments.