# EMAgnet: Parameter-Space EMA Regularization for Policy Gradient Self-Play in Large Games

arXiv: https://arxiv.org/abs/2606.23995 · HTML: https://mlsanity.com/paper/2606.23995/

## 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 23 of its 29 references that are in the map.
- First posted on arXiv 22 Jun 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, 23 of 23)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning](https://mlsanity.com/paper/1711.00832/) (2017)
- [OpenSpiel: A Framework for Reinforcement Learning in Games](https://mlsanity.com/paper/1908.09453/) (2019)
- [Deep Reinforcement Learning from Self-Play in Imperfect-Information Games](https://mlsanity.com/paper/1603.01121/) (2016)
- [Mastering the Game of Stratego with Model-Free Multiagent Reinforcement Learning](https://mlsanity.com/paper/2206.15378/) (2022)
- [Combining Deep Reinforcement Learning and Search for Imperfect-Information Games](https://mlsanity.com/paper/2007.13544/) (2020)
- [Exponential Moving Average of Weights in Deep Learning: Dynamics and Benefits](https://mlsanity.com/paper/2411.18704/) (2024)
- [A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Games](https://mlsanity.com/paper/2206.05825/) (2022)
- [Pipeline PSRO: A Scalable Approach for Finding Approximate Nash Equilibria in Large Games](https://mlsanity.com/paper/2006.08555/) (2020)
- [WARP: On the Benefits of Weight Averaged Rewarded Policies](https://mlsanity.com/paper/2406.16768/) (2024)
- [Slow and Steady Wins the Race: Maintaining Plasticity with Hare and Tortoise Networks](https://mlsanity.com/paper/2406.02596/) (2024)
- [DREAM: Deep Regret minimization with Advantage baselines and Model-free learning](https://mlsanity.com/paper/2006.10410/) (2020)
- [XDO: A Double Oracle Algorithm for Extensive-Form Games](https://mlsanity.com/paper/2103.06426/) (2021)
- [Vortices Instead of Equilibria in MinMax Optimization: Chaos and Butterfly Effects of Online Learning in Zero-Sum Games](https://mlsanity.com/paper/1905.08396/) (2019)
- [ESCHER: Eschewing Importance Sampling in Games by Computing a History Value Function to Estimate Regret](https://mlsanity.com/paper/2206.04122/) (2022)
- [NeuPL: Neural Population Learning](https://mlsanity.com/paper/2202.07415/) (2022)
- [Reevaluating Policy Gradient Methods for Imperfect-Information Games](https://mlsanity.com/paper/2502.08938/) (2025)
- [Scalable Decision Making for Games of Imperfect Information](https://mlsanity.com/paper/2511.07312/) (2025)
- [Data-Augmented Game Starts for Accelerating Self-Play Exploration in Imperfect Information Games](https://mlsanity.com/paper/2605.14379/) (2026)

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

- [FootsiesGym: A Fighting Game Benchmark for Two-Player Zero-Sum Imperfect-Information Games](https://mlsanity.com/paper/2607.06514/) (2026)

## Abstract (arXiv)

Recent work has established that regularized policy gradient methods such as PPO, when used in self-play, can match or exceed specialized game-theoretic algorithms for solving two-player zero-sum imperfect-information games. The uniform distribution has emerged as a strong policy regularization target for this purpose, but it regularizes equally toward all actions regardless of their viability. We introduce EMAgnet, which instead regularizes toward an exponential moving average (EMA) of the last-iterate policy's parameters, providing an adaptive regularization target that evolves with the agent's improving strategy. We evaluate EMAgnet on both standard two-player zero-sum benchmarks and modified benchmarks with exploration challenges and large numbers of strictly dominated strategies. Relative to PPO self-play with uniform-magnet regularization under both linear and power-law annealing schedules, EMAgnet achieves lower exploitability in the majority of tested environments, with consistent performance gains across games containing strictly dominated strategies.