# Minimizing Weighted Counterfactual Regret with Optimistic Online Mirror Descent

arXiv: https://arxiv.org/abs/2404.13891 · HTML: https://mlsanity.com/paper/2404.13891/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 33 references that are in the map.
- First posted on arXiv 22 Apr 2024.

## Builds on (most cited first, 18 of 18)

- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Fast Convergence of Regularized Learning in Games](https://mlsanity.com/paper/1507.00407/) (2015)
- [Deep Counterfactual Regret Minimization](https://mlsanity.com/paper/1811.00164/) (2018)
- [Solving Large Imperfect Information Games Using CFR+](https://mlsanity.com/paper/1407.5042/) (2014)
- [Solving Imperfect-Information Games via Discounted Regret Minimization](https://mlsanity.com/paper/1809.04040/) (2018)
- [From Poincar'e Recurrence to Convergence in Imperfect Information Games: Finding Equilibrium via Regularization](https://mlsanity.com/paper/2002.08456/) (2020)
- [Faster Game Solving via Predictive Blackwell Approachability: Connecting Regret Matching and Mirror Descent](https://mlsanity.com/paper/2007.14358/) (2020)
- [Safe and Nested Subgame Solving for Imperfect-Information Games](https://mlsanity.com/paper/1705.02955/) (2017)
- [Solving Imperfect Information Games Using Decomposition](https://mlsanity.com/paper/1303.4441/) (2013)
- [Depth-Limited Solving for Imperfect-Information Games](https://mlsanity.com/paper/1805.08195/) (2018)
- [Faster Rates for Convex-Concave Games](https://mlsanity.com/paper/1805.06792/) (2018)
- [Correlation in Extensive-Form Games: Saddle-Point Formulation and Benchmarks](https://mlsanity.com/paper/1905.12564/) (2019)
- [Acceleration through Optimistic No-Regret Dynamics](https://mlsanity.com/paper/1807.10455/) (2018)
- [Stable-Predictive Optimistic Counterfactual Regret Minimization](https://mlsanity.com/paper/1902.04982/) (2019)
- [Regret Matching+: (In)Stability and Fast Convergence in Games](https://mlsanity.com/paper/2305.14709/) (2023)
- [Equivalence Analysis between Counterfactual Regret Minimization and Online Mirror Descent](https://mlsanity.com/paper/2110.04961/) (2021)
- [Solving optimization problems with Blackwell approachability](https://mlsanity.com/paper/2202.12277/) (2022)

## Built on by (most cited first, 7 of 7)

- [Discovering Multiagent Learning Algorithms with Large Language Models](https://mlsanity.com/paper/2602.16928/) (2026)
- [Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Games](https://mlsanity.com/paper/2510.04407/) (2025)
- [Convergence of Regret Matching in Potential Games and Constrained Optimization](https://mlsanity.com/paper/2510.17067/) (2025)
- [Faster Game Solving via Asymmetry of Step Sizes](https://mlsanity.com/paper/2503.12770/) (2025)
- [Solving Pasur Using GPU-Accelerated Counterfactual Regret Minimization](https://mlsanity.com/paper/2508.06559/) (2025)
- [Deep (Predictive) Discounted Counterfactual Regret Minimization](https://mlsanity.com/paper/2511.08174/) (2025)
- [GPU-CFR: 80x Faster Counterfactual Regret Minimization by Compiling the Game to Static Dataflow and CUDA Graph Replay](https://mlsanity.com/paper/2609.11923/) (2026)

## Abstract (arXiv)

Counterfactual regret minimization (CFR) is a family of algorithms for effectively solving imperfect-information games. It decomposes the total regret into counterfactual regrets, utilizing local regret minimization algorithms, such as Regret Matching (RM) or RM+, to minimize them. Recent research establishes a connection between Online Mirror Descent (OMD) and RM+, paving the way for an optimistic variant PRM+ and its extension PCFR+. However, PCFR+ assigns uniform weights for each iteration when determining regrets, leading to substantial regrets when facing dominated actions. This work explores minimizing weighted counterfactual regret with optimistic OMD, resulting in a novel CFR variant PDCFR+. It integrates PCFR+ and Discounted CFR (DCFR) in a principled manner, swiftly mitigating negative effects of dominated actions and consistently leveraging predictions to accelerate convergence. Theoretical analyses prove that PDCFR+ converges to a Nash equilibrium, particularly under distinct weighting schemes for regrets and average strategies. Experimental results demonstrate PDCFR+'s fast convergence in common imperfect-information games. The code is available at https://github.com/rpSebastian/PDCFRPlus.