# Revisiting CFR+ and Alternating Updates

arXiv: https://arxiv.org/abs/1810.11542 · HTML: https://mlsanity.com/paper/1810.11542/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2018.

## Built on by (most cited first, 19 of 19)

- [Last-iterate Convergence in Extensive-Form Games](https://mlsanity.com/paper/2106.14326/) (2021)
- [Near-Optimal Learning of Extensive-Form Games with Imperfect Information](https://mlsanity.com/paper/2202.01752/) (2022)
- [A Survey on Self-play Methods in Reinforcement Learning](https://mlsanity.com/paper/2408.01072/) (2024)
- [Model-Free Learning for Two-Player Zero-Sum Partially Observable Markov Games with Perfect Recall](https://mlsanity.com/paper/2106.06279/) (2021)
- [Efficient Phi-Regret Minimization in Extensive-Form Games via Online Mirror Descent](https://mlsanity.com/paper/2205.15294/) (2022)
- [Regret Matching+: (In)Stability and Fast Convergence in Games](https://mlsanity.com/paper/2305.14709/) (2023)
- [Adapting to game trees in zero-sum imperfect information games](https://mlsanity.com/paper/2212.12567/) (2022)
- [HSVI can solve zero-sum Partially Observable Stochastic Games](https://mlsanity.com/paper/2210.14640/) (2022)
- [Last-Iterate Convergence Properties of Regret-Matching Algorithms in Games](https://mlsanity.com/paper/2311.00676/) (2023)
- [Conic Blackwell Algorithm: Parameter-Free Convex-Concave Saddle-Point Solving](https://mlsanity.com/paper/2105.13203/) (2021)
- [Solving optimization problems with Blackwell approachability](https://mlsanity.com/paper/2202.12277/) (2022)
- [Local and adaptive mirror descents in extensive-form games](https://mlsanity.com/paper/2309.00656/) (2023)
- [Revisiting Game Representations: The Hidden Costs of Efficiency in Sequential Decision-making Algorithms](https://mlsanity.com/paper/2112.10890/) (2021)
- [A Generalized Extensive-Form Fictitious Play Algorithm](https://mlsanity.com/paper/2310.09658/) (2023)
- [GPU-Accelerated Counterfactual Regret Minimization](https://mlsanity.com/paper/2408.14778/) (2024)
- [Efficient Last-Iterate Convergence in Regret Minimization via Adaptive Reward Transformation](https://mlsanity.com/paper/2509.13653/) (2025)
- [CFR without Unbiasedness: Deterministic Guarantees for Persistent Public-Chance Schedules](https://mlsanity.com/paper/2608.14761/) (2026)
- [Minimax Alternating Regret for the Experts Problem and Online Convex Optimization](https://mlsanity.com/paper/2608.25182/) (2026)
- [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)

The CFR+ algorithm for solving imperfect information games is a variant of the popular CFR algorithm, with faster empirical performance on a range of problems. It was introduced with a theoretical upper bound on solution error, but subsequent work showed an error in one step of the proof. We provide updated proofs to recover the original bound.