# Solving Large Sequential Games with the Excessive Gap Technique

arXiv: https://arxiv.org/abs/1810.03063 · HTML: https://mlsanity.com/paper/1810.03063/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2018.

## Built on by (most cited first, 16 of 16)

- [Near-Optimal Learning of Extensive-Form Games with Imperfect Information](https://mlsanity.com/paper/2202.01752/) (2022)
- [Model-Free Learning for Two-Player Zero-Sum Partially Observable Markov Games with Perfect Recall](https://mlsanity.com/paper/2106.06279/) (2021)
- [Beyond Time-Average Convergence: Near-Optimal Uncoupled Online Learning via Clairvoyant Multiplicative Weights Update](https://mlsanity.com/paper/2111.14737/) (2021)
- [Kernelized Multiplicative Weights for 0/1-Polyhedral Games: Bridging the Gap Between Learning in Extensive-Form and Normal-Form Games](https://mlsanity.com/paper/2202.00237/) (2022)
- [Better Regularization for Sequential Decision Spaces: Fast Convergence Rates for Nash, Correlated, and Team Equilibria](https://mlsanity.com/paper/2105.12954/) (2021)
- [Adapting to game trees in zero-sum imperfect information games](https://mlsanity.com/paper/2212.12567/) (2022)
- [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)
- [Fast Convergence of Optimistic Gradient Ascent in Network Zero-Sum Extensive Form Games](https://mlsanity.com/paper/2207.08426/) (2022)
- [Safe Search for Stackelberg Equilibria in Extensive-Form Games](https://mlsanity.com/paper/2102.01775/) (2021)
- [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)
- [Local and adaptive mirror descents in extensive-form games](https://mlsanity.com/paper/2309.00656/) (2023)
- [On the Optimality of Dilated Entropy and Lower Bounds for Online Learning in Extensive-Form Games](https://mlsanity.com/paper/2410.23398/) (2024)
- [Parallelizing Counterfactual Regret Minimization](https://mlsanity.com/paper/2605.14277/) (2026)
- [Abstraction Agent](https://mlsanity.com/paper/2609.04303/) (2026)
- [Efficient Last-Iterate Convergence in Regret Minimization via Adaptive Reward Transformation](https://mlsanity.com/paper/2509.13653/) (2025)

## Abstract (arXiv)

There has been tremendous recent progress on equilibrium-finding algorithms for zero-sum imperfect-information extensive-form games, but there has been a puzzling gap between theory and practice. First-order methods have significantly better theoretical convergence rates than any counterfactual-regret minimization (CFR) variant. Despite this, CFR variants have been favored in practice. Experiments with first-order methods have only been conducted on small- and medium-sized games because those methods are complicated to implement in this setting, and because CFR variants have been enhanced extensively for over a decade they perform well in practice. In this paper we show that a particular first-order method, a state-of-the-art variant of the excessive gap technique---instantiated with the dilated entropy distance function---can efficiently solve large real-world problems competitively with CFR and its variants. We show this on large endgames encountered by the Libratus poker AI, which recently beat top human poker specialist professionals at no-limit Texas hold'em. We show experimental results on our variant of the excessive gap technique as well as a prior version. We introduce a numerically friendly implementation of the smoothed best response computation associated with first-order methods for extensive-form game solving. We present, to our knowledge, the first GPU implementation of a first-order method for extensive-form games. We present comparisons of several excessive gap technique and CFR variants.