# Faster Game Solving via Hyperparameter Schedules

arXiv: https://arxiv.org/abs/2404.09097 · HTML: https://mlsanity.com/paper/2404.09097/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2024.

## 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)
- [Parallelizing Counterfactual Regret Minimization](https://mlsanity.com/paper/2605.14277/) (2026)
- [On the Power of Perturbation under Sampling in Solving Extensive-Form Games](https://mlsanity.com/paper/2501.16600/) (2025)
- [Faster Game Solving via Asymmetry of Step Sizes](https://mlsanity.com/paper/2503.12770/) (2025)
- [Approximating Nash Equilibria in General-Sum Games via Meta-Learning](https://mlsanity.com/paper/2504.18868/) (2025)

## Abstract (arXiv)

Counterfactual regret minimization (CFR) algorithms are a foundational class of methods for solving imperfect-information games, with the time average of their iterates converging to a Nash equilibrium in two-player zero-sum games. Prior state-of-the-art variants, Discounted CFR (DCFR) and Predictive CFR^+ (PCFR^+), achieved the fastest known practical performance by improving convergence rates over vanilla CFR through discounting early iterations with a fixed discounting scheme. More recently, Dynamic DCFR (DDCFR) introduced agent-learned dynamic discounting schemes to further accelerate convergence, at the cost of increased complexity. To address this, we propose Hyperparameter Schedules (HSs), a remarkably simple, training-free framework that dynamically adjusts CFR discounting over time. HSs aggressively downweight early updates and gradually transition to trusting late-stage strategies, leading to substantially faster convergence with only a few lines of code modifications. We show that HSs derived from just three small extensive-form games generalize effectively to 17 diverse games (including large-scale realistic poker) in both extensive-form and normal-form settings, without any game-specific tuning. Our method establishes a new state of the art for solving two-player zero-sum games.