# Near-Optimal No-Regret Learning Dynamics for General Convex Games

arXiv: https://arxiv.org/abs/2206.08742 · HTML: https://mlsanity.com/paper/2206.08742/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 66 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 21 of 21)

- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Optimization, Learning, and Games with Predictable Sequences](https://mlsanity.com/paper/1311.1869/) (2013)
- [Fast Convergence of Regularized Learning in Games](https://mlsanity.com/paper/1507.00407/) (2015)
- [More Adaptive Algorithms for Adversarial Bandits](https://mlsanity.com/paper/1801.03265/) (2018)
- [Near-Optimal No-Regret Learning in General Games](https://mlsanity.com/paper/2108.06924/) (2021)
- [Learning in games with continuous action sets and unknown payoff functions](https://mlsanity.com/paper/1608.07310/) (2016)
- [Hedging in games: Faster convergence of external and swap regrets](https://mlsanity.com/paper/2006.04953/) (2020)
- [Bias no more: high-probability data-dependent regret bounds for adversarial bandits and MDPs](https://mlsanity.com/paper/2006.08040/) (2020)
- [Adaptive Learning in Continuous Games: Optimal Regret Bounds and Convergence to Nash Equilibrium](https://mlsanity.com/paper/2104.12761/) (2021)
- [Near-Optimal No-Regret Learning for Correlated Equilibria in Multi-Player General-Sum Games](https://mlsanity.com/paper/2111.06008/) (2021)
- [Uncoupled Learning Dynamics with O(log T) Swap Regret in Multiplayer Games](https://mlsanity.com/paper/2204.11417/) (2022)
- [Improved Path-length Regret Bounds for Bandits](https://mlsanity.com/paper/1901.10604/) (2019)
- [Correlation in Extensive-Form Games: Saddle-Point Formulation and Benchmarks](https://mlsanity.com/paper/1905.12564/) (2019)
- [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)
- [Fast Rates for Nonparametric Online Learning: From Realizability to Learning in Games](https://mlsanity.com/paper/2111.08911/) (2021)
- [Let's be Honest: An Optimal No-Regret Framework for Zero-Sum Games](https://mlsanity.com/paper/1802.04221/) (2018)
- [Composite Self-Concordant Minimization](https://mlsanity.com/paper/1308.2867/) (2013)
- [A Newton Frank-Wolfe Method for Constrained Self-Concordant Minimization](https://mlsanity.com/paper/2002.07003/) (2020)
- [Adaptive Bandit Convex Optimization with Heterogeneous Curvature](https://mlsanity.com/paper/2202.06150/) (2022)

## Built on by (most cited first, 25 of 25)

- [Fast swap regret minimization and applications to approximate correlated equilibria](https://mlsanity.com/paper/2310.19647/) (2023)
- [Regret Matching+: (In)Stability and Fast Convergence in Games](https://mlsanity.com/paper/2305.14709/) (2023)
- [Multi-Player Zero-Sum Markov Games with Networked Separable Interactions](https://mlsanity.com/paper/2307.09470/) (2023)
- [Instance-Dependent Regret Bounds for Learning Two-Player Zero-Sum Games with Bandit Feedback](https://mlsanity.com/paper/2502.17625/) (2025)
- [Faster Rates for No-Regret Learning in General Games via Cautious Optimism](https://mlsanity.com/paper/2503.24340/) (2025)
- [Maximizing utility in multi-agent environments by anticipating the behavior of other learners](https://mlsanity.com/paper/2407.04889/) (2024)
- [Swap Regret and Correlated Equilibria Beyond Normal-Form Games](https://mlsanity.com/paper/2502.20229/) (2025)
- [Corrupted Learning Dynamics in Games](https://mlsanity.com/paper/2412.07120/) (2024)
- [No-regret learning in harmonic games: Extrapolation in the face of conflicting interests](https://mlsanity.com/paper/2412.20203/) (2024)
- [Adversarial Learning in Games with Bandit Feedback: Logarithmic Pure-Strategy Maximin Regret](https://mlsanity.com/paper/2602.06348/) (2026)
- [Near-Optimal Phi-Regret Learning in Extensive-Form Games](https://mlsanity.com/paper/2208.09747/) (2022)
- [Proximal Regret and Proximal Correlated Equilibria: A New Tractable Solution Concept for Online Learning and Games](https://mlsanity.com/paper/2511.01852/) (2025)
- [Constant Individual Regret in General Games](https://mlsanity.com/paper/2608.31166/) (2026)
- [Towards Characterizing the First-order Query Complexity of Learning (Approximate) Nash Equilibria in Zero-sum Matrix Games](https://mlsanity.com/paper/2304.12768/) (2023)
- [On the Optimality of Dilated Entropy and Lower Bounds for Online Learning in Extensive-Form Games](https://mlsanity.com/paper/2410.23398/) (2024)
- [Computational Intractability of Strategizing against Online Learners](https://mlsanity.com/paper/2503.04202/) (2025)
- [Comparator-Adaptive Phi-Regret: Improved Bounds, Simpler Algorithms, and Applications to Games](https://mlsanity.com/paper/2505.17277/) (2025)
- [Optimism Without Regularization: Constant Regret in Zero-Sum Games](https://mlsanity.com/paper/2506.16736/) (2025)
- [Optimal Alternating Regret for Online Learning and Games](https://mlsanity.com/paper/2608.24731/) (2026)
- [Constant regret in general games via higher-order optimism](https://mlsanity.com/paper/2609.04113/) (2026)
- [Optimistic Online Learning in Symmetric Cone Games](https://mlsanity.com/paper/2504.03592/) (2025)
- [Computing Pure-Strategy Nash Equilibria in a Two-Party Policy Competition: Existence and Algorithmic Approaches](https://mlsanity.com/paper/2512.22552/) (2025)
- [Minimax Alternating Regret for the Experts Problem and Online Convex Optimization](https://mlsanity.com/paper/2608.25182/) (2026)
- [Constant Swap Regret in General-Sum Games via Two-Scale Higher-Order Optimism](https://mlsanity.com/paper/2609.16751/) (2026)
- [A Horizon-Independent Regret Bound for Optimistic Hedge in General-Sum Games](https://mlsanity.com/paper/2609.22839/) (2026)

## Abstract (arXiv)

A recent line of work has established uncoupled learning dynamics such that, when employed by all players in a game, each player's regret after T repetitions grows polylogarithmically in T, an exponential improvement over the traditional guarantees within the no-regret framework. However, so far these results have only been limited to certain classes of games with structured strategy spaces -- such as normal-form and extensive-form games. The question as to whether O(polylog T) regret bounds can be obtained for general convex and compact strategy sets -- which occur in many fundamental models in economics and multiagent systems -- while retaining efficient strategy updates is an important question. In this paper, we answer this in the positive by establishing the first uncoupled learning algorithm with O(log T) per-player regret in general convex games, that is, games with concave utility functions supported on arbitrary convex and compact strategy sets. Our learning dynamics are based on an instantiation of optimistic follow-the-regularized-leader over an appropriately lifted space using a self-concordant regularizer that is, peculiarly, not a barrier for the feasible region. Further, our learning dynamics are efficiently implementable given access to a proximal oracle for the convex strategy set, leading to O(loglog T) per-iteration complexity; we also give extensions when access to only a linear optimization oracle is assumed. Finally, we adapt our dynamics to guarantee O(√T) regret in the adversarial regime. Even in those special cases where prior results apply, our algorithm improves over the state-of-the-art regret bounds either in terms of the dependence on the number of iterations or on the dimension of the strategy sets.