# Bandit learning in concave N-person games

arXiv: https://arxiv.org/abs/1810.01925 · HTML: https://mlsanity.com/paper/1810.01925/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2018.

## Built on by (most cited first, 30 of 35)

- [Who Leads and Who Follows in Strategic Classification?](https://mlsanity.com/paper/2106.12529/) (2021)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Scaling up Mean Field Games with Online Mirror Descent](https://mlsanity.com/paper/2103.00623/) (2021)
- [Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments](https://mlsanity.com/paper/2204.08281/) (2022)
- [Uncoupled and Convergent Learning in Two-Player Zero-Sum Markov Games with Bandit Feedback](https://mlsanity.com/paper/2303.02738/) (2023)
- [The Confluence of Networks, Games and Learning](https://mlsanity.com/paper/2105.08158/) (2021)
- [A unified stochastic approximation framework for learning in games](https://mlsanity.com/paper/2206.03922/) (2022)
- [Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimization](https://mlsanity.com/paper/2106.09082/) (2021)
- [Doubly Optimal No-Regret Online Learning in Strongly Monotone Games with Bandit Feedback](https://mlsanity.com/paper/2112.02856/) (2021)
- [Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problems](https://mlsanity.com/paper/2211.13668/) (2022)
- [Learning in Congestion Games with Bandit Feedback](https://mlsanity.com/paper/2206.01880/) (2022)
- [Stochastic Subgradient Descent Escapes Active Strict Saddles on Weakly Convex Functions](https://mlsanity.com/paper/2108.02072/) (2021)
- [Last-Iterate Convergence with Full and Noisy Feedback in Two-Player Zero-Sum Games](https://mlsanity.com/paper/2208.09855/) (2022)
- [Adaptively Perturbed Mirror Descent for Learning in Games](https://mlsanity.com/paper/2305.16610/) (2023)
- [Learning Stationary Nash Equilibrium Policies in n-Player Stochastic Games with Independent Chains](https://mlsanity.com/paper/2201.12224/) (2022)
- [Instance-dependent Sample Complexity Bounds for Zero-sum Matrix Games](https://mlsanity.com/paper/2303.10565/) (2023)
- [Stochastic Saddle Point Problems with Decision-Dependent Distributions](https://mlsanity.com/paper/2201.02313/) (2022)
- [Adaptive, Doubly Optimal No-Regret Learning in Strongly Monotone and Exp-Concave Games with Gradient Feedback](https://mlsanity.com/paper/2310.14085/) (2023)
- [Risk-Averse No-Regret Learning in Online Convex Games](https://mlsanity.com/paper/2203.08957/) (2022)
- [Multiplayer Federated Learning: Reaching Equilibrium with Less Communication](https://mlsanity.com/paper/2501.08263/) (2025)
- [The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback](https://mlsanity.com/paper/2604.16087/) (2026)
- [A Zeroth-Order Momentum Method for Risk-Averse Online Convex Games](https://mlsanity.com/paper/2209.02838/) (2022)
- [Exploiting hidden structures in non-convex games for convergence to Nash equilibrium](https://mlsanity.com/paper/2312.16609/) (2023)
- [Payoff-based learning with matrix multiplicative weights in quantum games](https://mlsanity.com/paper/2311.02423/) (2023)
- [Uncoupled Bandit Learning towards Rationalizability: Benchmarks, Barriers, and Algorithms](https://mlsanity.com/paper/2111.05486/) (2021)
- [No-regret learning for repeated non-cooperative games with lossy bandits](https://mlsanity.com/paper/2205.06968/) (2022)
- [Stochastic Direct Search Method for Blind Resource Allocation](https://mlsanity.com/paper/2210.05222/) (2022)
- [A Payoff-Based Policy Gradient Method in Stochastic Games with Long-Run Average Payoffs](https://mlsanity.com/paper/2405.09811/) (2024)
- [Decoupled SGDA for Games with Intermittent Strategy Communication](https://mlsanity.com/paper/2501.14652/) (2025)
- [Entry Barriers in Content Markets](https://mlsanity.com/paper/2509.01953/) (2025)

## Abstract (arXiv)

This paper examines the long-run behavior of learning with bandit feedback in non-cooperative concave games. The bandit framework accounts for extremely low-information environments where the agents may not even know they are playing a game; as such, the agents' most sensible choice in this setting would be to employ a no-regret learning algorithm. In general, this does not mean that the players' behavior stabilizes in the long run: no-regret learning may lead to cycles, even with perfect gradient information. However, if a standard monotonicity condition is satisfied, our analysis shows that no-regret learning based on mirror descent with bandit feedback converges to Nash equilibrium with probability 1. We also derive an upper bound for the convergence rate of the process that nearly matches the best attainable rate for single-agent bandit stochastic optimization.