# Contextual Games: Multi-Agent Learning with Side Information

arXiv: https://arxiv.org/abs/2107.06327 · HTML: https://mlsanity.com/paper/2107.06327/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 13 Jul 2021.

## Builds on (most cited first, 9 of 9)

- [Fast Convergence of Regularized Learning in Games](https://mlsanity.com/paper/1507.00407/) (2015)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [Efficient and Robust Algorithms for Adversarial Linear Contextual Bandits](https://mlsanity.com/paper/2002.00287/) (2020)
- [On the optimality of the Hedge algorithm in the stochastic regime](https://mlsanity.com/paper/1809.01382/) (2018)
- [Contextual Bandits with Cross-learning](https://mlsanity.com/paper/1809.09582/) (2018)
- [Nash Convergence of Gradient Dynamics in Iterated General-Sum Games](https://mlsanity.com/paper/1301.3892/) (2013)
- [No-Regret Learning in Unknown Games with Correlated Payoffs](https://mlsanity.com/paper/1909.08540/) (2019)
- [Improved Regret Bounds for Oracle-Based Adversarial Contextual Bandits](https://mlsanity.com/paper/1606.00313/) (2016)
- [Bounding Inefficiency of Equilibria in Continuous Actions Games using Submodularity and Curvature](https://mlsanity.com/paper/1903.00950/) (2019)

## Built on by (most cited first, 11 of 11)

- [Open-Ended Learning Leads to Generally Capable Agents](https://mlsanity.com/paper/2107.12808/) (2021)
- [Efficient Model-based Multi-agent Reinforcement Learning via Optimistic Equilibrium Computation](https://mlsanity.com/paper/2203.07322/) (2022)
- [Online Learning in Periodic Zero-Sum Games](https://mlsanity.com/paper/2111.03377/) (2021)
- [Movement Penalized Bayesian Optimization with Application to Wind Energy Systems](https://mlsanity.com/paper/2210.08087/) (2022)
- [Regret Minimization in Stackelberg Games with Side Information](https://mlsanity.com/paper/2402.08576/) (2024)
- [Is Nash Equilibrium Approximator Learnable?](https://mlsanity.com/paper/2108.07472/) (2021)
- [Adversarial Causal Bayesian Optimization](https://mlsanity.com/paper/2307.16625/) (2023)
- [Are Equivariant Equilibrium Approximators Beneficial?](https://mlsanity.com/paper/2301.11481/) (2023)
- [Robust Correlated Equilibrium: Definition and Computation](https://mlsanity.com/paper/2311.17592/) (2023)
- [Reward Design for Justifiable Sequential Decision-Making](https://mlsanity.com/paper/2402.15826/) (2024)
- [Learn to Bid as a Price-Maker Wind Power Producer](https://mlsanity.com/paper/2503.16107/) (2025)

## Abstract (arXiv)

We formulate the novel class of contextual games, a type of repeated games driven by contextual information at each round. By means of kernel-based regularity assumptions, we model the correlation between different contexts and game outcomes and propose a novel online (meta) algorithm that exploits such correlations to minimize the contextual regret of individual players. We define game-theoretic notions of contextual Coarse Correlated Equilibria (c-CCE) and optimal contextual welfare for this new class of games and show that c-CCEs and optimal welfare can be approached whenever players' contextual regrets vanish. Finally, we empirically validate our results in a traffic routing experiment, where our algorithm leads to better performance and higher welfare compared to baselines that do not exploit the available contextual information or the correlations present in the game.