# A Zeroth-Order Momentum Method for Risk-Averse Online Convex Games

arXiv: https://arxiv.org/abs/2209.02838 · HTML: https://mlsanity.com/paper/2209.02838/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 6 Sep 2022.

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

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Adaptive Sampling for Stochastic Risk-Averse Learning](https://mlsanity.com/paper/1910.12511/) (2019)
- [Bandit learning in concave N-person games](https://mlsanity.com/paper/1810.01925/) (2018)
- [Statistical Learning with Conditional Value at Risk](https://mlsanity.com/paper/2002.05826/) (2020)
- [No-Regret Learning in Unknown Games with Correlated Payoffs](https://mlsanity.com/paper/1909.08540/) (2019)
- [Risk-Averse Stochastic Convex Bandit](https://mlsanity.com/paper/1810.00737/) (2018)
- [Boosting One-Point Derivative-Free Online Optimization via Residual Feedback](https://mlsanity.com/paper/2010.07378/) (2020)
- [Risk-Averse No-Regret Learning in Online Convex Games](https://mlsanity.com/paper/2203.08957/) (2022)
- [No-regret Learning in Cournot Games](https://mlsanity.com/paper/1906.06612/) (2019)

## Built on by (most cited first, 3 of 3)

- [Risk-averse Learning with Non-Stationary Distributions](https://mlsanity.com/paper/2404.02988/) (2024)
- [Risk-averse learning with delayed feedback](https://mlsanity.com/paper/2409.16866/) (2024)
- [Risk-Averse Learning with Varying Risk Levels](https://mlsanity.com/paper/2512.22986/) (2025)

## Abstract (arXiv)

We consider risk-averse learning in repeated unknown games where the goal of the agents is to minimize their individual risk of incurring significantly high cost. Specifically, the agents use the conditional value at risk (CVaR) as a risk measure and rely on bandit feedback in the form of the cost values of the selected actions at every episode to estimate their CVaR values and update their actions. A major challenge in using bandit feedback to estimate CVaR is that the agents can only access their own cost values, which, however, depend on the actions of all agents. To address this challenge, we propose a new risk-averse learning algorithm with momentum that utilizes the full historical information on the cost values. We show that this algorithm achieves sub-linear regret and matches the best known algorithms in the literature. We provide numerical experiments for a Cournot game that show that our method outperforms existing methods.