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

TL;DR

This paper introduces a new risk-averse online learning algorithm with momentum for unknown games, effectively estimating CVaR with bandit feedback and outperforming existing methods in numerical experiments.

Contribution

It proposes a novel risk-averse learning algorithm with momentum that leverages full historical data to improve CVaR estimation in bandit feedback settings.

Findings

Achieves sub-linear regret in risk-averse online games

Matches the performance of the best existing algorithms

Outperforms existing methods in numerical experiments

Abstract

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.