Learning to Identify Top Elo Ratings: A Dueling Bandits Approach

TL;DR

This paper introduces a dueling bandits-based online scheduling algorithm to efficiently estimate top Elo ratings, significantly reducing the number of matches needed and improving convergence speed in competitive gaming and AI evaluation.

Contribution

It develops a novel bandit framework tailored for Elo rating estimation, achieving constant per-step complexity and sublinear regret, with extensions to multidimensional ratings for intransitive games.

Findings

Reduces sample complexity for top Elo estimation.

Achieves faster convergence and better efficiency in experiments.

Extends to multidimensional Elo ratings for complex games.

Abstract

The Elo rating system is widely adopted to evaluate the skills of (chess) game and sports players. Recently it has been also integrated into machine learning algorithms in evaluating the performance of computerised AI agents. However, an accurate estimation of the Elo rating (for the top players) often requires many rounds of competitions, which can be expensive to carry out. In this paper, to improve the sample efficiency of the Elo evaluation (for top players), we propose an efficient online match scheduling algorithm. Specifically, we identify and match the top players through a dueling bandits framework and tailor the bandit algorithm to the gradient-based update of Elo. We show that it reduces the per-step memory and time complexity to constant, compared to the traditional likelihood maximization approaches requiring $O(t)$ time. Our algorithm has a regret guarantee of $\tilde{O}(\sqrt{T})$, sublinear in the number of competition rounds and has been extended to the multidimensional Elo ratings for handling intransitive games. We empirically demonstrate that our method achieves superior convergence speed and time efficiency on a variety of gaming tasks.