Learning to Identify Top Elo Ratings: A Dueling Bandits Approach
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；University of Oxford（牛津大学）；University College London（伦敦大学学院）；Beijing Key Laboratory of Big Data Management and Analysis Methods, GSAI, Renmin University of China（中国人民大学高瓴人工智能学院大数据管理与分析方法北京市重点实验室）
Xue Yan, Yali Du, Binxin Ru, Jun Wang, Haifeng Zhang, Xu Chen
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.
DeepMind（深度思维）；University College London（伦敦大学学院）；Google（谷歌）；Carnegie Mellon University（卡内基梅隆大学）
Rating strategies in a game is an important area of research in game theory and artificial intelligence, and can be applied to any real-world competitive or cooperative setting. Traditionally, only transitive dependencies between strategies have been used to rate strategies (e.g. Elo), however recent work has expanded ratings to utilize game theoretic solutions to better rate strategies in non-transitive games. This work generalizes these ideas and proposes novel algorithms suitable for N-player, general-sum rating of strategies in normal-form games according to the payoff rating system. This …
This article discusses in detail the rating system that won the kaggle competition "Chess Ratings: Elo vs the rest of the world". The competition provided a historical dataset of outcomes for chess games, and aimed to discover whether novel approaches can predict the outcomes of future games, more accurately than the well-known Elo rating system. The winning rating system, called Elo++ in the rest of the article, builds upon the Elo rating system. Like Elo, Elo++ uses a single rating per player and predicts the outcome of a game, by using a logistic curve over the difference in ratings of the …
Stochastic analysis of the Elo rating algorithm in round-robin tournaments
Federal University of Santa Catarina（圣卡塔琳娜联邦大学）；INRS–Institut National de la Recherche Scientific（国家科学研究院（INRS））；Federal University of Technology - Paraná（巴拉那联邦理工大学）
Rating systems play an important role in competitive sports and games. They provide a measure of player skill, which incentivizes competitive performances and enables balanced match-ups. In this paper, we present a novel Bayesian rating system for contests with many participants. It is widely applicable to competition formats with discrete ranked matches, such as online programming competitions, obstacle courses races, and some video games. The simplicity of our system allows us to prove theoretical bounds on robustness and runtime. In addition, we show that the system aligns incentives: that …
Institut National de la Recherche Scientifique（加拿大国家科学研究院）
In this work we develop a new algorithm for rating of teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals), also known as a margin of victory (MOV). Our objective is to obtain the Elo-style algorithm whose operation is simple to implement and to understand intuitively. This is done in three steps: first, we define the probabilistic model between the teams' skills and the discretized MOV variable: this generalizes the model underpinning the Elo algorithm, where the MOV variable is discretized into three categories (win/loss/draw). Secon…
No-press Diplomacy is a complex strategy game involving both cooperation and competition that has served as a benchmark for multi-agent AI research. While self-play reinforcement learning has resulted in numerous successes in purely adversarial games like chess, Go, and poker, self-play alone is insufficient for achieving optimal performance in domains involving cooperation with humans. We address this shortcoming by first introducing a planning algorithm we call DiL-piKL that regularizes a reward-maximizing policy toward a human imitation-learned policy. We prove that this is a no-regret lear…
Institute for Theoretical Physics（理论物理研究所）；Goethe University Frankfurt（法兰克福歌德大学）
The recent observation of neural power-law scaling relations has made a significant impact in the field of deep learning. A substantial amount of attention has been dedicated as a consequence to the description of scaling laws, although mostly for supervised learning and only to a reduced extent for reinforcement learning frameworks. In this paper we present an extensive study of performance scaling for a cornerstone reinforcement learning algorithm, AlphaZero. On the basis of a relationship between Elo rating, playing strength and power-law scaling, we train AlphaZero agents on the games Conn…
Tsinghua University（清华大学）；UC Santa Barbara（加州大学圣巴巴拉分校）
This paper introduces two metrics (cycle-based and memory-based metrics), grounded on a dynamical game-theoretic solution concept called sink equilibrium, for the evaluation, ranking, and computation of policies in multi-agent learning. We adopt strict best response dynamics (SBRD) to model selfish behaviors at a meta-level for multi-agent reinforcement learning. Our approach can deal with dynamical cyclical behaviors (unlike approaches based on Nash equilibria and Elo ratings), and is more compatible with single-agent reinforcement learning than alpha-rank which relies on weakly better respon…
Institut National de la Recherche Scientifique（国家科学研究院）；University of Montreal（蒙特利尔大学）
In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new game by exploiting the probabilistic models of the relationship between the skills and the game outcome. We propose a Bayesian approach which may be seen as an approximate Kalman filter and which is generic in the sense that it can be used with any skills-outcome model and can be applied in the individual -- as well as in the group-sports. We show how the well…
