Simplified Kalman filter for online rating: one-fits-all approach

• URL: http://arxiv.org/abs/2104.14012v1
• Date: Wed, 28 Apr 2021 20:44:10 GMT
• Title: Simplified Kalman filter for online rating: one-fits-all approach
• Authors: Leszek Szczecinski and Rapha\"elle Tihon
• Abstract summary: 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.
• Score: 4.010371060637208
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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-know algorithms (such as the Elo, the Glicko, and the TrueSkill algorithms) may be seen as instances of the one-fits-all approach we propose. In order to clarify the conditions under which the gains of the Bayesian approach over the simpler solutions can actually materialize, we critically compare the known and the new algorithms by means of numerical examples using the synthetic as well as the empirical data.

Related papers

• FIVB ranking: Misstep in the right direction [1.4419517737536705]
  This work uses a statistical framework to present and evaluate the ranking algorithm that has been used by F'ed'eration Internationale de Volleyball (FIVB) since 2020. The salient feature of the FIVB ranking is the use of the probabilistic model, which explicitly calculates the probabilities of the games to come.
  arXiv  Detail & Related papers  (2024-08-02T23:46:55Z)
• Neural Population Learning beyond Symmetric Zero-sum Games [52.20454809055356]
  We introduce NeuPL-JPSRO, a neural population learning algorithm that benefits from transfer learning of skills and converges to a Coarse Correlated (CCE) of the game. Our work shows that equilibrium convergent population learning can be implemented at scale and in generality.
  arXiv  Detail & Related papers  (2024-01-10T12:56:24Z)
• Hardness of Independent Learning and Sparse Equilibrium Computation in Markov Games [70.19141208203227]
  We consider the problem of decentralized multi-agent reinforcement learning in Markov games. We show that no algorithm attains no-regret in general-sum games when executed independently by all players. We show that our lower bounds hold even for seemingly easier setting in which all agents are controlled by a centralized algorithm.
  arXiv  Detail & Related papers  (2023-03-22T03:28:12Z)
• Finding mixed-strategy equilibria of continuous-action games without gradients using randomized policy networks [83.28949556413717]
  We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. We model players' strategies using artificial neural networks. This paper is the first to solve general continuous-action games with unrestricted mixed strategies and without any gradient information.
  arXiv  Detail & Related papers  (2022-11-29T05:16:41Z)
• FIFA ranking: Evaluation and path forward [2.050873301895484]
  We analyze the parameters it currently uses, show the formal probabilistic model from which it can be derived, and optimize the latter. We postulate the algorithm to be rooted in the formal modelling principle, where the Davidson model proposed in 1970 seems to be an excellent candidate. The results indicate that the predictive capability of the algorithm is notably improved by using the home-field advantage and the explicit model for the draws in the game.
  arXiv  Detail & Related papers  (2021-12-20T21:08:12Z)
• Contextual Games: Multi-Agent Learning with Side Information [57.76996806603094]
  We formulate the novel class of contextual 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. We propose a novel online (meta) algorithm that exploits such correlations to minimize the contextual regret of individual players.
  arXiv  Detail & Related papers  (2021-07-13T18:37:37Z)
• G-Elo: Generalization of the Elo algorithm by modelling the discretized margin of victory [2.050873301895484]
  We develop a new algorithm for rating teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals) Our objective is to obtain the Elo-style algorithm whose operation is simple to implement and to understand intuitively.
  arXiv  Detail & Related papers  (2020-10-20T03:55:30Z)
• Faster Algorithms for Optimal Ex-Ante Coordinated Collusive Strategies in Extensive-Form Zero-Sum Games [123.76716667704625]
  We focus on the problem of finding an optimal strategy for a team of two players that faces an opponent in an imperfect-information zero-sum extensive-form game. In that setting, it is known that the best the team can do is sample a profile of potentially randomized strategies (one per player) from a joint (a.k.a. correlated) probability distribution at the beginning of the game. We provide an algorithm that computes such an optimal distribution by only using profiles where only one of the team members gets to randomize in each profile.
  arXiv  Detail & Related papers  (2020-09-21T17:51:57Z)
• Efficient Competitive Self-Play Policy Optimization [20.023522000925094]
  We propose a new algorithmic framework for competitive self-play reinforcement learning in two-player zero-sum games. Our method trains several agents simultaneously, and intelligently takes each other as opponent based on simple adversarial rules. We prove theoretically that our algorithm converges to an approximate equilibrium with high probability in convex-concave games.
  arXiv  Detail & Related papers  (2020-09-13T21:01:38Z)
• Learning to Play Sequential Games versus Unknown Opponents [93.8672371143881]
  We consider a repeated sequential game between a learner, who plays first, and an opponent who responds to the chosen action. We propose a novel algorithm for the learner when playing against an adversarial sequence of opponents. Our results include algorithm's regret guarantees that depend on the regularity of the opponent's response.
  arXiv  Detail & Related papers  (2020-07-10T09:33:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.