Related papers: New insights into Elo algorithm for practitioners …
We present a theoretical analysis of the Elo rating system, a popular method for ranking skills of players in an online setting. In particular, we study Elo under the Bradley--Terry--Luce model and, using techniques from Markov chain…
Large language models (LLMs) have recently advanced in reasoning when optimized with reinforcement learning (RL) under verifiable rewards. Existing methods primarily rely on outcome-based supervision to strengthen internal LLM reasoning,…
Many environments assign several Elo ratings to the same agent: a chess player has classical, rapid, and blitz ratings; an online platform may rate by time control, mode, or format; an evaluator may rate performance across tasks or roles.…
Pairwise evaluation of Large Language Models (LLMs) is a common paradigm, but it is prone to preference bias, where judges systematically favor certain outputs, such as their own. This bias leads to inconsistent and skewed rankings across…
Separating signal from noise is central to experiments. Applying well-established statistical methods effectively to LLM evals requires consideration of their unique noise characteristics. We clearly define and measure three types of noise:…
The expectation--maximization (EM) algorithm combines global monotonicity, local linear convergence, and strong practical robustness, but these features are usually analyzed separately. Global descent is nonlinear, whereas local convergence…
GRPO is a standard approach to endowing pretrained LLMs with reasoning capabilities. It estimates the advantage of an outcome from a group of $K$ outcomes, and promotes those with positive advantages inside a trust region. Since GRPO…
Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of…
In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting…
Competition is a primary driver of player satisfaction and engagement in multiplayer online games. Traditional matchmaking systems aim at creating matches involving teams of similar aggregated individual skill levels, such as Elo score or…
A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly concave around its maximizing argument. Examples include…
Reinforcement learning (RL) has become a central component of post-training for large language models (LLMs), particularly for complex reasoning tasks that require stable optimization over long generation horizons. However, achieving…
Stochastic min-max optimization has gained interest in the machine learning community with the advancements in GANs and adversarial training. Although game optimization is fairly well understood in the deterministic setting, some issues…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
Unbiased recommender learning (URL) and off-policy evaluation/learning (OPE/L) techniques are effective in addressing the data bias caused by display position and logging policies, thereby consistently improving the performance of…
Mixtures-of-Experts (MoE) are conditional mixture models that have shown their performance in modeling heterogeneity in data in many statistical learning approaches for prediction, including regression and classification, as well as for…
This article is devoted to the forecast of the FIFA World Cup 2022 via nested zero-inflated generalized Poisson regression. Our regression model incorporates the Elo points of the participating teams, the location of the matches and the of…
Human feedback is widely used to train agents in many domains. However, previous works rarely consider the uncertainty when humans provide feedback, especially in cases that the optimal actions are not obvious to the trainers. For example,…
Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…