For deterministic feedback, we additionally present a gap-independent algorithm that identifies a Condorcet winning team withinO(nklog(k)+k5)duels.

We consider the problem of regret minimization in non-parametric stochastic bandits. When the rewards are known to be bounded from above, there exists asymptotically optimal algorithms, with asymptotic regret depending on an infi-mum of Kullback-Leibler divergences (KL).

In a regression task, a predictor is given a set of instances, along with a real value for each point. Subsequently, she has to identify the value of a new instance as accurately as possible. In this work, we initiate the study of strategic predictions in machine learning. We consider a regression task tackled by two players, where the payoff of each player is the proportion of the points she predicts more accurately than the other player. We first revise the probably approximately correct learning framework to deal with the case of a duel between two predictors. We then devise an algorithm which finds a linear regression predictor that is a best response to any (not necessarily linear) regression algorithm. We show that it has linearithmic sample complexity, and polynomial time complexity when the dimension of the instances domain is fixed. We also test our approach in a high-dimensional setting, and show it significantly defeats classical regression algorithms in the prediction duel. Together, our work introduces a novel machine learning task that lends itself well to current competitive online settings, provides its theoretical foundations, and illustrates its applicability.

We consider the problem of regret minimization in non-parametric stochastic bandits. When the rewards are known to be bounded from above, there exists asymptotically optimal algorithms, with asymptotic regret depending on an infi-mum of Kullback-Leibler divergences (KL).

In this paper, we propose the first re-sampling based algorithm that is asymptotically optimal for several classes of possibly un-bounded parametric distributions.

Estimation of football players' skills is one of the key tasks in sports analytics. This paper introduces multiple extensions to a widely used model, expected possession value (EPV), to address some key challenges such as selection problem. First, we assign greater weights to events occurring immediately prior to the shot rather than those preceding them (decay effect). Second, our model incorporates possession risk more accurately by considering the decay effect and effective playing time. Third, we integrate the assessment of individual player ability to win aerial and ground duels. Using the extended EPV model, we predict this metric for various football players for the upcoming season, particularly taking into account the strength of their opponents.

With recent empirical observations, it has been argued that the most significant aspect of developing accurate language models may be the proper dataset content and training strategy compared to the number of neural parameters, training duration or dataset size. Following this argument, we opted to fine tune a one billion parameter size trained general purpose causal language model with a dataset curated on team statistics of the Italian football league first ten game weeks, using low rank adaptation. The limited training dataset was compiled based on a framework where a powerful commercial large language model provides distilled paragraphs and question answer pairs as intended. The training duration was kept relatively short to provide a basis for our minimal setting exploration. We share our key observations on the process related to developing a specific purpose language model which is intended to interpret soccer data with constrained resources in this article.

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.