Related papers: Alpha-NML Universal Predictors

We derive a new variational formula for the R\'enyi family of divergences, $R_\alpha(Q\|P)$, between probability measures $Q$ and $P$. Our result generalizes the classical Donsker-Varadhan variational formula for the Kullback-Leibler…

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over $K$ episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in…

In this work, we aim to create a completely online algorithmic framework for prediction with expert advice that is translation-free and scale-free of the expert losses. Our goal is to create a generalized algorithm that is suitable for use…

Online optimization has emerged as powerful tool in large scale optimization. In this paper, we introduce efficient online algorithms based on the alternating directions method (ADM). We introduce a new proof technique for ADM in the batch…

We consider a variation on the problem of prediction with expert advice, where new forecasters that were unknown until then may appear at each round. As often in prediction with expert advice, designing an algorithm that achieves…

Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…

This paper studies statistical aggregation procedures in regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of…

We address online linear optimization problems when the possible actions of the decision maker are represented by binary vectors. The regret of the decision maker is the difference between her realized loss and the best loss she would have…

In this paper, we consider the problem of predicting observations generated online by an unknown, partially observed linear system, which is driven by stochastic noise. For such systems the optimal predictor in the mean square sense is the…

This paper explores generalised probabilistic modelling and uncertainty estimation in comparative LLM-as-a-judge frameworks. We show that existing Product-of-Experts methods are specific cases of a broader framework, enabling diverse…

The literature on game-theoretic equilibrium finding predominantly focuses on single games or their repeated play. Nevertheless, numerous real-world scenarios feature playing a game sampled from a distribution of similar, but not identical…

As a popular meta-learning approach, the model-agnostic meta-learning (MAML) algorithm has been widely used due to its simplicity and effectiveness. However, the convergence of the general multi-step MAML still remains unexplored. In this…

We provide consistent random algorithms for sequential decision under partial monitoring, i.e. when the decision maker does not observe the outcomes but receives instead random feedback signals. Those algorithms have no internal regret in…

We prove that a classic sub-Gaussian mixture proposed by Robbins in a stochastic setting actually satisfies a path-wise (deterministic) regret bound. For every path in a natural ``Ville event'' $\mathcal E_\alpha$, this regret till time $T$…

The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…

We consider the problem of length generalization in sequence prediction. We define a new metric of performance in this setting -- the Asymmetric-Regret -- which measures regret against a benchmark predictor with longer context length than…

We propose a new neural sequence model training method in which the objective function is defined by $\alpha$-divergence. We demonstrate that the objective function generalizes the maximum-likelihood (ML)-based and reinforcement learning…

We consider model selection for classic Reinforcement Learning (RL) environments -- Multi Armed Bandits (MABs) and Markov Decision Processes (MDPs) -- under general function approximations. In the model selection framework, we do not know…

In standard RL, a learner attempts to learn an optimal policy for a Markov Decision Process whose structure (e.g. state space) is known. In online model selection, a learner attempts to learn an optimal policy for an MDP knowing only that…

The standard model of online prediction deals with serial processing of inputs by a single processor. However, in large-scale online prediction problems, where inputs arrive at a high rate, an increasingly common necessity is to distribute…