Related papers: Precise Regret Bounds for Log-loss via a Truncated…

In the convex optimization approach to online regret minimization, many methods have been developed to guarantee a $O(\sqrt{T})$ bound on regret for subdifferentiable convex loss functions with bounded subgradients, by using a reduction to…

This paper initiates the study of data-dependent regret bounds in constrained MAB settings. These bounds depend on the sequence of losses that characterize the problem instance. Thus, they can be much smaller than classical…

Bayesian bandit algorithms with approximate Bayesian inference have been widely used in real-world applications. However, there is a large discrepancy between the superior practical performance of these approaches and their theoretical…

In online inverse linear optimization, a learner observes time-varying sets of feasible actions and an agent's optimal actions, selected by solving linear optimization over the feasible actions. The learner sequentially makes predictions of…

We consider the problem setting of prediction with expert advice with possibly heavy-tailed losses, i.e. the only assumption on the losses is an upper bound on their second moments, denoted by $\theta$. We develop adaptive algorithms that…

We consider prediction with expert advice under the log-loss with the goal of deriving efficient and robust algorithms. We argue that existing algorithms such as exponentiated gradient, online gradient descent and online Newton step do not…

Consider the sequential optimization of an expensive to evaluate and possibly non-convex objective function $f$ from noisy feedback, that can be considered as a continuum-armed bandit problem. Upper bounds on the regret performance of…

We study batch learning with log-loss in the individual setting, where the outcome sequence is deterministic. Because empirical statistics are not directly applicable in this regime, obtaining regret guarantees for batch learning has long…

We revisit the classical problem of universal prediction of stochastic sequences with a finite time horizon $T$ known to the learner. The question we investigate is whether it is possible to derive vanishing regret bounds that hold with…

The analysis of online least squares estimation is at the heart of many stochastic sequential decision making problems. We employ tools from the self-normalized processes to provide a simple and self-contained proof of a tail bound of a…

We provide an online learning algorithm that obtains regret $G\|w_\star\|\sqrt{T\log(\|w_\star\|G\sqrt{T})} + \|w_\star\|^2 + G^2$ on $G$-Lipschitz convex losses for any comparison point $w_\star$ without knowing either $G$ or…

We introduce a general framework of stochastic online convex optimization to obtain fast-rate stochastic regret bounds. We prove that algorithms such as online newton steps and a scale-free 10 version of Bernstein online aggregation achieve…

Bayesian bandit algorithms with approximate Bayesian inference have been widely used in real-world applications. Despite the superior practical performance, their theoretical justification is less investigated in the literature, especially…

This paper is in the field of stochastic Multi-Armed Bandits (MABs), i.e. those sequential selection techniques able to learn online using only the feedback given by the chosen option (a.k.a. $arm$). We study a particular case of the rested…

We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…

Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…

In this paper, we study gap-dependent regret guarantees for risk-sensitive reinforcement learning based on the entropic risk measure. We propose a novel definition of sub-optimality gaps, which we call cascaded gaps, and we discuss their…

A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to constraints, and then observes stochastic weights of these items and receives their sum as…

Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this…

This paper addresses the Bayesian optimization problem (also referred to as the Bayesian setting of the Gaussian process bandit), where the learner seeks to minimize the regret under a function drawn from a known Gaussian process (GP).…