Related papers: X-Armed Bandits
Motivated by economic applications such as recommender systems, we study the behavior of stochastic bandits algorithms under \emph{strategic behavior} conducted by rational actors, i.e., the arms. Each arm is a \emph{self-interested}…
We consider a stochastic multi-armed bandit (MAB) problem motivated by ``large'' action spaces, and endowed with a population of arms containing exactly $K$ arm-types, each characterized by a distinct mean reward. The decision maker is…
We consider a stochastic bandit problem with a possibly infinite number of arms. We write $p^*$ for the proportion of optimal arms and $\Delta$ for the minimal mean-gap between optimal and sub-optimal arms. We characterize the optimal…
We consider a stochastic multi-armed bandit setting and study the problem of constrained regret minimization over a given time horizon. Each arm is associated with an unknown, possibly multi-dimensional distribution, and the merit of an arm…
Motivated by dynamic parameter optimization in finite, but large action (configurations) spaces, this work studies the nonstochastic multi-armed bandit (MAB) problem in metric action spaces with oblivious Lipschitz adversaries. We propose…
We consider stochastic multi-armed bandits where the expected reward is a unimodal function over partially ordered arms. This important class of problems has been recently investigated in (Cope 2009, Yu 2011). The set of arms is either…
We consider stochastic bandit problems with a continuous set of arms and where the expected reward is a continuous and unimodal function of the arm. No further assumption is made regarding the smoothness and the structure of the expected…
We consider a stochastic bandit problem with countably many arms that belong to a finite set of types, each characterized by a unique mean reward. In addition, there is a fixed distribution over types which sets the proportion of each type…
We study stochastic linear optimization problem with bandit feedback. The set of arms take values in an $N$-dimensional space and belong to a bounded polyhedron described by finitely many linear inequalities. We provide a lower bound for…
We consider a stochastic bandit problem with infinitely many arms. In this setting, the learner has no chance of trying all the arms even once and has to dedicate its limited number of samples only to a certain number of arms. All previous…
Canonical algorithms for multi-armed bandits typically assume a stationary reward environment where the size of the action space (number of arms) is small. More recently developed methods typically relax only one of these assumptions:…
We consider stochastic multi-armed bandit problems where the expected reward is a Lipschitz function of the arm, and where the set of arms is either discrete or continuous. For discrete Lipschitz bandits, we derive asymptotic problem…
In this work, we extend the concept of the $p$-mean welfare objective from social choice theory (Moulin 2004) to study $p$-mean regret in stochastic multi-armed bandit problems. The $p$-mean regret, defined as the difference between the…
In this paper, we consider the multi-armed bandit problem with high-dimensional features. First, we prove a minimax lower bound, $\mathcal{O}\big((\log d)^{\frac{\alpha+1}{2}}T^{\frac{1-\alpha}{2}}+\log T\big)$, for the cumulative regret,…
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…
The Lipschitz multi-armed bandit (MAB) problem generalizes the classical multi-armed bandit problem by assuming one is given side information consisting of a priori upper bounds on the difference in expected payoff between certain pairs of…
We consider the setting of stochastic bandit problems with a continuum of arms. We first point out that the strategies considered so far in the literature only provided theoretical guarantees of the form: given some tuning parameters, the…
We consider bandit optimization of a smooth reward function, where the goal is cumulative regret minimization. This problem has been studied for $\alpha$-H\"older continuous (including Lipschitz) functions with $0<\alpha\leq 1$. Our main…
One of the key drivers of complexity in the classical (stochastic) multi-armed bandit (MAB) problem is the difference between mean rewards in the top two arms, also known as the instance gap. The celebrated Upper Confidence Bound (UCB)…
This paper investigates stochastic multi-armed bandit algorithms that are robust to adversarial attacks, where an attacker can first observe the learner's action and {then} alter their reward observation. We study two cases of this model,…