Related papers: Lipschitz Bandits: Regret Lower Bounds and Optimal…
Upper Confidence Bound (UCB) algorithms are a widely-used class of sequential algorithms for the $K$-armed bandit problem. Despite extensive research over the past decades aimed at understanding their asymptotic and (near) minimax…
Many sequential decision-making problems in communication networks can be modeled as contextual bandit problems, which are natural extensions of the well-known multi-armed bandit problem. In contextual bandit problems, at each time, an…
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…
In this study, we propose a new method for constructing UCB-type algorithms for stochastic multi-armed bandits based on general convex optimization methods with an inexact oracle. We derive the regret bounds corresponding to the convergence…
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 the combinatorial multi-armed bandit (CMAB) problem, where the reward function is nonlinear. In this setting, the agent chooses a batch of arms on each round and receives feedback from each arm of the batch. The reward that the…
Lipschitz bandit is a variant of stochastic bandits that deals with a continuous arm set defined on a metric space, where the reward function is subject to a Lipschitz constraint. In this paper, we introduce a new problem of Lipschitz…
We consider the thresholding bandit problem, whose goal is to find arms of mean rewards above a given threshold $\theta$, with a fixed budget of $T$ trials. We introduce LSA, a new, simple and anytime algorithm that aims to minimize the…
I introduce and analyse an anytime version of the Optimally Confident UCB (OCUCB) algorithm designed for minimising the cumulative regret in finite-armed stochastic bandits with subgaussian noise. The new algorithm is simple, intuitive (in…
This paper presents a finite-time analysis of the KL-UCB algorithm, an online, horizon-free index policy for stochastic bandit problems. We prove two distinct results: first, for arbitrary bounded rewards, the KL-UCB algorithm satisfies a…
This paper investigates stochastic and adversarial combinatorial multi-armed bandit problems. In the stochastic setting under semi-bandit feedback, we derive a problem-specific regret lower bound, and discuss its scaling with the dimension…
We study regret minimization in a stochastic multi-armed bandit setting and establish a fundamental trade-off between the regret suffered under an algorithm, and its statistical robustness. Considering broad classes of underlying arms'…
Lipschitz bandits is a prominent version of multi-armed bandits that studies large, structured action spaces such as the $[0,1]$ interval, where similar actions are guaranteed to have similar rewards. A central theme here is the adaptive…
We consider the problem of online learning in misspecified linear stochastic multi-armed bandit problems. Regret guarantees for state-of-the-art linear bandit algorithms such as Optimism in the Face of Uncertainty Linear bandit (OFUL) hold…
We present the first high-probability optimal regret bound for a policy optimization technique applied to the problem of stochastic contextual multi-armed bandit (CMAB) with general offline function approximation. Our algorithm is both…
Recent studies have shown that reinforcement learning with KL-regularized objectives can enjoy faster rates of convergence or logarithmic regret, in contrast to the classical $\sqrt{T}$-type regret in the unregularized setting. However, the…
We study a regret minimization problem with the existence of multiple best/near-optimal arms in the multi-armed bandit setting. We consider the case when the number of arms/actions is comparable or much larger than the time horizon, and…
Symmetry arises in many optimization and decision-making problems, and has attracted considerable attention from the optimization community: By utilizing the existence of such symmetries, the process of searching for optimal solutions can…
Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the reward…
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…