Related papers: UCB Exploration for Fixed-Budget Bayesian Best Arm…
The contextual combinatorial semi-bandit problem with linear payoff functions is a decision-making problem in which a learner chooses a set of arms with the feature vectors in each round under given constraints so as to maximize the sum of…
The best-arm identification (BAI) problem is one of the most fundamental problems in interactive machine learning, which has two flavors: the fixed-budget setting (FB) and the fixed-confidence setting (FC). For $K$-armed bandits with the…
We study the online resource allocation problem in which at each round, a budget $B$ must be allocated across $K$ arms under censored feedback. An arm yields a reward if and only if two conditions are satisfied: (i) the arm is activated…
The multi-armed bandit (MAB) problem is a foundational framework in sequential decision-making under uncertainty, extensively studied for its applications in areas such as clinical trials, online advertising, and resource allocation.…
We address the problem of finding the maximizer of a nonlinear smooth function, that can only be evaluated point-wise, subject to constraints on the number of permitted function evaluations. This problem is also known as fixed-budget best…
In this paper, we study the behavior of the Upper Confidence Bound-Variance (UCB-V) algorithm for the Multi-Armed Bandit (MAB) problems, a variant of the canonical Upper Confidence Bound (UCB) algorithm that incorporates variance estimates…
We investigate the fixed-budget best-arm identification (BAI) problem for linear bandits in a potentially non-stationary environment. Given a finite arm set $\mathcal{X}\subset\mathbb{R}^d$, a fixed budget $T$, and an unpredictable sequence…
We study the nonstationary stochastic Multi-Armed Bandit (MAB) problem in which the distribution of rewards associated with each arm are assumed to be time-varying and the total variation in the expected rewards is subject to a variation…
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 study the problem of best-arm identification (BAI) in the fixed-budget setting with heterogeneous reward variances. We propose two variance-adaptive BAI algorithms for this setting: SHVar for known reward variances and SHAdaVar for…
Kernelized bandits, also known as Bayesian optimization (BO), has been a prevalent method for optimizing complicated black-box reward functions. Various BO algorithms have been theoretically shown to enjoy upper bounds on their cumulative…
In fixed-confidence best arm identification (BAI), the objective is to quickly identify the optimal option while controlling the probability of error below a desired threshold. Despite the plethora of BAI algorithms, existing methods…
Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defenseless against even a single corruption of sufficient…
This paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multi-armed bandit problems. The algorithm, also known as Thompson Sampling,…
The challenge of identifying the best feasible arm within a fixed budget has attracted considerable interest in recent years. However, a notable gap remains in the literature: the exact exponential rate at which the error probability…
Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration…
Multi-armed bandit problems are considered as a paradigm of the trade-off between exploring the environment to find profitable actions and exploiting what is already known. In the stationary case, the distributions of the rewards do not…
This study investigates the experimental design problem for identifying the arm with the highest expected outcome, referred to as best arm identification (BAI). In our experiments, the number of treatment-allocation rounds is fixed. During…
This paper focuses on selecting the arm with the highest variance from a set of $K$ independent arms. Specifically, we focus on two settings: (i) misallocation minimization setting, that penalizes the number of pulls of suboptimal arms in…
We study a structured multi-agent multi-armed bandit (MAMAB) problem in a dynamic environment. A graph reflects the information-sharing structure among agents, and the arms' reward distributions are piecewise-stationary with several unknown…