Related papers: Multi-Armed Sequential Hypothesis Testing by Betti…
We study the combinatorial pure exploration problem Best-Set in stochastic multi-armed bandits. In a Best-Set instance, we are given $n$ arms with unknown reward distributions, as well as a family $\mathcal{F}$ of feasible subsets over the…
The assumption of free will - the ability of an experimentalist to make random choices - is central to proving the indeterminism of quantum resources, the primary tool in quantum cryptography. Relaxing the assumption in a Bell test allows…
We study a sequential resource allocation problem between a fixed number of arms. On each iteration the algorithm distributes a resource among the arms in order to maximize the expected success rate. Allocating more of the resource to a…
We consider a general infinite horizon Heterogeneous Restless multi-armed Bandit (RMAB). Heterogeneity is a fundamental problem for many real-world systems largely because it resists many concentration arguments. In this paper, we assume…
We consider a novel multi-armed bandit framework where the rewards obtained by pulling the arms are functions of a common latent random variable. The correlation between arms due to the common random source can be used to design a…
We propose the first fully-adaptive algorithm for pure exploration in linear bandits---the task to find the arm with the largest expected reward, which depends on an unknown parameter linearly. While existing methods partially or entirely…
We address the problem of identifying the optimal policy with a fixed confidence level in a multi-armed bandit setup, when \emph{the arms are subject to linear constraints}. Unlike the standard best-arm identification problem which is well…
Restless multi-armed bandits are often used to model budget-constrained resource allocation tasks where receipt of the resource is associated with an increased probability of a favorable state transition. Prior work assumes that individual…
We study exploration in stochastic multi-armed bandits when we have access to a divisible resource that can be allocated in varying amounts to arm pulls. We focus in particular on the allocation of distributed computing resources, where we…
Combinatorial bandits with semi-bandit feedback generalize multi-armed bandits, where the agent chooses sets of arms and observes a noisy reward for each arm contained in the chosen set. The action set satisfies a given structure such as…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
This study investigates minimax and Bayes optimal strategies for fixed-budget best-arm identification. We consider an adaptive procedure consisting of a sampling phase followed by a recommendation phase, and we design an adaptive experiment…
Experimentation involves risk. The investigator expends time and money in the pursuit of data that supports a hypothesis. In the end, the investigator may find that all of these costs were for naught and the data fail to reject the null.…
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…
Scientific experimentation is largely driven by statistical hypothesis testing to determine significant differences in interventions. Traditionally, experimenters allocate samples uniformly between each intervention. However, such an…
This paper revisits the classical problem of determining the bias of a weighted coin, where the bias is known to be either $p = 1/2 + \varepsilon$ or $p = 1/2 - \varepsilon$, while minimizing the expected number of coin tosses and the error…
We present a robust framework with computational algorithms to support decision makers in sequential games. Our framework includes methods to solve games with complete information, assess the robustness of such solutions and, finally,…
The Win Ratio has gained significant traction in cardiovascular trials as a novel method for analyzing composite endpoints (Pocock and others, 2012). Compared with conventional approaches based on time to the first event, the Win Ratio…
We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The…