Related papers: How to sample and when to stop sampling: The gener…

Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…

This paper introduces the framework of multi-armed sampling, which serves as the sampling counterpart to the optimization problem of multi-armed bandits. Our primary motivation is to rigorously examine the exploration-exploitation trade-off…

The question of selecting the "best" amongst different choices is a common problem in statistics. In drug development, our motivating setting, the question becomes, for example: what is the dose that gives me a pre-specified risk of…

This paper studies the off-policy evaluation problem, where one aims to estimate the value of a target policy based on a sample of observations collected by another policy. We first consider the multi-armed bandit case, establish a minimax…

We consider a sequential decision-making problem where an agent can take one action at a time and each action has a stochastic temporal extent, i.e., a new action cannot be taken until the previous one is finished. Upon completion, the…

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an…

Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum…

Sequential Bayesian experimental design typically assumes that the number of experiments is fixed before data collection begins. In practical campaigns, however, experimentation may need to terminate early because additional measurements…

We consider the best-choice problem for independent (not necessarily iid) observations $X_1, \cdots, X_n$ with the aim of selecting the sample minimum. We show that in this full generality the monotone case of optimal stopping holds and the…

We consider a multi-hypothesis testing problem involving a K-armed bandit. Each arm's signal follows a distribution from a vector exponential family. The actual parameters of the arms are unknown to the decision maker. The decision maker…

We propose a novel technique for analyzing adaptive sampling called the {\em Simulator}. Our approach differs from the existing methods by considering not how much information could be gathered by any fixed sampling strategy, but how…

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…

In this paper, we study the problem of estimating uniformly well the mean values of several distributions given a finite budget of samples. If the variance of the distributions were known, one could design an optimal sampling strategy by…

We aim to efficiently allocate a fixed simulation budget to identify the top-mc designs for each context among a finite number of contexts. The performance of each design under a context is measured by an identifiable statistical…

We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…

In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…

This study considers the treatment choice problem when outcome variables are binary. We focus on statistical treatment rules that plug in fitted values based on nonparametric kernel regression and show that optimizing two parameters enables…

We study the problem of off-policy evaluation in the multi-armed bandit model with bounded rewards, and develop minimax rate-optimal procedures under three settings. First, when the behavior policy is known, we show that the Switch…

In treatment allocation problems the individuals to be treated often arrive sequentially. We study a problem in which the policy maker is not only interested in the expected cumulative welfare but is also concerned about the…

The principle of allocating an equal number of patients to each arm in a randomized controlled trial remains widely believed to be optimal for maximising statistical power. However, this long-held belief only holds true if the treatment…