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We study the minimax sample complexity of $\varepsilon$-best arm identification in linear bandits. Given a compact action set $\mathcal{X}$ that spans $\mathbb{R}^d$ and an unknown reward vector $\theta\in\mathbb{R}^d$, the goal is to…
Multi-arm multi-stage trial designs can bring notable gains in efficiency to the drug development process. However, for normally distributed endpoints, the determination of a design typically depends on the assumption that the patient…
Mid-study design modifications are becoming increasingly accepted in confirmatory clinical trials, so long as appropriate methods are applied such that error rates are controlled. It is therefore unfortunate that the important case of…
This PhD thesis covers breakthroughs in several areas of adaptive experiment design: (i) (Chapter 2) Novel clinical trial designs and statistical methods in the era of precision medicine. (ii) (Chapter 3) Multi-armed bandit theory, with…
This paper studies active learning in the context of robust statistics. Specifically, we propose a variant of the Best Arm Identification problem for \emph{contaminated bandits}, where each arm pull has probability $\varepsilon$ of…
We propose a new integrated phase I/II trial design to identify the most efficacious dose combination that also satisfies certain safety requirements for drug-combination trials. We first take a Bayesian copula-type model for dose finding…
Indirect experiments provide a valuable framework for estimating treatment effects in situations where conducting randomized control trials (RCTs) is impractical or unethical. Unlike RCTs, indirect experiments estimate treatment effects by…
For indications where only unstable reference treatments are available and use of placebo is ethically justified, three-arm `gold standard' designs with an experimental, reference and placebo arm are recommended for non-inferiority trials.…
State of the art online learning procedures focus either on selecting the best alternative ("best arm identification") or on minimizing the cost (the "regret"). We merge these two objectives by providing the theoretical analysis of cost…
We consider the best arm identification problem in the stochastic multi-armed bandit framework where each arm has a tiny probability of realizing large rewards while with overwhelming probability the reward is zero. A key application of…
Robotic arms are highly common in various automation processes such as manufacturing lines. However, these highly capable robots are usually degraded to simple repetitive tasks such as pick-and-place. On the other hand, designing an optimal…
We consider the problem of near-optimal arm identification in the fixed confidence setting of the infinitely armed bandit problem when nothing is known about the arm reservoir distribution. We (1) introduce a PAC-like framework within which…
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…
The generalized P\`olya urn (GPU) models and their variants have been investigated in several disciplines. However, typical assumptions made with respect to the GPU do not include urn models with diagonal replacement matrix, which arise in…
In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are…
Adaptive Random Testing (ART) has faced criticism, particularly for its computational inefficiency, as highlighted by Arcuri and Briand. Their analysis clarified how ART requires a quadratic number of distance computations as the number of…
We consider the question introduced by \cite{Mason2020} of identifying all the $\varepsilon$-optimal arms in a finite stochastic multi-armed bandit with Gaussian rewards. We give two lower bounds on the sample complexity of any algorithm…
We study the problem of estimating the average treatment effect (ATE) in adaptive experiments where treatment can only be encouraged -- rather than directly assigned -- via a binary instrumental variable. Building on semiparametric…
This paper illustrates asymptotic properties for a response-adaptive design generated by a two-color, randomly reinforced urn model. The design considered is optimal in the sense that it assigns patients to the best treatment, with…
In the experimental design literature, Neyman allocation refers to the practice of allocating units into treated and control groups, potentially in unequal numbers proportional to their respective standard deviations, with the objective of…