A PAC algorithm in relative precision for bandit problem with costly sampling

This paper considers the problem of maximizing an expectation function over a finite set, or finite-arm bandit problem. We first propose a naive stochastic bandit algorithm for obtaining a probably approximately correct (PAC) solution to this discrete optimization problem in relative precision, that is a solution which solves the optimization problem up to a relative error smaller than a prescribed tolerance, with high probability. We also propose an adaptive stochastic bandit algorithm which provides a PAC-solution with the same guarantees. The adaptive algorithm outperforms the mean complexity of the naive algorithm in terms of number of generated samples and is particularly well suited for applications with high sampling cost

Adaptive Identification of Populations with Treatment Benefit in Clinical Trials: Machine Learning Challenges and Solutions

We study the problem of adaptively identifying patient subpopulations that benefit from a given treatment during a confirmatory clinical trial. This type of adaptive clinical trial has been thoroughly studied in biostatistics, but has been allowed only limited adaptivity so far. Here, we aim to relax classical restrictions on such designs and investigate how to incorporate ideas from the recent machine learning literature on adaptive and online experimentation to make trials more flexible and efficient. We find that the unique characteristics of the subpopulation selection problem -- most importantly that (i) one is usually interested in finding subpopulations with any treatment benefit (and not necessarily the single subgroup with largest effect) given a limited budget and that (ii) effectiveness only has to be demonstrated across the subpopulation on average -- give rise to interesting challenges and new desiderata when designing algorithmic solutions. Building on these findings, we propose AdaGGI and AdaGCPI, two meta-algorithms for subpopulation construction. We empirically investigate their performance across a range of simulation scenarios and derive insights into their (dis)advantages across different settings.Comment: To appear in the Proceedings of the 40th International Conference on Machine Learning, Honolulu, Hawaii, USA. PMLR 202, 202

Online Sign Identification: Minimization of the Number of Errors in Thresholding Bandits

International audienceIn the fixed budget thresholding bandit problem, an algorithm sequentially allocates a budgeted number of samples to different distributions. It then predicts whether the mean of each distribution is larger or lower than a given threshold. We introduce a large family of algorithms (containing most existing relevant ones), inspired by the Frank-Wolfe algorithm, and provide a thorough yet generic analysis of their performance. This allowed us to construct new explicit algorithms, for a broad class of problems, whose losses are within a small constant factor of the non-adaptive oracle ones. Quite interestingly, we observed that adaptive methods empirically greatly out-perform non-adaptive oracles, an uncommon behavior in standard online learning settings, such as regret minimization. We explain this surprising phenomenon on an insightful toy problem

Essays In Algorithmic Market Design Under Social Constraints

Rapid technological advances over the past few decades---in particular, the rise of the internet---has significantly reshaped and expanded the meaning of our everyday social activities, including our interactions with our social circle, the media, and our political and economic activities This dissertation aims to tackle some of the unique societal challenges underlying the design of automated online platforms that interact with people and organizations---namely, those imposed by legal, ethical, and strategic considerations. I narrow down attention to fairness considerations, learning with repeated trials, and competition for market share. In each case, I investigate the broad issue in a particular context (i.e. online market), and present the solution my research offers to the problem in that application. Addressing interdisciplinary problems, such as the ones in this dissertation, requires drawing ideas and techniques from various disciplines, including theoretical computer science, microeconomics, and applied statistics. The research presented here utilizes a combination of theoretical and data analysis tools to shed light on some of the key challenges in designing algorithms for today\u27s online markets, including crowdsourcing and labor markets, online advertising, and social networks among others