We develop a meta-learning framework for simple regret minimization in bandits. In this framework, a learning agent interacts with a sequence of bandit tasks, which are sampled i.i.d. from an unknown prior distribution, and learns its meta-parameters to perform better on future tasks. We propose the first Bayesian and frequentist meta-learning algorithms for this setting. The Bayesian algorithm has access to a prior distribution over the meta-parameters and its meta simple regret over m bandit tasks with horizon n is mere O(m / √n). On the other hand, the meta simple regret of the frequentist algorithm is O(n√m + m/ √n). While its regret is worse, the frequentist algorithm is more general because it does not need a prior distribution over the meta-parameters. It can also be analyzed in more settings. We instantiate our algorithms for several classes of bandit problems. Our algorithms are general and we complement our theory by evaluating them empirically in several environments.

Best-arm identification (BAI) in a fixed-budget setting is a bandit problem where the learning agent maximizes the probability of identifying the optimal (best) arm after a fixed number of observations. Most works on this topic study unstructured problems with a small number of arms, which limits their applicability. We propose a general tractable algorithm that incorporates the structure, by successively eliminating suboptimal arms based on their mean reward estimates from a joint generalization model. We analyze our algorithm in linear and generalized linear models (GLMs), and propose a practical implementation based on a G-optimal design. In linear models, our algorithm has competitive error guarantees to prior works and performs at least as well empirically. In GLMs, this is the first practical algorithm with analysis for fixed-budget BAI.

In recent years, automated data-driven decision-making systems have enjoyed a tremendous success in a variety of fields (e.g., to make product recommendations, or to guide the production of entertainment). More recently, these algorithms are increasingly being used to assist socially sensitive decisionmaking (e.g., to decide who to admit into a degree program or to prioritize individuals for public housing). Yet, these automated tools may result in discriminative decision-making in the sense that they may treat individuals unfairly or unequally based on membership to a category or a minority, resulting in disparate treatment or disparate impact and violating both moral and ethical standards. This may happen when the training dataset is itself biased (e.g., if individuals belonging to a particular group have historically been discriminated upon). However, it may also happen when the training dataset is unbiased, if the errors made by the system affect individuals belonging to a category or minority differently (e.g., if misclassification rates for Blacks are higher than for Whites). In this paper, we unify the definitions of unfairness across classification and regression. We propose a versatile mixed-integer optimization framework for learning optimal and fair decision trees and variants thereof to prevent disparate treatment and/or disparate impact as appropriate. This translates to a flexible schema for designing fair and interpretable policies suitable for socially sensitive decision-making. We conduct extensive computational studies that show that our framework improves the state-of-the-art in the field (which typically relies on heuristics) to yield non-discriminative decisions at lower cost to overall accuracy.