Efficient and Robust Algorithms for Adversarial Linear Contextual Bandits

We consider an adversarial variant of the classic $K$-armed linear contextual bandit problem where the sequence of loss functions associated with each arm are allowed to change without restriction over time. Under the assumption that the $d$-dimensional contexts are generated i.i.d.~at random from a known distributions, we develop computationally efficient algorithms based on the classic Exp3 algorithm. Our first algorithm, RealLinExp3, is shown to achieve a regret guarantee of $\widetilde{O}(\sqrt{KdT})$ over $T$ rounds, which matches the best available bound for this problem. Our second algorithm, RobustLinExp3, is shown to be robust to misspecification, in that it achieves a regret bound of $\widetilde{O}((Kd)^{1/3}T^{2/3}) + \varepsilon \sqrt{d} T$ if the true reward function is linear up to an additive nonlinear error uniformly bounded in absolute value by $\varepsilon$. To our knowledge, our performance guarantees constitute the very first results on this problem setting

A Neural Networks Committee for the Contextual Bandit Problem

This paper presents a new contextual bandit algorithm, NeuralBandit, which does not need hypothesis on stationarity of contexts and rewards. Several neural networks are trained to modelize the value of rewards knowing the context. Two variants, based on multi-experts approach, are proposed to choose online the parameters of multi-layer perceptrons. The proposed algorithms are successfully tested on a large dataset with and without stationarity of rewards.Comment: 21st International Conference on Neural Information Processin

Online and Distribution-Free Robustness: Regression and Contextual Bandits with Huber Contamination

In this work we revisit two classic high-dimensional online learning problems, namely linear regression and contextual bandits, from the perspective of adversarial robustness. Existing works in algorithmic robust statistics make strong distributional assumptions that ensure that the input data is evenly spread out or comes from a nice generative model. Is it possible to achieve strong robustness guarantees even without distributional assumptions altogether, where the sequence of tasks we are asked to solve is adaptively and adversarially chosen? We answer this question in the affirmative for both linear regression and contextual bandits. In fact our algorithms succeed where conventional methods fail. In particular we show strong lower bounds against Huber regression and more generally any convex M-estimator. Our approach is based on a novel alternating minimization scheme that interleaves ordinary least-squares with a simple convex program that finds the optimal reweighting of the distribution under a spectral constraint. Our results obtain essentially optimal dependence on the contamination level $\eta$, reach the optimal breakdown point, and naturally apply to infinite dimensional settings where the feature vectors are represented implicitly via a kernel map.Comment: 66 pages, 1 figure, v3: refined exposition and improved rate

Bias-Robust Bayesian Optimization via Dueling Bandits

We consider Bayesian optimization in settings where observations can be adversarially biased, for example by an uncontrolled hidden confounder. Our first contribution is a reduction of the confounded setting to the dueling bandit model. Then we propose a novel approach for dueling bandits based on information-directed sampling (IDS). Thereby, we obtain the first efficient kernelized algorithm for dueling bandits that comes with cumulative regret guarantees. Our analysis further generalizes a previously proposed semi-parametric linear bandit model to non-linear reward functions, and uncovers interesting links to doubly-robust estimation