Regularized Contextual Bandits

International audienceWe consider the stochastic contextual bandit problem with additional regularization. The motivation comes from problems where the policy of the agent must be close to some baseline policy known to perform well on the task. To tackle this problem we use a nonparametric model and propose an algorithm splitting the context space into bins, solving simultaneously-and independently-regularized multi-armed bandit instances on each bin. We derive slow and fast rates of convergence, depending on the unknown complexity of the problem. We also consider a new relevant margin condition to get problem-independent convergence rates, yielding intermediate rates interpolating between the aforementioned slow and fast rates

Fixed-Budget Best-Arm Identification in Contextual Bandits: A Static-Adaptive Algorithm

We study the problem of best-arm identification (BAI) in contextual bandits in the fixed-budget setting. We propose a general successive elimination algorithm that proceeds in stages and eliminates a fixed fraction of suboptimal arms in each stage. This design takes advantage of the strengths of static and adaptive allocations. We analyze the algorithm in linear models and obtain a better error bound than prior work. We also apply it to generalized linear models (GLMs) and bound its error. This is the first BAI algorithm for GLMs in the fixed-budget setting. Our extensive numerical experiments show that our algorithm outperforms the state of art.Comment: 23 page

A Frank-Wolfe Framework for Efficient and Effective Adversarial Attacks

Depending on how much information an adversary can access to, adversarial attacks can be classified as white-box attack and black-box attack. For white-box attack, optimization-based attack algorithms such as projected gradient descent (PGD) can achieve relatively high attack success rates within moderate iterates. However, they tend to generate adversarial examples near or upon the boundary of the perturbation set, resulting in large distortion. Furthermore, their corresponding black-box attack algorithms also suffer from high query complexities, thereby limiting their practical usefulness. In this paper, we focus on the problem of developing efficient and effective optimization-based adversarial attack algorithms. In particular, we propose a novel adversarial attack framework for both white-box and black-box settings based on a variant of Frank-Wolfe algorithm. We show in theory that the proposed attack algorithms are efficient with an $O(1/\sqrt{T})$ convergence rate. The empirical results of attacking the ImageNet and MNIST datasets also verify the efficiency and effectiveness of the proposed algorithms. More specifically, our proposed algorithms attain the best attack performances in both white-box and black-box attacks among all baselines, and are more time and query efficient than the state-of-the-art.Comment: 25 pages, 1 figure, 7 table

Linear Partial Monitoring for Sequential Decision-Making: Algorithms, Regret Bounds and Applications

Partial monitoring is an expressive framework for sequential decision-making with an abundance of applications, including graph-structured and dueling bandits, dynamic pricing and transductive feedback models. We survey and extend recent results on the linear formulation of partial monitoring that naturally generalizes the standard linear bandit setting. The main result is that a single algorithm, information-directed sampling (IDS), is (nearly) worst-case rate optimal in all finite-action games. We present a simple and unified analysis of stochastic partial monitoring, and further extend the model to the contextual and kernelized setting

Non-Asymptotic Pure Exploration by Solving Games

Pure exploration (aka active testing) is the fundamental task of sequentially gathering information to answer a query about a stochastic environment. Good algorithms make few mistake

Best Arm Identification in Stochastic Bandits: Beyond β−\beta-optimality

This paper investigates a hitherto unaddressed aspect of best arm identification (BAI) in stochastic multi-armed bandits in the fixed-confidence setting. Two key metrics for assessing bandit algorithms are computational efficiency and performance optimality (e.g., in sample complexity). In stochastic BAI literature, there have been advances in designing algorithms to achieve optimal performance, but they are generally computationally expensive to implement (e.g., optimization-based methods). There also exist approaches with high computational efficiency, but they have provable gaps to the optimal performance (e.g., the $\beta$-optimal approaches in top-two methods). This paper introduces a framework and an algorithm for BAI that achieves optimal performance with a computationally efficient set of decision rules. The central process that facilitates this is a routine for sequentially estimating the optimal allocations up to sufficient fidelity. Specifically, these estimates are accurate enough for identifying the best arm (hence, achieving optimality) but not overly accurate to an unnecessary extent that creates excessive computational complexity (hence, maintaining efficiency). Furthermore, the existing relevant literature focuses on the family of exponential distributions. This paper considers a more general setting of any arbitrary family of distributions parameterized by their mean values (under mild regularity conditions). The optimality is established analytically, and numerical evaluations are provided to assess the analytical guarantees and compare the performance with those of the existing ones