Experimental Design for Regret Minimization in Linear Bandits

Abstract

In this paper we propose a novel experimental design-based algorithm to minimize regret in online stochastic linear and combinatorial bandits. While existing literature tends to focus on optimism-based algorithms--which have been shown to be suboptimal in many cases--our approach carefully plans which action to take by balancing the tradeoff between information gain and reward, overcoming the failures of optimism. In addition, we leverage tools from the theory of suprema of empirical processes to obtain regret guarantees that scale with the Gaussian width of the action set, avoiding wasteful union bounds. We provide state-of-the-art finite time regret guarantees and show that our algorithm can be applied in both the bandit and semi-bandit feedback regime. In the combinatorial semi-bandit setting, we show that our algorithm is computationally efficient and relies only on calls to a linear maximization oracle. In addition, we show that with slight modification our algorithm can be used for pure exploration, obtaining state-of-the-art pure exploration guarantees in the semi-bandit setting. Finally, we provide, to the best of our knowledge, the first example where optimism fails in the semi-bandit regime, and show that in this setting our algorithm succeeds.

References in corpus (8)

• Minimal Exploration in Structured Stochastic Bandits
• Leveraging Side Observations in Stochastic Bandits
• Combinatorial semi-bandit with known covariance
• An Empirical Process Approach to the Union Bound: Practical Algorithms for Combinatorial and Linear Bandits
• Information Directed Sampling for Linear Partial Monitoring
• An Asymptotically Optimal Primal-Dual Incremental Algorithm for Contextual Linear Bandits
• Efficient Pure Exploration for Combinatorial Bandits with Semi-Bandit Feedback
• Asymptotically Optimal Strategies For Combinatorial Semi-Bandits in Polynomial Time