A Bandit Approach to Maximum Inner Product Search

There has been substantial research on sub-linear time approximate algorithms for Maximum Inner Product Search (MIPS). To achieve fast query time, state-of-the-art techniques require significant preprocessing, which can be a burden when the number of subsequent queries is not sufficiently large to amortize the cost. Furthermore, existing methods do not have the ability to directly control the suboptimality of their approximate results with theoretical guarantees. In this paper, we propose the first approximate algorithm for MIPS that does not require any preprocessing, and allows users to control and bound the suboptimality of the results. We cast MIPS as a Best Arm Identification problem, and introduce a new bandit setting that can fully exploit the special structure of MIPS. Our approach outperforms state-of-the-art methods on both synthetic and real-world datasets.Comment: AAAI 201

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

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