Collaborative Pure Exploration in Kernel Bandit

TL;DR

This paper introduces a novel multi-agent kernel bandit framework with algorithms that optimize decision-making under limited communication, providing theoretical guarantees and empirical validation for improved learning efficiency.

Contribution

The paper formulates the CoPE-KB model, designs optimal algorithms with kernelized estimators, and establishes matching bounds demonstrating their efficiency and optimality in multi-task decision making.

Findings

Algorithms achieve computation and communication efficiency.

Theoretical bounds quantify task similarity effects.

Empirical results validate theoretical claims and show superior performance.

Abstract

In this paper, we formulate a Collaborative Pure Exploration in Kernel Bandit problem (CoPE-KB), which provides a novel model for multi-agent multi-task decision making under limited communication and general reward functions, and is applicable to many online learning tasks, e.g., recommendation systems and network scheduling. We consider two settings of CoPE-KB, i.e., Fixed-Confidence (FC) and Fixed-Budget (FB), and design two optimal algorithms CoopKernelFC (for FC) and CoopKernelFB (for FB). Our algorithms are equipped with innovative and efficient kernelized estimators to simultaneously achieve computation and communication efficiency. Matching upper and lower bounds under both the statistical and communication metrics are established to demonstrate the optimality of our algorithms. The theoretical bounds successfully quantify the influences of task similarities on learning acceleration and only depend on the effective dimension of the kernelized feature space. Our analytical techniques, including data dimension decomposition, linear structured instance transformation and (communication) round-speedup induction, are novel and applicable to other bandit problems. Empirical evaluations are provided to validate our theoretical results and demonstrate the performance superiority of our algorithms.