Collaborative Pure Exploration in Kernel Bandit
This work addresses decision-making challenges in online learning tasks like recommendation systems and network scheduling, but it is incremental as it builds upon existing kernel bandit frameworks with collaborative extensions.
The paper tackles the problem of multi-agent multi-task decision making under limited communication and general reward functions by formulating the Collaborative Pure Exploration in Kernel Bandit (CoPE-KB) problem, and it designs optimal algorithms (CoopKernelFC and CoopKernelFB) with matching upper and lower bounds that quantify task similarity influences on learning acceleration.
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.