Pure Exploration in Kernel and Neural Bandits
This addresses the curse of dimensionality in bandit problems for researchers and practitioners, offering a novel approach to kernel and neural bandits, though it is incremental in extending existing methods to new settings.
The paper tackles pure exploration in bandits with high-dimensional features by adaptively embedding them into lower-dimensional spaces to handle model misspecification, achieving sample complexity guarantees based on effective dimensions and demonstrating efficacy in experiments on synthetic and real-world datasets.
We study pure exploration in bandits, where the dimension of the feature representation can be much larger than the number of arms. To overcome the curse of dimensionality, we propose to adaptively embed the feature representation of each arm into a lower-dimensional space and carefully deal with the induced model misspecification. Our approach is conceptually very different from existing works that can either only handle low-dimensional linear bandits or passively deal with model misspecification. We showcase the application of our approach to two pure exploration settings that were previously under-studied: (1) the reward function belongs to a possibly infinite-dimensional Reproducing Kernel Hilbert Space, and (2) the reward function is nonlinear and can be approximated by neural networks. Our main results provide sample complexity guarantees that only depend on the effective dimension of the feature spaces in the kernel or neural representations. Extensive experiments conducted on both synthetic and real-world datasets demonstrate the efficacy of our methods.