Tighter Confidence Bounds for Sequential Kernel Regression

arXiv:2403.12732v1 Announce Type: cross
Abstract: Confidence bounds are an essential tool for rigorously quantifying the uncertainty of predictions. In this capacity, they can inform the exploration-exploitation trade-off and form a core component in many sequential learning and decision-making algorithms. Tighter confidence bounds give rise to algorithms with better empirical performance and better performance guarantees. In this work, we use martingale tail bounds and finite-dimensional reformulations of infinite-dimensional convex programs to establish new confidence bounds for sequential kernel regression. We prove …

abstract algorithms arxiv capacity confidence core cs.lg decision exploitation exploration form kernel making performance predictions regression stat.ml tool trade trade-off type uncertainty