핵심 개념
New confidence bounds improve empirical performance in kernel bandit algorithms.
초록
The content discusses the development of tighter confidence bounds for sequential kernel regression. It introduces new algorithms, such as Kernel CMM-UCB, Kernel DMM-UCB, and Kernel AMM-UCB, and compares them with existing methods like AY-GP-UCB and IGP-UCB. Theoretical analysis shows that the new confidence bounds are always tighter. Experiments demonstrate that Kernel DMM-UCB performs best in terms of cumulative regret over 1000 rounds. The study highlights the importance of replacing existing confidence bounds with new ones to enhance algorithm performance.
Introduction
Confidence bounds quantify uncertainty in predictions.
Essential for exploration-exploitation trade-off.
Problem Statement
Sequential kernel regression problem defined.
Unknown function f ∗ in reproducing kernel Hilbert space.
Related Work
Various confidence sequences/bounds proposed.
Comparison against existing methods like AY-GP-UCB and IGP-UCB.
Confidence Bounds for Kernel Regression
Tail bound from Flynn et al., 2023 used.
Martingale mixture tail bounds applied.
Confidence Sequences
Construction of confidence sequences for f ∗ discussed.
Implicit Confidence Bounds
Reformulations of exact upper confidence bound UCBFt(x) presented.
Explicit Confidence Bounds
Upper bound on UCBFt(x) derived using dual problem approach.
Inquiry and Critical Thinking
How can these new confidence bounds be applied to other learning problems?
What are the limitations of assuming known values for B and σ?
Can model selection methods be used to learn upper bounds on ∥f ∗∥H?
통계
Tighter confidence bounds give rise to algorithms with better empirical performance.
New confidence bounds are always tighter than existing ones in this setting.
인용구
"Our new confidence bounds are always tighter than existing ones in this setting."
"Tighter confidence bounds give rise to sequential learning and decision-making algorithms with better empirical performance."