Regret analysis of Structure-Aware LCB

Establish a theoretical regret bound for the Structure-Aware LCB (SA-LCB) algorithm, which replaces the standard confidence bound with the structure-aware confidence bound for the Timing Bandit problem.

Background

SA-LCB is evaluated as a baseline that incorporates the paper’s structure-aware confidence bound into a standard lower-confidence-bound algorithm. Empirically, it performs competitively, particularly when the number of arms is small.

Despite this empirical performance, the paper does not provide a regret analysis for SA-LCB. Establishing such an analysis would clarify whether the algorithm can theoretically exploit the arm-cost composition and consecutive-feedback structures as effectively as BCAE and OE-BCAE.