Why Most Optimism Bandit Algorithms Have the Same Regret Analysis: A Simple Unifying Theorem
Machine Learning
2025-12-23 v1 Systems and Control
Systems and Control
Machine Learning
Abstract
Several optimism-based stochastic bandit algorithms -- including UCB, UCB-V, linear UCB, and finite-arm GP-UCB -- achieve logarithmic regret using proofs that, despite superficial differences, follow essentially the same structure. This note isolates the minimal ingredients behind these analyses: a single high-probability concentration condition on the estimators, after which logarithmic regret follows from two short deterministic lemmas describing radius collapse and optimism-forced deviations. The framework yields unified, near-minimal proofs for these classical algorithms and extends naturally to many contemporary bandit variants.
Keywords
Cite
@article{arxiv.2512.18409,
title = {Why Most Optimism Bandit Algorithms Have the Same Regret Analysis: A Simple Unifying Theorem},
author = {Vikram Krishnamurthy},
journal= {arXiv preprint arXiv:2512.18409},
year = {2025}
}