Research Proposal: Gap-Independent Robust Multi-Armed Bandits under Adversarial Corruptions

A detailed research plan to design, analyze, and empirically validate bandit algorithms that achieve gap-independent regret bounds with additive dependence on adversarial corruption budgets. The goal is to obtain guarantees of the form O(√(KT) + C) (up to log factors), even when the arm gaps are unknown, extending the ARM framework and closing open gaps identified in Lykouris et al. (2018). The proposal includes hypotheses, algorithmic ideas, theoretical methods, experimental designs, data-analysis strategies, potential implications, and a work plan with milestones and risk mitigation strategies.