Improved Dimension Dependence for Bandit Convex Optimization with Gradient Variations

The paper presents an improved analysis of non‑consecutive gradient variation in Bandit Convex Optimization (BCO) with two‑point feedback, leading to better dimension dependence for both convex and strongly convex functions compared to prior work. It also derives new problem‑dependent guarantees such as gradient‑variance and small‑loss regret bounds, extends the technique to one‑point bandit linear optimization over hyper‑rectangular domains, and establishes the first gradient‑variation dynamic and universal regret bounds for two‑point BCO.

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• reinforcement-learning