Logarithmic High-Probability Regret for Online Convex Optimization with Two-Point Bandit Feedback
We study online convex optimization (OCO) with two-point bandit feedback against a non-anticipating adaptive adversary. In this setting, a learner competes with an adversarial sequence of convex losses while observing each loss only through two function evaluations. For strongly convex losses, Agarwal, Dekel, and Xiao~\citeyearpar{agarwal2010optimal} proved a comparator-wise logarithmic regret bound in expectation. Consequently, by minimizing outside the probability space, their result yields a pseudo-regret guarantee of the form $\EB A_T-\min_{x\in\mathcal K}\EB L_T(x)$, where $A_T$ is the algorithm's two-query cumulative loss and $L_T(x)$ is the comparator's cumulative loss. They asked ...
| Authors | Haishan Ye |
|---|---|
| Primary category | cs.LG |
| Published | 26 March 2026 |
| Last updated at source | 9 July 2026 |
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