Sharp Oracle-Regret Tradeoffs for Projection-Free Online Convex Optimization
We characterize the regret attainable in online convex optimization when access to the feasible set is limited to an exact linear optimization oracle. The learner is given an inscribed ball and a diameter bound and must remain feasible on every consistent instance. For convex $G$-Lipschitz losses, diameter at most $D$, a total allowance of $Q$ oracle calls, and a strict limit of $B$ calls per round, the dimension-free minimax expected regret is $Θ(GD\max\{\sqrt T,T/(1+\min\{Q,BT\})^{1/4}\})$. The lower bound applies to arbitrary randomized learners. Universal feasibility first forces each action into the hull of the supplied ball and the preceding oracle replies. A fixed-body construction...
| Authors | Vaneet Aggarwal |
|---|---|
| Primary category | cs.LG |
| Published | 23 September 2026 |
| Last updated at source | 23 September 2026 |
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