arXiv Machine Learning By Yanyi Li, Wendao Wu, Haihan Zhang, Qinshi Wang, Chenheng Zhang, Chunyuan Zheng, Cong Fang, Haoxuan Li, Zhouchen Lin

Dimension-Optimal Dynamic Regret in Exp-Concave Online Learning

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arXiv Machine Learning
Oct 3

Sharp Oracle-Regret Tradeoffs for Projection-Free Online Convex Optimization

The paper studies online convex optimization when the learner can only query an exact linear optimization oracle. It establishes a dimension‑free minimax expected regret bound of θ(GD max{√T, T/(1+min{Q,BT})^{1/4}}) for convex G‑Lipschitz losses, where Q is the total oracle budget and B the per‑round limit. The authors provide matching lower and upper bounds, showing how strict per‑round or total‑budget constraints affect the achievable regret, and extend the analysis to smooth losses with curvature‑dependent bounds.

By Vaneet Aggarwal
Hugging Face Trending Papers
Jul 21

The Price of Hidden Curvature: An $\widetildeΩ (d^{5/4} \sqrt{T})$ Lower Bound for Bandit Convex Optimization

We establish a $\widetildeΩ(d^{5/4}\sqrt T)$ lower bound on the minimax expected regret of stochastic bandit convex optimization of $1$-Lipschitz functions on the Euclidean ball. This presents the first nontrivial regret lower bound that grows faster than $d\sqrt{T}$ for this problem, establishing that stochastic bandit convex optimization is fundamentally harder than linear bandits.