Online Learning on Hidden-Convex Losses via Algorithmic Equivalence: Optimal Regret, Geometric Barrier, and Bandit Feedback
arXiv:2605.26373v1 Announce Type: new Abstract: We study adversarial online learning with hidden-convex losses, i.e., nonconvex losses that become convex after a nonlinear reparameterization. Ghai, Lu and Hazan (2022) proved that, under geometric and smoothness assumptions, online gradient descent (OGD) on such nonconvex losses approximately simulates online mirror descent (OMD) on the underlying convex losses with a suitable regularizer, yielding $\mathcal{O}(T^{2/3})$ regret. They left open whether the optimal $\Theta(\sqrt{T})$ regret from online convex optimization can be recovered in this
This is a new publication from arXiv cs.LG, representing ongoing academic research in online learning algorithms.
This research is highly technical and theoretical, focusing on specific algorithmic improvements in online learning, rather than immediate real-world implications.
No immediate change in the broader tech landscape. It contributes to the incremental advancement of AI optimization techniques.
Further theoretical understanding of online learning algorithms with hidden-convex losses.
Potential for marginal improvements in the efficiency of specific machine learning models over a long time horizon.
Does not project to have significant impact on commercial AI development without further applied research.
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Read at arXiv cs.LG