On the Hardness of Online Nonconvex Optimization with Single Oracle Feedback
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: online nonconvex optimization, local regret, optimal rate analysis
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
TL;DR: We consider online nonconvex optimization with single oracle feedback, and provide matching lower and upper bounds on the local regret.
Abstract: Online nonconvex optimization has been an active area of research recently. Previous studies either considered the global regret with full information about the objective functions, or studied the local regret with window-smoothed objective functions, which required access to unlimited number of gradient oracles per time step. In this paper, we focus on the more challenging and practical setting, where access to only a single oracle is allowed per time step, and take the local regret of the original (i.e., unsmoothed) objective functions as the performance metric. Specifically, for both settings respectively with a single exact and stochastic gradient oracle feedback, we derive lower bounds on the local regret and show that the classical online (stochastic) gradient descent algorithms are optimal. Moreover, for the more challenging setting with a single function value oracle feedback, we develop an online algorithm based on a one-point running difference gradient estimator, and show that such an algorithm achieves a local regret that a generic stochastic gradient oracle can best achieve.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Primary Area: optimization
Submission Number: 4679
Loading