Non-convex online learning via algorithmic equivalence

• URL: http://arxiv.org/abs/2205.15235v1
• Date: Mon, 30 May 2022 16:50:34 GMT
• Title: Non-convex online learning via algorithmic equivalence
• Authors: Udaya Ghai, Zhou Lu, Elad Hazan
• Abstract summary: algorithmic equivalence technique non gradient descent convex mirror descent theory is presented. Our analysis is based on a new simple algorithmic method prove an $frac23$.
• Score: 30.038975353298117
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study an algorithmic equivalence technique between nonconvex gradient descent and convex mirror descent. We start by looking at a harder problem of regret minimization in online non-convex optimization. We show that under certain geometric and smoothness conditions, online gradient descent applied to non-convex functions is an approximation of online mirror descent applied to convex functions under reparameterization. In continuous time, the gradient flow with this reparameterization was shown to be exactly equivalent to continuous-time mirror descent by Amid and Warmuth 2020, but theory for the analogous discrete time algorithms is left as an open problem. We prove an $O(T^{\frac{2}{3}})$ regret bound for non-convex online gradient descent in this setting, answering this open problem. Our analysis is based on a new and simple algorithmic equivalence method.

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