Open Problem: Anytime Convergence Rate of Gradient Descent

Guy Kornowski; Ohad Shamir

Open Problem: Anytime Convergence Rate of Gradient Descent

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arxiv 2406.13888 v1 pith:ANZRGPLZ submitted 2024-06-19 math.OC cs.LG

Guy Kornowski , Ohad Shamir This is my paper · ORCID

classification math.OCcs.LG

keywords descentgradientconvergenceratestepsizeacceleratedacceleratesanytime

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abstract

Recent results show that vanilla gradient descent can be accelerated for smooth convex objectives, merely by changing the stepsize sequence. We show that this can lead to surprisingly large errors indefinitely, and therefore ask: Is there any stepsize schedule for gradient descent that accelerates the classic $\mathcal{O}(1/T)$ convergence rate, at \emph{any} stopping time $T$?

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Finite Horizon Optimization: Framework and Applications
math.OC 2024-12 reject novelty 6.0 of 10

A finite-horizon stepsize rule for the primal-dual method on LP, found via a 4x4 SDP, is claimed to accelerate convergence at the T-th iteration and to give about 3.9x speedup on Netlib instances.

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