Reproduce “Convergence rates for the Adam optimizer” on OpenResearch

About this paper

Steffen Dereich, Arnulf Jentzen

Researchers from the University of Münster and CUHK-Shenzhen establish optimal convergence rates for the original Adam optimizer in stochastic optimization problems, demonstrating that Adam converges to the zeros of a newly identified "Adam vector field" rather than directly to the objective function's gradient zeros. They show this limit point approaches the true minimizer at a rate of M⁻¹ as mini-batch size M increases.

Key insights

• Adam optimizer typically converges to the zeros of a newly defined "Adam vector field," rather than directly to the critical points (zeros of the gradient) of the objective function.
• The Adam vector field captures the macroscopic behavior of the optimizer, showing how its dynamics incorporate not just gradient information but also its moments.
• The convergence point of Adam (the zero of its vector field) approaches the true global minimizer of the stochastic optimization problem as the mini-batch size increases.

Summary by alphaXiv.