The Power of Factorial Powers: New Parameter settings for (Stochastic) Optimization
This work addresses a theoretical bottleneck in optimization for researchers, but it appears incremental as it builds on existing methods with new parameter settings.
The paper tackles the problem of selecting constants in optimization convergence proofs by introducing factorial powers as a flexible tool, resulting in simplified or improved convergence rates for methods like momentum, accelerated gradient, and SVRG.
The convergence rates for convex and non-convex optimization methods depend on the choice of a host of constants, including step sizes, Lyapunov function constants and momentum constants. In this work we propose the use of factorial powers as a flexible tool for defining constants that appear in convergence proofs. We list a number of remarkable properties that these sequences enjoy, and show how they can be applied to convergence proofs to simplify or improve the convergence rates of the momentum method, accelerated gradient and the stochastic variance reduced method (SVRG).