Performance of noisy higher-order accelerated gradient flow dynamics for strongly convex quadratic optimization problems
Samantha Samuelson, Hesameddin Mohammadi, Mihailo R. Jovanović · 2023
We study performance of momentum-based accelerated first-order optimization algorithms in the presence of additive white stochastic disturbances. For strongly convex quadratic problems with a condition number κ, we determine the best possible convergence rate of continuous-time gradient flow dynamics of order n. We also demonstrate that additional momentum terms do not affect the tradeoffs between convergence rate and variance amplification that exist for gradient flow dynamics with n = 2.