Convergence of SGD with momentum in the nonconvex case: A time window-based analysis

Understand

The stochastic gradient descent method with momentum (SGDM) is a common approach for solving large-scale and stochastic optimization problems.

• Despite its popularity, the convergence behavior of SGDM remains less understood in nonconvex scenarios.
• This is primarily due to the absence of a sufficient descent property and challenges in simultaneously controlling the momentum and stochastic errors in an almost sure sense.
• To address these challenges, we investigate the behavior of SGDM over specific time windows, rather than examining the descent of consecutive iterates as in traditional studies.