Convergence of mini-batch stochastic gradient descent

Determine whether convergence results analogous to the almost-sure and expected convergence-rate results established for stochastic gradient descent with polynomially controlled conditional variance also hold for mini-batch stochastic gradient descent (MSGD).

Background

The paper analyzes stochastic gradient descent under global Łojasiewicz-type gradient domination, polynomially controlled conditional noise variance, and polynomially decaying step sizes. It derives almost-sure and expected convergence rates under two sets of regularity and stability assumptions.

The authors explicitly identify other stochastic optimization schemes as a direction for future research and name MSGD as a specific example. The unresolved issue is whether the convergence behavior established for SGD extends to MSGD.