Under step sizes with infinite sum and finite p-th power sum for p>2, SGD's function values and gradients converge almost surely to a critical point in non-convex smooth problems.
Stochastic approximation: a dynamical systems viewpoint, volume 9
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Stochastic Gradient Descent in Non-Convex Problems: Asymptotic Convergence with Relaxed Step-Size via Stopping Time Methods
Under step sizes with infinite sum and finite p-th power sum for p>2, SGD's function values and gradients converge almost surely to a critical point in non-convex smooth problems.