What are the minimal conditions we know of under which we can prove that a stochastic gradient based algorithm can convergence to criticality on a non-convex objective?
Are there any necessary conditions that we know of that the objective, algorithm and the oracle have to satisfy to get convergence?
For example : I would be very interested to know of proofs which do not need to assume that the objective has bounded gradients (or that the function is upperbounded). These look very rare to satisfy in usual learning situations! (What are natural non-convex learning situations which have bounded gradient losses?)
I am not considering methods like NSVRG which allow the algorithm to compute the exact gradients sometimes. I am specifically looking at algorithms where the gradient oracle is the only oracle being invoked and it is necessarily always noisy.