Convergence Rates for Stochastic Approximation on a Boundary. (arXiv:2208.07243v2 [stat.ML] UPDATED)

We analyze the behavior of projected stochastic gradient descent focusing on
the case where the optimum is on the boundary of the constraint set and the
gradient does not vanish at the optimum. Here iterates may in expectation make
progress against the objective at each step. When this and an appropriate
moment condition on noise holds, we prove that the convergence rate to the
optimum of the constrained stochastic gradient descent will be different and
typically be faster than the …

approximation arxiv convergence ml stochastic