Nonasymptotic convergence of stochastic proximal point algorithms for constrained convex optimization

Understand

A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD).

• Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under certain circumstances, there is recent evidence of its convergence difficulties and instability for unappropriate parameters choice.
• To avoid these drawbacks naturally introduced by the SGD scheme, the stochastic proximal point algorithms have been recently considered in the literature.
• We introduce a new variant of the stochastic proximal point method (SPP) for solving stochastic convex optimization problems subject to (in)finite intersection of constraints satisfying a linear regularity type condition.