Stochastic Successive Convex Approximation for Non-Convex Constrained Stochastic Optimization

TL;DR

This paper introduces a novel constrained stochastic successive convex approximation (CSSCA) algorithm capable of handling non-convex stochastic optimization problems with both objective and constraint functions involving expectations, enabling solutions to more complex real-world problems.

Contribution

The CSSCA algorithm extends existing methods by addressing stochastic non-convex constraints and supports a wide range of surrogate functions for improved flexibility and performance.

Findings

CSSCA converges to a stationary point from a feasible initial point.

The algorithm demonstrates superior performance in simulations.

Supports parallel implementation for large-scale problems.

Abstract

This paper proposes a constrained stochastic successive convex approximation (CSSCA) algorithm to find a stationary point for a general non-convex stochastic optimization problem, whose objective and constraint functions are non-convex and involve expectations over random states. Most existing methods for non-convex stochastic optimization, such as the stochastic (average) gradient and stochastic majorization-minimization, only consider minimizing a stochastic non-convex objective over a deterministic convex set. The proposed CSSCA algorithm can also handle stochastic non-convex constraints in optimization problems, and it opens the way to solving more challenging optimization problems that occur in many applications. The algorithm is based on solving a sequence of convex objective/feasibility optimization problems obtained by replacing the objective/constraint functions in the original problems with some convex surrogate functions. The CSSCA algorithm allows a wide class of surrogate functions and thus provides many freedoms to design good surrogate functions for specific applications. Moreover, it also facilitates parallel implementation for solving large scale stochastic optimization problems, which arise naturally in today's signal processing such as machine learning and big data analysis. We establish the convergence of CSSCA algorithm with a feasible initial point, and customize the algorithmic framework to solve several important application problems. Simulations show that the CSSCA algorithm can achieve superior performance over existing solutions.