Trust-Region Stochastic Optimization with Variance Reduction Technique

Abstract: We propose a novel algorithm, TR-SVR, for solving unconstrained stochastic optimization problems. This method builds on the trust-region framework, which effectively balances local and global exploration in optimization tasks. TR-SVR incorporates variance reduction techniques to improve both computational efficiency and stability when addressing stochastic objective functions. The algorithm applies a sequential quadratic programming (SQP) approach within the trust-region framework, solving each subproblem approximately using variance-reduced gradient estimators. This integration ensures a robust convergence mechanism while maintaining efficiency, making TR-SVR particularly suitable for large-scale stochastic optimization challenges.