Dualityfree Methods for Stochastic Composition Optimization.

Area of Science:

• Machine Learning
• Optimization Theory
• Statistical Learning

Background:

• Many machine learning problems involve optimizing composite functions with two expected-value functions.
• Standard optimization algorithms struggle with the nested structure and computational expense of these problems.

Purpose of the Study:

• To develop an efficient and scalable optimization method for stochastic composition problems.
• To address the limitations of traditional gradient-based methods in handling inner expectations.

Main Methods:

• A duality-free stochastic composition method is proposed, integrating variance reduction techniques.
• Stochastic variance reduction gradient (SVRG) and stochastic average gradient (SAG) methods are used for inner function estimation.
• The duality-free method is employed for outer function estimation.

Main Results:

• The proposed method achieves a linear convergence rate for convex composition problems.
• Linear convergence is also proven for problems with nonconvex outer functions and a strongly convex objective function.
• Experimental results demonstrate the effectiveness of the developed methods.

Conclusions:

• The proposed duality-free stochastic composition method offers an efficient solution for complex optimization tasks in machine learning.
• The method's proven convergence rates highlight its potential for solving challenging problems in reinforcement learning and nonlinear embedding.