Stochastic Gauss-Newton Algorithms for Nonconvex Compositional Optimization

• URL: http://arxiv.org/abs/2002.07290v2
• Date: Thu, 2 Jul 2020 20:41:20 GMT
• Title: Stochastic Gauss-Newton Algorithms for Nonconvex Compositional Optimization
• Authors: Quoc Tran-Dinh and Nhan H. Pham and Lam M. Nguyen
• Abstract summary: We develop two new Gauss-Newton algorithms for solving a class of non- compositional optimization problems. We consider both the expectation and finite-sum settings under standard assumptions.
• Score: 26.313415590777858
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop two new stochastic Gauss-Newton algorithms for solving a class of non-convex stochastic compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard assumptions, and use both classical stochastic and SARAH estimators for approximating function values and Jacobians. In the expectation case, we establish $\mathcal{O}(\varepsilon^{-2})$ iteration-complexity to achieve a stationary point in expectation and estimate the total number of stochastic oracle calls for both function value and its Jacobian, where $\varepsilon$ is a desired accuracy. In the finite sum case, we also estimate $\mathcal{O}(\varepsilon^{-2})$ iteration-complexity and the total oracle calls with high probability. To our best knowledge, this is the first time such global stochastic oracle complexity is established for stochastic Gauss-Newton methods. Finally, we illustrate our theoretical results via two numerical examples on both synthetic and real datasets.

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