Papers › Stochastic Gauss-Newton Algorithms for Nonconvex Compositional Optimization

Stochastic Gauss-Newton Algorithms for Nonconvex Compositional Optimization

17 Feb 2020ICML 2020 1arXiv:2002.07290archive 2025-07-28

Quoc Tran-Dinh, Nhan H. Pham, Lam M. Nguyen

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 𝒪(ε⁻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 ε is a desired accuracy. In the finite sum case, we also estimate 𝒪(ε⁻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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