## Stochastic Gauss-Newton Algorithms for Nonconvex Compositional Optimization

### Quoc Tran-Dinh · Nhan H Pham · Lam Nguyen

Keywords: [ Non-convex Optimization ] [ Supervised Learning ] [ Optimization - Non-convex ]

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 $\BigO{\varepsilon^{-2}}$ 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 $\BigO{\varepsilon^{-2}}$ 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.