Talks & Lectures
28 Oct 2019
Babbio Center Room 220

## Abstract:

We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We illustrate the relevance of this problem by applications to stochastic variational inequalities, reinforcement learning, and risk-averse optimization.

We propose a single time-scale stochastic approximation algorithm, which we call the Nested Averaged Stochastic Approximation (NASA), to find an approximate stationary point of the problem. The algorithm has two auxiliary averaged sequences (filters) which estimate the gradient of the composite objective function and the inner function value. By using a special Lyapunov function, we show that NASA achieves the sample complexity of ${\cal O}(1/\epsilon^{2})$ for finding an $\epsilon$-approximate stationary point, thus outperforming all extant methods for nested stochastic approximation. Our method and its analysis are the same for both unconstrained and constrained problems, without any need of batch samples for constrained nonconvex stochastic optimization. We also present a simplified parameter-free variant of the NASA method for solving constrained single level stochastic optimization problems, and we prove the same complexity result for both unconstrained and constrained problems.

This is a joint work with Saeed Ghadimi and Mengdi Wang from Princeton University.

## Bio

Andrzej Ruszczynski received his PhD and habilitation degrees in control engineering from Warsaw University of Technology. He has been affiliated with Warsaw University of Technology (Poland), University of Zurich (Switzerland), International Institute of Applied Systems Analysis (Laxenburg, Austria), Princeton University, University of Wisconsin-Madison, and Rutgers University. Dr. Ruszczynski is one of the creators of and main contributors to the field of risk-averse optimization, author of "Nonlinear Optimization" (Princeton University Press, 2006), co-author of "Lectures on Stochastic Programming" (SIAM, 2009), "Stochastic Programming" (Elsevier, 2003), and author of more than 100 articles in the area of optimization. He is the recipient of the 2018 Dantzig Prize of SIAM and the Mathematical Optimization Society, and an INFORMS fellow.

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