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Home > Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 36 > No. 4: AAAI-22 Technical Tracks 4

Sample Average Approximation for Stochastic Optimization with Dependent Data: Performance Guarantees and Tractability

February 1, 2023

Authors

Yafei Wang

University of Alberta


Bo Pan

University of Alberta


Wei Tu

Queen's University


Peng Liu

University of Kent


Bei Jiang

University of Alberta


Chao Gao

Huawei Canada Research Center


Wei Lu

Huawei Canada


Shangling Jui

Huawei Kirin Solution


Linglong Kong

University of Alberta


Proceedings:

No. 4: AAAI-22 Technical Tracks 4

Volume

Issue:

Proceedings of the AAAI Conference on Artificial Intelligence, 36

Track:

AAAI Technical Track on Constraint Satisfaction and Optimization

Downloads:

Download PDF

Abstract:

Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not known to hold generally with dependent samples, such as in online learning with time series data or distributed computing with Markovian training samples. In this paper, we show that SAA remains tractable when the distribution of unknown parameters is only observable through dependent instances and still enjoys asymptotic consistency and finite sample guarantees. Specifically, we provide a rigorous probability error analysis to derive 1 - beta confidence bounds for the out-of-sample performance of SAA estimators and show that these estimators are asymptotically consistent. We then, using monotone operator theory, study the performance of a class of stochastic first-order algorithms trained on a dependent source of data. We show that approximation error for these algorithms is bounded and concentrates around zero, and establish deviation bounds for iterates when the underlying stochastic process is phi-mixing. The algorithms presented can be used to handle numerically inconvenient loss functions such as the sum of a smooth and non-smooth function or of non-smooth functions with constraints. To illustrate the usefulness of our results, we present several stochastic versions of popular algorithms such as stochastic proximal gradient descent (S-PGD), stochastic relaxed Peaceman-Rachford splitting algorithms (S-rPRS), and numerical experiment.

DOI:

10.1609/aaai.v36i4.20301


AAAI

Proceedings of the AAAI Conference on Artificial Intelligence, 36



Topics: AAAI

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