A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

Cui, Shisheng; Shanbhag, Uday V.; Staudigl, Mathias

doi:10.1007/s10957-025-02683-8

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

Journal Article · Sat May 10 00:00:00 EDT 2025 · Journal of Optimization Theory and Applications

DOI:https://doi.org/10.1007/s10957-025-02683-8· OSTI ID:3010477

Cui, Shisheng ^[1]; Shanbhag, Uday V. ^[2]; ^[3]

Beijing Institute of Technology (China)
Univ. of Michigan, Ann Arbor, MI (United States)
Univ. of Mannheim (Germany)

We consider an N-player hierarchical game in which the ith player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

View Accepted Manuscript (DOE)

Research Organization:: Rutgers Univ., Piscataway, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0023303

OSTI ID:: 3010477

Journal Information:: Journal of Optimization Theory and Applications, Journal Name: Journal of Optimization Theory and Applications Journal Issue: 1 Vol. 206; ISSN 1573-2878; ISSN 0022-3239

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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