Zihao Chen

EECS Department, University of California, Berkeley

Technical Report No. UCB/

May 1, 2025

This dissertation investigates the design and analysis of methods for a few foundational problems in optimization, statistics, and automated discovery. We begin with a theoretical exploration of finding zeros of monotone operators—which generalize convex minimization and convex-concave saddle point problems—providing a geometric characterization of continuous-time oscillatory behavior and introducing a regularization framework for stabilization and acceleration of discrete methods. We then study robust mean estimation under affine equivariance constraints, proposing a high-dimensional median-based estimator and establishing that this natural stability property incurs a dimension-dependent statistical cost. Finally, we present a decision-making methodology that combines machine learning with adaptive experimentation to guide materials discovery, demonstrating improved efficiency in exploring chemical spaces.

Advisors: Laurent El Ghaoui

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BibTeX citation:

@phdthesis{Chen:31908,
    Author= {Chen, Zihao},
    Title= {Algorithmic Pursuits of Structure: Monotone Operators, Robust Estimation, and Automated Discovery},
    School= {EECS Department, University of California, Berkeley},
    Year= {2025},
    Number= {UCB/},
    Abstract= {This dissertation investigates the design and analysis of methods for a few foundational problems in optimization, statistics, and automated discovery. We begin with a theoretical exploration of finding zeros of monotone operators—which generalize convex minimization and convex-concave saddle point problems—providing a geometric characterization of continuous-time oscillatory behavior and introducing a regularization framework for stabilization and acceleration of discrete methods. We then study robust mean estimation under affine equivariance constraints, proposing a high-dimensional median-based estimator and establishing that this natural stability property incurs a dimension-dependent statistical cost. Finally, we present a decision-making methodology that combines machine learning with adaptive experimentation to guide materials discovery, demonstrating improved efficiency in exploring chemical spaces.},
}

EndNote citation:

%0 Thesis
%A Chen, Zihao 
%T Algorithmic Pursuits of Structure: Monotone Operators, Robust Estimation, and Automated Discovery
%I EECS Department, University of California, Berkeley
%D 2025
%8 May 1
%@ UCB/
%F Chen:31908