Subject: [Phd-coc-announce] CSE Ph.D. Thesis Announcement
Title: Optimizing Decision-making under Uncertainty: A Data-driven Perspective
Date: June. 3rd , 2024
Time: 2 PM – 4 PM EST
Location: Virtual (Zoom)
https://gatech.zoom.us/j/3996903091?omn=98003172648
Lingkai Kong
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Committee
Dr. Chao Zhang - School of Computational Science and Engineering, Georgia Institute of Technology (Advisor)
Dr. B Aditya Prakash - School of Computational Science and Engineering, Georgia Institute of Technology
Dr. Bo Dai - School of Computational Science and Engineering, Georgia Institute of Technology
Dr. Yao Xie - School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Tuo Zhao - School of Industrial and Systems Engineering, Georgia Institute of Technology
Abstract
Decision-making processes are fundamental to many aspects of daily life, from allocating educational resources and optimizing logistics routes to scheduling renewable energy generation and distributing vaccines. These complex problems are typically framed as mathematical optimization problems, where decision-makers seek the best action from a set of alternatives under given constraints. However, unique challenges arise: (1) How can we handle unknown and uncertain parameters of the optimization objective? (2) How can we address the misalignment between predictive models' learning objectives and the true costs of decision-making? (3) How can we manage constraints when their analytical expressions are unavailable? This thesis leverages the vast data available in modern systems alongside algorithmic innovations to improve the accuracy, speed, and resilience of decision-making against uncertainty. The main contributions are three-fold:
(1) Efficient Uncertainty Quantification for DNNs: We propose SDE-Net, an efficient method for uncertainty quantification in DNNs through the lens of dynamical systems. The central idea is to interpret DNN transformations as the state progression of a Stochastic Differential Equation (SDE), incorporating a Brownian motion term to capture epistemic uncertainty.
(2) Accelerating and Generalizing Decision-Focused Learning (DFL): We introduce SO-EBM, which fuses uncertainty-aware deep models for enhanced decision-making via DFL. Unlike existing methods, our approach, grounded in energy-based models, is general and not confined to convex objectives. Additionally, it offers superior computational efficiency.
(3) Optimization under Unknown Constraints with Diffusion Models: We propose DiffOPT to perform optimization within the data manifold using diffusion models to address unknown constraints. To constrain the optimization process to the data manifold, we reformulate the original optimization problem as a sampling problem from the product of the Boltzmann distribution defined by the objective function and the data distribution learned by the diffusion model.