Optimizing Decision-Making under Uncertainty -- A Data-Driven Perspective

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) 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. To enhance ML models' robustness beyond the training distribution, We further propose a smoothness regularizer to calibrate uncertainty for both in- and out-of-distribution data. (2) Aligning learning with decision-making. We propose a general and efficient decision-focused learning (DFL) method to bridge the gap between model learning and the downstream decision-making using energy-based models. Our method is not restricted to convex objectives and can be 136 times faster than existing methods in training. Further, I designed the first distribution-free DFL to handle the high uncertain environment. (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.

Level thesis:degree_level

Doctoral

Department dc:contributor.department

Computational Science and Engineering

Grantor dc:publisher

Georgia Institute of Technology

Year dc:date.issued

2024

Author dc:creator

• Kong, Lingkai

Advisors dc:contributor.advisor

• Zhang, Chao
• Arkin, Ronald C.

Committee members dc:contributor.committeemember

• Prakash, B. Aditya
• Dai, Bo
• Xie, Yao
• Zhao, Tuo

• machine learning
• decision-making under uncertainty
• optimization

Language dc:language.iso

en_US

Handle dc:identifier.uri

https://hdl.handle.net/1853/75641

OAI identifier oai:identifier

oai:repository.gatech.edu:1853/75641