I am a fourth-year PhD student in Operations, Information & Technology at the Stanford Graduate School of Business. I am interested in optimization algorithms, and applying large scale optimization algorithms to statistical inference problems, revenue management problems, and economics modeling with specific interests in auctions and mechanism design.
The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. Unfortunately, the multi-block ADMM, with more than two blocks, is not guaranteed to be convergent. In this paper, we add more randomness into the ADMM by developing a randomly assembled cyclic ADMM (RAC-ADMM) where the decision variables in each block are randomly assembled. We discuss the theoretical properties of RAC-ADMM and show when random assembling helps and when it hurts, and develop a criterion to guarantee that it converges almost surely. Using the theoretical guidance on RAC-ADMM, we conduct multiple numerical tests on solving both randomly generated and large-scale benchmark quadratic optimization problems, which include continuous, and binary graph-partition and quadratic assignment, and selected machine learning problems. Our numerical tests show that the RAC-ADMM could significantly improve the computation efficiency on solving most quadratic optimization problems.
Work in Progress
We studied fast convergence algorithm under weak and strong data privacy constraints. We proposed a sharing algorithm that gives better prediction and improves efficiency on convergence under data privacy constraint, compared with traditional optimization algorithms including SGD, Stochastic Newton and other first and second order algorithms. We also established the worst case scenario under strong data privacy constraints for convergence rate.
We studied dynamic optimal credit line for the online lender under uncertainty of borrower’s type. We proved that the online lender’s optimal strategy is a mixture of exploration and exploitation. We also provided analytical solution to the optimal policy for the dynamic control problem under certain class of distributions.