Lecture 1

Recent Progresses on Online Linear Programming and Applications 

Abstract: A natural optimization model that formulates many online learning and resource allocation decision-making with uncertainty is online linear programming (OLP), where the noisy constraint column vectors, along with the objective coefficients and decision variables, are revealed and decided sequentially in real time. In this talk, we review the near optimal algorithms and theories for solving this surprisingly general class of online (binary) linear programs and convex optimization problems. Then we present few recent developments of model/algorithms and applications in this area, including fast online-gradient learning and decision making, Bandit with Knapsacks setting, the Fisher Market with online pricing, Decoupling strategy of learning and decision-making, Wait-Less algorithms with mixed LP resolving and online gradient methods, Online learning and decision-making with batches, OLP with non-stationary inputs, Hyper-gradient methods with online scaling/pre-conditioning for the gradient-based algorithms.

Lecture 2

SDP Relaxation for NP-Hard Optimization on GPU 

Abstract: We present breakthroughs in the SDP Optimization solver development on the GPU computational platform. First, we give a computational proof of the well-known Quantum ordered search problem via SDP. Secondly, we illustrate approximation results of the SDP relaxation plus rounding theories/algorithms for solving various huge-scale nonconvex and NP-hard combinatorial problems and show their advantages over other heuristic approaches.

Personal Website：https://web.stanford.edu/~yyye/