Salar Fatahi, Tianyi Lin, and Sheng Liu respectively.

Salar Fatahi
Exploiting structure in large-scale optimization: from energy systems to machine learning

Abstract: Today’s real-world problems are complex and large, often with an overwhelmingly large number of unknown variables which render them doomed to the so-called “curse of dimensionality”. For instance, in energy systems, system operators should solve optimal power flow, unit commitment, and transmission switching problems with tens of thousands of continuous and discrete variables in the day-ahead or real-time operation of the power networks. In control systems, a long-standing question is how to efficiently design a distributed controller with externally-enforced sparsity constraints that can optimally control a large-scale dynamical system. In machine learning, it is important to obtain a simple and parsimonious model of a collected set of high-dimensional data. In this talk, we briefly explain our recent results on how to exploit the underlying structure of these problems to efficiently solve them to optimality or near-optimality in a timely manner. In some cases, we resort to convex relaxation of the problem and introduce theoretical foundations that guarantee the exactness of the relaxation. In some other instances, we present our developed numerical algorithms that take advantage of the underlying sparsity of the problem and are highly efficient in practice; we solve instances of Graphical Lasso—a well-known conic optimization problem in machine learning—with more than 3.2 billion variables in less than 30 minutes on a normal computer, while other state-of-the-art methods cannot even start their iterations within 4 hours.

Biography: Salar Fattahi is a Ph.D. student in Industrial Engineering and Operations Research at UC Berkeley. He received the B.Sc. in Electrical Engineering from Sharif University of Technology, Iran and the M.Sc. in Electrical Engineering from Columbia University. Salar Fattahi’s work focuses on developing efficient and real-time algorithms to address the fundamental challenges in large-scale optimization problems. He has been invited to present his work at several federal agencies, including Federal Energy Regulatory Commission (FERC) and Defense Advanced Research Projects Agency (DARPA). Salar Fattahi is the recipient of Katta G. Murty best paper prize and the finalist for the best paper prize in American Control Conference. He is the co-author of 21 papers and has won several prestigious awards, including the best reviewer award from Power & Energy Society, Outstanding Graduate Student Instructor award, and Marshall-Oliver-Rosenberger fellowship award from UC Berkeley. He is a mentor in the Summer Undergraduate Program in Engineering Research at Berkeley (SUPERB) and Energy for Sustainable World (ESW) Program. He has served as chair and technical program committee member in different international conferences.

Tianyi Lin
Relaxed Wasserstein with Applications to GANs

We propose a novel class of statistical divergences called \textit{Relaxed Wasserstein} (RW) divergence. RW divergence generalizes Wasserstein divergence and is parametrized by a class of strictly convex and differentiable functions. We establish for RW divergence several probabilistic properties, which are critical for the success of Wasserstein divergence. In particular, we show that RW divergence is dominated by Total Variation (TV) and Wasserstein-L2 divergence and that RW divergence has continuity, differentiability and duality representation. Finally, we provide a nonasymptotic moment estimate and a concentration inequality for RW divergence.

Our experiments on the image generation task demonstrate that RW divergence is a suitable choice for GANs. Indeed, the performance of RWGANs with Kullback-Leibler (KL) divergence is very competitive with other state-of-the-art GANs approaches. Furthermore, RWGANs possess better convergence properties than the existing WGANs with competitive inception scores. To the best of our knowledge, our new conceptual framework is the first to not only provide the flexibility in designing effective GANs scheme, but also the possibility in studying different losses under a unified mathematical framework.

Sheng Liu
Data Analytics for Order Assignment in Last Mile Delivery

Food delivery market is rising across the world. In China, retailing giants
are providing a fast food delivery service from their physical stores. A key challenge for them is how to improve the on-time performance of their delivery services. Working with a major food delivery service provider in China, we develop a data-driven optimization framework to minimize the expected delivery delay. Driven by the real-world dataset, we propose a machine learning approach to predict the actual travel distance considering drivers’ behaviors. This approach is flexible and yields significantly better prediction accuracy than existing models that assume drivers are traveling along the shortest-distance routes.