Jul 12, 2020
Key problems arising in web applications (with millions of users and thousands of items) can be formulated as Linear Programs (LP) involving billions to trillions of decision variables and constraints. Despite the appeal of LP formulations, solving problems at these scales is well beyond the capabilities of existing LP solvers. Often ad-hoc decomposition rules are used to approximately solve these LPs, which have limited optimality guarantees and lead to sub-optimal performance in practice. In this work, we propose a distributed solver that solves a perturbation of the LP problems at scale. We propose a gradient-based algorithm on the smooth dual of the perturbed LP with computational guarantees. The main workhorses of our algorithm are distributed matrix-vector multiplications (with load balancing) and efficient projection operations on distributed machines. Experiments on real-world data show that our proposed LP solver, ECLIPSE, can solve problems with 10^12 decision variables – well beyond the capabilities of current solvers.
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
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