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arXiv 2021年

作者： Alomrani, Mohammad Ali Moravej, Reza Khalil, Elias B. Department of Electrical & Computer Engineering University of Toronto Canada Department of Mechanical & Industrial Engineering SCALE AI Research in Data-Driven Algorithms for Modern Supply Chains University of Toronto Canada

The challenge in the widely applicable online matching problem lies in making irrevocable assignments while there is uncertainty about future inputs. Most theoretically-grounded policies are myopic or greedy in nature. In real-world applications where the matching process is repeated on a regular basis, the underlying data distribution can be leveraged for better decision-making. We present an end-to-end Reinforcement Learning framework for deriving better matching policies based on trial-and-error on historical data. We devise a set of neural network architectures, design feature representations, and empirically evaluate them across two online matching problems: Edge-Weighted Online Bipartite Matching and Online Submodular Bipartite Matching. We show that most of the learning approaches perform consistently better than classical baseline algorithms on four synthetic and real-world datasets. On average, our proposed models improve the matching quality by 3-10% on a variety of synthetic and real-world datasets. Our code is publicly available at https://***/lyeskhalil/CORL. © 2021, CC BY.

关键词： Reinforcement learning

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Finding Backdoors to Integer Programs: A Monte Carlo Tree Search Framework

arXiv

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arXiv 2021年

作者： Khalil, Elias B. Vaezipoor, Pashootan Dilkina, Bistra Department of Mechanical & Industrial Engineering University of Toronto Canada Scale AI Research Chair in Data-Driven Algorithms for Modern Supply Chains Department of Computer Science University of Toronto Canada Vector Institute for Artificial Intelligence Canada Department of Computer Science University of Southern California United States

In Mixed Integer Linear Programming (MIP), a (strong) backdoor is a "small" subset of an instance's integer variables with the following property: in a branch-and-bound procedure, the instance can be solved to global optimality by branching only on the variables in the backdoor. Constructing datasets of pre-computed backdoors for widely used MIP benchmark sets or particular problem families can enable new questions around novel structural properties of a MIP, or explain why a problem that is hard in theory can be solved efficiently in practice. Existing algorithms for finding backdoors rely on sampling candidate variable subsets in various ways, an approach which has demonstrated the existence of backdoors for some instances from MIPLIB2003 and MIPLIB2010. However, these algorithms fall short of consistently succeeding at the task due to an imbalance between exploration and exploitation. We propose BaMCTS, a Monte Carlo Tree Search framework for finding backdoors to MIPs. Extensive algorithmic engineering, hybridization with traditional MIP concepts, and close integration with the CPLEX solver have enabled our method to outperform baselines on MIPLIB2017 instances, finding backdoors more frequently and more efficiently. © 2021, CC BY.

关键词： Integer programming

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