University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）；Mila, Polytechnique Montréal（蒙特利尔综合理工学院Mila）；University of Toronto（多伦多大学）；CERC, Polytechnique Montréal（蒙特利尔综合理工学院CERC）；Mila, Université de Montréal（蒙特利尔大学Mila）
Prateek Gupta, Maxime Gasse, Elias B. Khalil, M. Pawan Kumar, Andrea Lodi, Yoshua Bengio
备注：
34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada
A recent Graph Neural Network (GNN) approach for learning to branch has been shown to successfully reduce the running time of branch-and-bound algorithms for Mixed Integer Linear Programming (MILP). While the GNN relies on a GPU for inference, MILP solvers are purely CPU-based. This severely limits its application as many practitioners may not have access to high-end GPUs. In this work, we ask two key questions. First, in a more realistic setting where only a CPU is available, is the GNN model still competitive? Second, can we devise an alternate computationally inexpensive model that retains the predictive power of the GNN architecture? We answer the first question in the negative, and address the second question by proposing a new hybrid architecture for efficient branching on CPU machines. The proposed architecture combines the expressive power of GNNs with computationally inexpensive multi-layer perceptrons (MLP) for branching. We evaluate our methods on four classes of MILP problems, and show that they lead to up to 26% reduction in solver running time compared to state-of-the-art methods without a GPU, while extrapolating to harder problems than it was trained on. The code for this project is publicly available at https://github.com/pg2455/Hybrid-learn2branch.
University of Toronto（多伦多大学）；Polytechnique Montréal（蒙特利尔理工学院）；University of Oxford（牛津大学）；Mila（米拉（魁北克人工智能研究所））；Université de Montréal（蒙特利尔大学）；The Alan Turing Institute（阿兰·图灵研究所）；Cornell Tech（康奈尔科技校区）；Technion - IIT（以色列理工学院）
The expressive and computationally inexpensive bipartite Graph Neural Networks (GNN) have been shown to be an important component of deep learning based Mixed-Integer Linear Program (MILP) solvers. Recent works have demonstrated the effectiveness of such GNNs in replacing the branching (variable selection) heuristic in branch-and-bound (B&B) solvers. These GNNs are trained, offline and on a collection of MILPs, to imitate a very good but computationally expensive branching heuristic, strong branching. Given that B&B results in a tree of sub-MILPs, we ask (a) whether there are strong dependenci…
Branch and Bound (B&B) is the exact tree search method typically used to solve Mixed-Integer Linear Programming problems (MILPs). Learning branching policies for MILP has become an active research area, with most works proposing to imitate the strong branching rule and specialize it to distinct classes of problems. We aim instead at learning a policy that generalizes across heterogeneous MILPs: our main hypothesis is that parameterizing the state of the B&B search tree can aid this type of generalization. We propose a novel imitation learning framework, and introduce new input features and arc…
Delft University of Technology（代尔夫特理工大学）；Polytechnique Montréal（蒙特利尔工程学院）；Mila（米拉人工智能研究所）；Jacobs Technion-Cornell Institute（雅各布斯特克尼恩-康奈尔研究所）；Cornell Tech（康奈尔科技校区）；Technion - IIT（以色列理工学院）
State-of-the-art Mixed Integer Linear Program (MILP) solvers combine systematic tree search with a plethora of hard-coded heuristics, such as the branching rule. The idea of learning branching rules from data has received increasing attention recently, and promising results have been obtained by learning fast approximations of the strong branching expert. In this work, we instead propose to learn branching rules from scratch via Reinforcement Learning (RL). We revisit the work of Etheve et al. (2020) and propose tree Markov Decision Processes, or tree MDPs, a generalization of temporal MDPs th…
Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search tree of increasingly constrained sub-problems. In practice, its solving time performance is dependent on heuristics, such as the choice of the next variable to constrain ('branching'). Recently, machine learning (ML) has emerged as a promising paradigm for branching. However, prior works have struggled to apply reinforcement learning (RL), citing sparse rewar…
University of Toronto（多伦多大学）；University of Waterloo（滑铁卢大学）；Borealis AI（北极光人工智能）
We present a novel hybrid algorithm for training Deep Neural Networks that combines the state-of-the-art Gradient Descent (GD) method with a Mixed Integer Linear Programming (MILP) solver, outperforming GD and variants in terms of accuracy, as well as resource and data efficiency for both regression and classification tasks. Our GD+Solver hybrid algorithm, called GDSolver, works as follows: given a DNN $D$ as input, GDSolver invokes GD to partially train $D$ until it gets stuck in a local minima, at which point GDSolver invokes an MILP solver to exhaustively search a region of the loss landsca…
Islamic Azad University（伊斯兰阿扎德大学）；Yonsei University（延世大学）
The banking industry is very important for an economic cycle of each country and provides some quality of services for us. With the advancement in technology and rapidly increasing of the complexity of the business environment, it has become more competitive than the past so that efficiency analysis in the banking industry attracts much attention in recent years. From many aspects, such analyses at the branch level are more desirable. Evaluating the branch performance with the purpose of eliminating deficiency can be a crucial issue for branch managers to measure branch efficiency. This work n…
DBHN-Net: Dual-Branch Hybrid Neural Network For Low-Complexity Monaural Speech Enhancement
State Key Laboratory of Opto-Electronic Information Acquisition and Protection Technology, (School of Computer Science and Technology), Anhui University（光电信息获取与防护技术国家重点实验室（计算机科学与技术学院），安徽大学）；China Telecom Artificial Intelligence Technology (Beijing) Co., Ltd（中国电信人工智能技术（北京）有限公司）；Institute of Acoustics, University of Chinese Academy of Sciences（中国科学院声学研究所）；Institute of Artificial Intelligence (TeleAI), China Telecom, China（人工智能研究所（TeleAI），中国电信，中国）
