Related papers: ReLU Networks as Surrogate Models in Mixed-Integer…

Verifying the robustness property of a general Rectified Linear Unit (ReLU) network is an NP-complete problem [Katz, Barrett, Dill, Julian and Kochenderfer CAV17]. Although finding the exact minimum adversarial distortion is hard, giving a…

Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…

We solve large-scale mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This is motivated by the MILPs being able to model problems in multi-agent autonomy, e.g., task assignment problems and…

The robustness of deep neural networks has received significant interest recently, especially when being deployed in safety-critical systems, as it is important to analyze how sensitive the model output is under input perturbations. While…

By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers…

Rectified Linear Units (ReLUs) have been shown to ameliorate the vanishing gradient problem, allow for efficient backpropagation, and empirically promote sparsity in the learned parameters. They have led to state-of-the-art results in a…

We study the Rectified Linear Unit (ReLU) dual, an existing dual formulation for stochastic programs that reformulates non-anticipativity constraints using ReLU functions to generate tight, non-convex, and mixed-integer representable cuts.…

Mixed-integer linear programs (MILPs) are extensively used to model practical problems such as planning and scheduling. A prominent method for solving MILPs is large neighborhood search (LNS), which iteratively seeks improved solutions…

While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating…

Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this…

Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant…

In this paper, we focus on fully connected deep neural networks utilizing the Rectified Linear Unit (ReLU) activation function for nonparametric estimation. We derive non-asymptotic bounds that lead to convergence rates, addressing both…

Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…

In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing. Meanwhile, the structure…

Deploying deep learning models, comprising of non-linear combination of millions, even billions, of parameters is challenging given the memory, power and compute constraints of the real world. This situation has led to research into model…

In spite of finite dimension ReLU neural networks being a consistent factor behind recent deep learning successes, a theory of feature learning in these models remains elusive. Currently, insightful theories still rely on assumptions…

Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…

Influence diagrams represent decision-making problems with interdependencies between random events, decisions, and consequences. Traditionally, they have been solved using algorithms that determine the expected utility-maximizing decision…

Compared to legacy wavelength division multiplexing networks, elastic optical networks (EON) have added flexibility to network deployment and management. EONs can include previously available technology, such as signal regeneration and…

Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit…