Related papers: Learning to Solve Combinatorial Optimization under…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
Combinatorial optimization (CO) aims to efficiently find the best solution to NP-hard problems ranging from statistical physics to social media marketing. A wide range of CO applications can benefit from local search methods because they…
In most optimization problems, users have a clear understanding of the function to optimize (e.g., minimize the makespan for scheduling problems). However, the constraints may be difficult to state and their modelling often requires…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
The backpropagation of error algorithm used to train deep neural networks has been fundamental to the successes of deep learning. However, it requires sequential backward updates and non-local computations, which make it challenging to…
We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…
This paper focuses on integrating the networks and adversarial training into constrained optimization problems to develop a framework algorithm for constrained optimization problems. For such problems, we first transform them into minimax…
Combinatorial optimization (CO) underlies decision-making from logistics to chip design, where infeasible solutions are operationally unusable and small quality gains translate into substantial economic value. Recent work uses large…
The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for…
Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
This paper addresses Online Convex Optimization (OCO) problems where the constraints have additive perturbations that (i) vary over time and (ii) are not known at the time to make a decision. Perturbations may not be i.i.d. generated and…
The design of complex engineering systems leads to solving very large optimization problems involving different disciplines. Strategies allowing disciplines to optimize in parallel by providing sub-objectives and splitting the problem into…
We consider Constrained Online Convex Optimization (COCO) with adversarially chosen constraints. At each round, the learner chooses an action before observing the loss and constraint function for that round. The goal is to achieve small…
Unsupervised neural combinatorial optimization (NCO) offers an appealing alternative to supervised approaches by training learning-based solvers without ground-truth solutions, directly minimizing instance objectives and constraint…
Iterative methods have led to better understanding and solving problems such as missing sampling, deconvolution, inverse systems, impulsive and Salt and Pepper noise removal problems. However, the challenges such as the speed of convergence…
In the field of quantum computing, combinatorial optimization problems are typically addressed using QUBO (Quadratic Unconstrained Binary Optimization) solvers. However, these solvers are often insufficient for tackling higher-order…
Combinatorial optimization problems like the Traveling Salesman Problem are critical in industry yet NP-hard. Neural Combinatorial Optimization has shown promise, but its reliance on online reinforcement learning (RL) hampers deployment and…
This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. The main tools mainly come from variational and…
In this paper, we propose a machine learning (ML) method to learn how to solve a generic constrained continuous optimization problem. To the best of our knowledge, the generic methods that learn to optimize, focus on unconstrained…