Curriculum-Learning and Quantum-Inspired Approaches to Large-scale Optimization with Applications to Quantum Sensing and Computing
Abstract
In many real-world optimization applications, instances of the same type of optimization problem are repeatedly solved on a regularbasis, with the same problem structure and differing mainly in their data. That is, values of the coefficients in the objective function or constraints can be thought of as being sampled from the same underlying distribution. In principle, there exists a mapping from the problem data space to the space of the optimum solutions. In diverse scientific and commercial settings, one may be willingto invest in upfront, offline computation and learning of such a mapping so as to speed up real-time decision-making and improve its quality. Motivated by this, the proposed research program develops a new framework for solving optimization problems. Under such aframework, for a given class of optimization problems, first, a deep neural network is trained offline; then during the online stage, a given problem instance is solved by feed-forward execution of the trained network. The advantages of such an approach are two folds: (1) The performance can approach the optimum for each problem instance; and (2) The main computational burden corresponding totraining is moved offline, and the complexity of the online computation corresponding to solving different problem instances is low. We explore the potential of neural networks to learn the solutions of a target family of continuous or combinatorial optimization problems. In order for the trained network to attain the optimum and to speed up the training process, we propose to take a principled approach based on the notion that learning is more efficient when simple tasks are learned before more complex ones, and investigate various curriculum learning techniques. The learned neural network#s forward pass produces near-optimal solutions, thereby affording significant computational savings compared to existing optimization solvers. We will apply the proposed framework to a number of applications foundin quantum information processing that involve large-scale optimization, including quantum detection, quantum estimation, quantum machine learning, and quantum circuit simulation. Moreover, motivated by a structural connection between quantum wave functions and functions realizable by deep neural networks, we also propose a quantum-inspired methodology for the design of deep networks used in these optimization tasks based on entanglement measures. This abstract is publicly releasable.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 11, 2024
- Source ID
- N000142412212
Entities
People
- Xiaodong Wang
Organizations
- Office of Naval Research
- Trustees of Columbia University in the City of New York
- United States Navy