Quantum-Inspired Mean Field Probabilistic Model for Combinatorial Optimization Problems
- URL: http://arxiv.org/abs/2406.03502v1
- Date: Sat, 1 Jun 2024 01:53:11 GMT
- Title: Quantum-Inspired Mean Field Probabilistic Model for Combinatorial Optimization Problems
- Authors: Yuhan Huang, Siyuan Jin, Yichi Zhang, Ling Pan, Qiming Shao,
- Abstract summary: We develop a novel Quantum-Inspired Mean Field (QIMF) probabilistic model that approximates solutions to Quadratic Unconstrained Binary Optimization problems.
Our empirical studies demonstrate significant improvements in solution evaluation for large-scale problems of portfolio selection, the weighted maxcut problem, and the Ising model.
- Score: 15.435730759218776
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Combinatorial optimization problems are pivotal across many fields. Among these, Quadratic Unconstrained Binary Optimization (QUBO) problems, central to fields like portfolio optimization, network design, and computational biology, are NP-hard and require exponential computational resources. To address these challenges, we develop a novel Quantum-Inspired Mean Field (QIMF) probabilistic model that approximates solutions to QUBO problems with enhanced accuracy and efficiency. The QIMF model draws inspiration from quantum measurement principles and leverages the mean field probabilistic model. We incorporate a measurement grouping technique and an amplitude-based shot allocation strategy, both critical for optimizing cost functions with a polynomial speedup over traditional methods. Our extensive empirical studies demonstrate significant improvements in solution evaluation for large-scale problems of portfolio selection, the weighted maxcut problem, and the Ising model. Specifically, using S&P 500 data from 2022 and 2023, QIMF improves cost values by 152.8% and 12.5%, respectively, compared to the state-of-the-art baselines. Furthermore, when evaluated on increasingly larger datasets for QUBO problems, QIMF's scalability demonstrates its potential for large-scale QUBO challenges.
Related papers
- Differentiation Through Black-Box Quadratic Programming Solvers [16.543673072027136]
We introduce dQP, a modular framework that enables plug-and-play differentiation for any quadratic programming (QP) solver.
Our solution is based on the core theoretical insight that knowledge of the active constraint set at the QP optimum allows for explicit differentiation.
Our implementation, which will be made publicly available, interfaces with an existing framework that supports over 15 state-of-the-art QP solvers.
arXiv Detail & Related papers (2024-10-08T20:01:39Z) - Quantum Relaxation for Solving Multiple Knapsack Problems [7.003282322403712]
Combinatorial problems are a common challenge in business, requiring finding optimal solutions under specified constraints.
In this study, we investigate a hybrid quantum-classical method for constrained optimization problems.
Our proposed method relies on relaxations to local quantum Hamiltonians, defined through commutative maps.
arXiv Detail & Related papers (2024-04-30T11:40:07Z) - Optimizing Solution-Samplers for Combinatorial Problems: The Landscape
of Policy-Gradient Methods [52.0617030129699]
We introduce a novel theoretical framework for analyzing the effectiveness of DeepMatching Networks and Reinforcement Learning methods.
Our main contribution holds for a broad class of problems including Max-and Min-Cut, Max-$k$-Bipartite-Bi, Maximum-Weight-Bipartite-Bi, and Traveling Salesman Problem.
As a byproduct of our analysis we introduce a novel regularization process over vanilla descent and provide theoretical and experimental evidence that it helps address vanishing-gradient issues and escape bad stationary points.
arXiv Detail & Related papers (2023-10-08T23:39:38Z) - Exploring the synergistic potential of quantum annealing and gate model
computing for portfolio optimization [2.432141667343098]
We extend upon a study to use the best of both quantum annealing and gate-based quantum computing systems.
We conduct tests on real-world stock data from the Indian stock market on up to 64 assets.
Our findings suggest that hybrid annealer-gate quantum computing can be a valuable tool for portfolio managers seeking to optimize their investment portfolios.
arXiv Detail & Related papers (2023-05-02T15:02:13Z) - DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization [51.517956081644186]
We introduce a new graph-based diffusion framework, namely DIFUSCO.
Our framework casts NPC problems as discrete 0, 1-vector optimization problems.
For the MIS problem, DIFUSCO outperforms the previous state-of-the-art neural solver on the challenging SATLIB benchmark.
arXiv Detail & Related papers (2023-02-16T11:13:36Z) - Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning [89.31889875864599]
We propose an efficient model-based reinforcement learning algorithm for learning in multi-agent systems.
Our main theoretical contributions are the first general regret bounds for model-based reinforcement learning for MFC.
We provide a practical parametrization of the core optimization problem.
arXiv Detail & Related papers (2021-07-08T18:01:02Z) - Quantum variational optimization: The role of entanglement and problem
hardness [0.0]
We study the role of entanglement, the structure of the variational quantum circuit, and the structure of the optimization problem.
Our numerical results indicate an advantage in adapting the distribution of entangling gates to the problem's topology.
We find evidence that applying conditional value at risk type cost functions improves the optimization, increasing the probability of overlap with the optimal solutions.
arXiv Detail & Related papers (2021-03-26T14:06:54Z) - Modeling the Second Player in Distributionally Robust Optimization [90.25995710696425]
We argue for the use of neural generative models to characterize the worst-case distribution.
This approach poses a number of implementation and optimization challenges.
We find that the proposed approach yields models that are more robust than comparable baselines.
arXiv Detail & Related papers (2021-03-18T14:26:26Z) - Offline Model-Based Optimization via Normalized Maximum Likelihood
Estimation [101.22379613810881]
We consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points.
This problem setting emerges in many domains where function evaluation is a complex and expensive process.
We propose a tractable approximation that allows us to scale our method to high-capacity neural network models.
arXiv Detail & Related papers (2021-02-16T06:04:27Z) - High Dimensional Level Set Estimation with Bayesian Neural Network [58.684954492439424]
This paper proposes novel methods to solve the high dimensional Level Set Estimation problems using Bayesian Neural Networks.
For each problem, we derive the corresponding theoretic information based acquisition function to sample the data points.
Numerical experiments on both synthetic and real-world datasets show that our proposed method can achieve better results compared to existing state-of-the-art approaches.
arXiv Detail & Related papers (2020-12-17T23:21:53Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.