Nonequilibrium Monte Carlo for unfreezing variables in hard combinatorial optimization

• URL: http://arxiv.org/abs/2111.13628v1
• Date: Fri, 26 Nov 2021 17:45:32 GMT
• Title: Nonequilibrium Monte Carlo for unfreezing variables in hard combinatorial optimization
• Authors: Masoud Mohseni, Daniel Eppens, Johan Strumpfer, Raffaele Marino, Vasil Denchev, Alan K. Ho, Sergei V. Isakov, Sergio Boixo, Federico Ricci-Tersenghi, Hartmut Neven
• Abstract summary: We introduce a quantum-inspired family of nonlocal Nonequilibrium Monte Carlo (NMC) algorithms by developing an adaptive gradient-free strategy. We observe significant speedup and robustness over both specialized solvers and generic solvers.
• Score: 1.1783108699768
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Optimizing highly complex cost/energy functions over discrete variables is at the heart of many open problems across different scientific disciplines and industries. A major obstacle is the emergence of many-body effects among certain subsets of variables in hard instances leading to critical slowing down or collective freezing for known stochastic local search strategies. An exponential computational effort is generally required to unfreeze such variables and explore other unseen regions of the configuration space. Here, we introduce a quantum-inspired family of nonlocal Nonequilibrium Monte Carlo (NMC) algorithms by developing an adaptive gradient-free strategy that can efficiently learn key instance-wise geometrical features of the cost function. That information is employed on-the-fly to construct spatially inhomogeneous thermal fluctuations for collectively unfreezing variables at various length scales, circumventing costly exploration versus exploitation trade-offs. We apply our algorithm to two of the most challenging combinatorial optimization problems: random k-satisfiability (k-SAT) near the computational phase transitions and Quadratic Assignment Problems (QAP). We observe significant speedup and robustness over both specialized deterministic solvers and generic stochastic solvers. In particular, for 90% of random 4-SAT instances we find solutions that are inaccessible for the best specialized deterministic algorithm known as Survey Propagation (SP) with an order of magnitude improvement in the quality of solutions for the hardest 10% instances. We also demonstrate two orders of magnitude improvement in time-to-solution over the state-of-the-art generic stochastic solver known as Adaptive Parallel Tempering (APT).

Related papers

• Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling [0.0]
  This study proposes a different approach that integrates gradient-based update through continuous relaxation, combined with Quasi-Quantum Annealing (QQA) Numerical experiments demonstrate that our method is a competitive general-purpose solver, achieving performance comparable to iSCO and learning-based solvers.
  arXiv  Detail & Related papers  (2024-09-02T12:55:27Z)
• Analysis of the Non-variational Quantum Walk-based Optimisation Algorithm [0.0]
  This paper introduces in detail a non-variational quantum algorithm designed to solve a wide range of optimisation problems. The algorithm returns optimal and near-optimal solutions from repeated preparation and measurement of an amplified state.
  arXiv  Detail & Related papers  (2024-07-29T13:54:28Z)
• Federated Conditional Stochastic Optimization [110.513884892319]
  Conditional optimization has found in a wide range of machine learning tasks, such as in-variant learning tasks, AUPRC, andAML. This paper proposes algorithms for distributed federated learning.
  arXiv  Detail & Related papers  (2023-10-04T01:47:37Z)
• Numerical Methods for Convex Multistage Stochastic Optimization [86.45244607927732]
  We focus on optimisation programming (SP), Optimal Control (SOC) and Decision Processes (MDP) Recent progress in solving convex multistage Markov problems is based on cutting planes approximations of the cost-to-go functions of dynamic programming equations. Cutting plane type methods can handle multistage problems with a large number of stages, but a relatively smaller number of state (decision) variables.
  arXiv  Detail & Related papers  (2023-03-28T01:30:40Z)
• Constrained mixers for the quantum approximate optimization algorithm [55.41644538483948]
  We present a framework for constructing mixing operators that restrict the evolution to a subspace of the full Hilbert space. We generalize the "XY"-mixer designed to preserve the subspace of "one-hot" states to the general case of subspaces given by a number of computational basis states. Our analysis also leads to valid Trotterizations for "XY"-mixer with fewer CX gates than is known to date.
  arXiv  Detail & Related papers  (2022-03-11T17:19:26Z)
• Sampling diverse near-optimal solutions via algorithmic quantum annealing [0.3506539188356145]
  One of the main open problems is the lack of ergodicity, or mode collapse, for typical Monte Carlo solvers. Here, we introduce a new diversity measure for quantifying the number of independent approximate solutions for NP-hard optimization problems.
  arXiv  Detail & Related papers  (2021-10-20T13:33:37Z)
• Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling [86.85697555068168]
  Two-stage algorithmic optimization plays a critical role in various engineering and scientific applications. There still lack efficient algorithms, especially when the long-term and short-term variables are coupled in the constraints. We show that PDD-SSCA can achieve superior performance over existing solutions.
  arXiv  Detail & Related papers  (2021-05-05T03:36:00Z)
• Adaptive variational quantum eigensolvers for highly excited states [4.038971004196936]
  Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization. We propose an adaptive variational algorithm, adaptive VQE-X, that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian $H$.
  arXiv  Detail & Related papers  (2021-04-26T15:03:51Z)
• Stochastic Saddle-Point Optimization for Wasserstein Barycenters [69.68068088508505]
  We consider the populationimation barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. We employ the structure of the problem and obtain a convex-concave saddle-point reformulation of this problem. In the setting when the distribution of random probability measures is discrete, we propose an optimization algorithm and estimate its complexity.
  arXiv  Detail & Related papers  (2020-06-11T19:40:38Z)
• Hardness of Random Optimization Problems for Boolean Circuits, Low-Degree Polynomials, and Langevin Dynamics [78.46689176407936]
  We show that families of algorithms fail to produce nearly optimal solutions with high probability. For the case of Boolean circuits, our results improve the state-of-the-art bounds known in circuit complexity theory.
  arXiv  Detail & Related papers  (2020-04-25T05:45:59Z)
• Bayesian optimization of variable-size design space problems [0.0]
  Two alternative Bayesian Optimization-based approaches are proposed in order to solve this type of optimization problems. The first approach consists in a budget allocation strategy allowing to focus the computational budget on the most promising design sub-spaces. The second approach, instead, is based on the definition of a kernel function allowing to compute the covariance between samples characterized by partially different sets of variables.
  arXiv  Detail & Related papers  (2020-03-06T16:30:44Z)

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.