Characterization of Locality in Spin States and Forced Moves for Optimizations

• URL: http://arxiv.org/abs/2312.02544v2
• Date: Wed, 14 Feb 2024 10:13:37 GMT
• Title: Characterization of Locality in Spin States and Forced Moves for Optimizations
• Authors: Yoshiki Sato, Makiko Konoshima, Hirotaka Tamura, Jun Ohkubo
• Abstract summary: In optimization problems, the existence of local minima in energy landscapes is problematic to use to seek the global minimum. We develop an algorithm to get out of the local minima efficiently while it does not yield the exact samplings. As the proposed algorithm is based on a rejection-free algorithm, the computational cost is low.
• Score: 0.36868085124383626
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Ising formulations are widely utilized to solve combinatorial optimization problems, and a variety of quantum or semiconductor-based hardware has recently been made available. In combinatorial optimization problems, the existence of local minima in energy landscapes is problematic to use to seek the global minimum. We note that the aim of the optimization is not to obtain exact samplings from the Boltzmann distribution, and there is thus no need to satisfy detailed balance conditions. In light of this fact, we develop an algorithm to get out of the local minima efficiently while it does not yield the exact samplings. For this purpose, we utilize a feature that characterizes locality in the current state, which is easy to obtain with a type of specialized hardware. Furthermore, as the proposed algorithm is based on a rejection-free algorithm, the computational cost is low. In this work, after presenting the details of the proposed algorithm, we report the results of numerical experiments that demonstrate the effectiveness of the proposed feature and algorithm.

Related papers

• Using Differential Evolution to avoid local minima in Variational Quantum Algorithms [0.0]
  Variational Quantum Algorithms (VQAs) are among the most promising NISQ-era algorithms for harnessing quantum computing. Our goal in this paper is to study alternative optimization methods that can avoid or reduce the effect of local minima and barren plateau problems.
  arXiv  Detail & Related papers  (2023-03-21T20:31:06Z)
• A Particle-based Sparse Gaussian Process Optimizer [5.672919245950197]
  We present a new swarm-swarm-based framework utilizing the underlying dynamical process of descent. The biggest advantage of this approach is greater exploration around the current state before deciding descent descent.
  arXiv  Detail & Related papers  (2022-11-26T09:06:15Z)
• Quantization-Based Optimization: Alternative Stochastic Approximation of Global Optimization [0.0]
  We propose a global optimization algorithm based on quantizing the energy level of an objective function in an NP-hard problem. Numerical experiments show that the proposed algorithm outperforms conventional learning methods in solving NP-hard optimization problems.
  arXiv  Detail & Related papers  (2022-11-08T03:01:45Z)
• Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization [28.862321453597918]
  Non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed proximal-gradient algorithm with random reshuffling to solve the problem.
  arXiv  Detail & Related papers  (2021-11-06T07:29:55Z)
• Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex Decentralized Optimization Over Time-Varying Networks [79.16773494166644]
  We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network. We design two optimal algorithms that attain these lower bounds. We corroborate the theoretical efficiency of these algorithms by performing an experimental comparison with existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-06-08T15:54:44Z)
• Community detection using fast low-cardinality semidefinite programming [94.4878715085334]
  We propose a new low-cardinality algorithm that generalizes the local update to maximize a semidefinite relaxation derived from Leiden-k-cut. This proposed algorithm is scalable, outperforms state-of-the-art algorithms, and outperforms in real-world time with little additional cost.
  arXiv  Detail & Related papers  (2020-12-04T15:46:30Z)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• Sequential Subspace Search for Functional Bayesian Optimization Incorporating Experimenter Intuition [63.011641517977644]
  Our algorithm generates a sequence of finite-dimensional random subspaces of functional space spanned by a set of draws from the experimenter's Gaussian Process. Standard Bayesian optimisation is applied on each subspace, and the best solution found used as a starting point (origin) for the next subspace. We test our algorithm in simulated and real-world experiments, namely blind function matching, finding the optimal precipitation-strengthening function for an aluminium alloy, and learning rate schedule optimisation for deep networks.
  arXiv  Detail & Related papers  (2020-09-08T06:54:11Z)
• Aligning Partially Overlapping Point Sets: an Inner Approximation Algorithm [80.15123031136564]
  We propose a robust method to align point sets where there is no prior information about the value of the transformation. Our algorithm does not need regularization on transformation, and thus can handle the situation where there is no prior information about the values of the transformations. Experimental results demonstrate the better robustness of the proposed method over state-of-the-art algorithms.
  arXiv  Detail & Related papers  (2020-07-05T15:23:33Z)
• Second-Order Guarantees in Centralized, Federated and Decentralized Nonconvex Optimization [64.26238893241322]
  Simple algorithms have been shown to lead to good empirical results in many contexts. Several works have pursued rigorous analytical justification for studying non optimization problems. A key insight in these analyses is that perturbations play a critical role in allowing local descent algorithms.
  arXiv  Detail & Related papers  (2020-03-31T16:54:22Z)

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.