Finite-Bit Quantization For Distributed Algorithms With Linear Convergence

• URL: http://arxiv.org/abs/2107.11304v1
• Date: Fri, 23 Jul 2021 15:31:31 GMT
• Title: Finite-Bit Quantization For Distributed Algorithms With Linear Convergence
• Authors: Chang-Shen Lee, Nicol\`o Michelusi, Gesualdo Scutari
• Abstract summary: We study distributed algorithms for (strongly convex) composite optimization problems over mesh networks subject to quantized communications. A new quantizer coupled with a communication-efficient encoding scheme is proposed, which efficiently implements the Biased Compression (BC-)rule. Numerical results validate our theoretical findings and show that distributed algorithms equipped with the proposed quantizer have more favorable communication complexity than algorithms using existing quantization rules.
• Score: 6.293059137498172
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: This paper studies distributed algorithms for (strongly convex) composite optimization problems over mesh networks, subject to quantized communications. Instead of focusing on a specific algorithmic design, we propose a black-box model casting distributed algorithms in the form of fixed-point iterates, converging at linear rate. The algorithmic model is coupled with a novel (random) Biased Compression (BC-)rule on the quantizer design, which preserves linear convergence. A new quantizer coupled with a communication-efficient encoding scheme is also proposed, which efficiently implements the BC-rule using a finite number of bits. This contrasts with most of existing quantization rules, whose implementation calls for an infinite number of bits. A unified communication complexity analysis is developed for the black-box model, determining the average number of bit required to reach a solution of the optimization problem within the required accuracy. Numerical results validate our theoretical findings and show that distributed algorithms equipped with the proposed quantizer have more favorable communication complexity than algorithms using existing quantization rules.

Related papers

• Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice [0.0]
  Variational quantum algorithms and, in particular, variants of the varational quantum eigensolver have been proposed to address optimization (CO) problems. We numerically investigate what this scaling result means in practice for solving CO problems using Max-Cut as a benchmark.
  arXiv  Detail & Related papers  (2024-08-06T09:57:34Z)
• An Efficient Algorithm for Clustered Multi-Task Compressive Sensing [60.70532293880842]
  Clustered multi-task compressive sensing is a hierarchical model that solves multiple compressive sensing tasks. The existing inference algorithm for this model is computationally expensive and does not scale well in high dimensions. We propose a new algorithm that substantially accelerates model inference by avoiding the need to explicitly compute these covariance matrices.
  arXiv  Detail & Related papers  (2023-09-30T15:57:14Z)
• End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
  We provide a complete quantum circuit-level description of the algorithm from problem input to problem output. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
  arXiv  Detail & Related papers  (2022-11-22T18:54:48Z)
• Ising formulation of integer optimization problems for utilizing quantum annealing in iterative improvement strategy [1.14219428942199]
  We propose an Ising formulation of integer optimization problems to utilize quantum annealing in the iterative improvement strategy. We analytically show that a first-order phase transition is successfully avoided for a fully connected ferro Potts model if the overlap between a ground state and a candidate solution exceeds a threshold.
  arXiv  Detail & Related papers  (2022-11-08T02:12:49Z)
• Quantum Sparse Coding [5.130440339897477]
  We develop a quantum-inspired algorithm for sparse coding. The emergence of quantum computers and Ising machines can potentially lead to more accurate estimations. We conduct numerical experiments with simulated data on Lightr's quantum-inspired digital platform.
  arXiv  Detail & Related papers  (2022-09-08T13:00:30Z)
• Towards Mixed-Precision Quantization of Neural Networks via Constrained Optimization [28.76708310896311]
  We present a principled framework to solve the mixed-precision quantization problem. We show that our method is derived in a principled way and much more computationally efficient.
  arXiv  Detail & Related papers  (2021-10-13T08:09:26Z)
• Joint Deep Reinforcement Learning and Unfolding: Beam Selection and Precoding for mmWave Multiuser MIMO with Lens Arrays [54.43962058166702]
  millimeter wave (mmWave) multiuser multiple-input multiple-output (MU-MIMO) systems with discrete lens arrays have received great attention. In this work, we investigate the joint design of a beam precoding matrix for mmWave MU-MIMO systems with DLA.
  arXiv  Detail & Related papers  (2021-01-05T03:55:04Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems [59.804810122136345]
  We propose a framework for deep-unfolding, where a general form of iterative algorithm induced deep-unfolding neural network (IAIDNN) is developed. An efficient IAIDNN based on the structure of the classic weighted minimum mean-square error (WMMSE) iterative algorithm is developed. We show that the proposed IAIDNN efficiently achieves the performance of the iterative WMMSE algorithm with reduced computational complexity.
  arXiv  Detail & Related papers  (2020-06-15T02:57:57Z)
• Quantum state preparation with multiplicative amplitude transduction [0.0]
  Two variants of the algorithm with different emphases are introduced. One variant uses fewer qubits and no controlled gates, while the other variant potentially requires fewer gates overall. A general analysis is given to estimate the number of qubits necessary to achieve a desired precision in the amplitudes of the computational basis states.
  arXiv  Detail & Related papers  (2020-06-01T14:36:50Z)
• Channel Assignment in Uplink Wireless Communication using Machine Learning Approach [54.012791474906514]
  This letter investigates a channel assignment problem in uplink wireless communication systems. Our goal is to maximize the sum rate of all users subject to integer channel assignment constraints. Due to high computational complexity, machine learning approaches are employed to obtain computational efficient solutions.
  arXiv  Detail & Related papers  (2020-01-12T15:54:20Z)

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.