skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Communication-Efficient Projection-Free Algorithm for Nonconvex Constrained Learning Models
Recently decentralized optimization attracts much attention in machine learning because it is more communication-efficient than the centralized fashion. Quantization is a promising method to reduce the communication cost via cutting down the budget of each single communication using the gradient compression. To further improve the communication efficiency, more recently, some quantized decentralized algorithms have been studied. However, the quantized decentralized algorithm for nonconvex constrained machine learning problems is still limited. Frank-Wolfe (a.k.a., conditional gradient or projection-free) method is very efficient to solve many constrained optimization tasks, such as low-rank or sparsity-constrained models training. In this paper, to fill the gap of decentralized quantized constrained optimization, we propose a novel communication-efficient Decentralized Quantized Stochastic Frank-Wolfe (DQSFW) algorithm for non-convex constrained learning models. We first design a new counterexample to show that the vanilla decentralized quantized stochastic Frank-Wolfe algorithm usually diverges. Thus, we propose DQSFW algorithm with the gradient tracking technique to guarantee the method will converge to the stationary point of non-convex optimization safely. In our theoretical analysis, we prove that to achieve the stationary point our DQSFW algorithm achieves the same gradient complexity as the standard stochastic Frank-Wolfe and centralized Frank-Wolfe algorithms, but has much less communication cost. Experiments on matrix completion and model compression applications demonstrate the efficiency of our new algorithm.  more » « less
Award ID(s):
2040588
PAR ID:
10289670
Author(s) / Creator(s):
Date Published:
Journal Name:
35th AAAI Conference on Artificial Intelligence (AAAI 2021)
Page Range / eLocation ID:
10405-10413
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, IEEE International Symposium on Information Theory (ISIT))
    null (Ed.)
    In this paper, we study communication-efficient decentralized training of large-scale machine learning models over a network. We propose and analyze SQuARM-SGD, a decentralized training algorithm, employing momentum and compressed communication between nodes regulated by a locally computable triggering rule. In SQuARM-SGD, each node performs a fixed number of local SGD (stochastic gradient descent) steps using Nesterov's momentum and then sends sparisified and quantized updates to its neighbors only when there is a significant change in its model parameters since the last time communication occurred. We provide convergence guarantees of our algorithm for strongly-convex and non-convex smooth objectives. We believe that ours is the first theoretical analysis for compressed decentralized SGD with momentum updates. We show that SQuARM-SGD converges at rate O(1/nT) for strongly-convex objectives, while for non-convex objectives it converges at rate O(1/√nT), thus matching the convergence rate of \emphvanilla distributed SGD in both these settings. We corroborate our theoretical understanding with experiments and compare the performance of our algorithm with the state-of-the-art, showing that without sacrificing much on the accuracy, SQuARM-SGD converges at a similar rate while saving significantly in total communicated bits. 
    more » « less
  2. ; (, IMA Journal of Numerical Analysis)
    Abstract We study stochastic projection-free methods for constrained optimization of smooth functions on Riemannian manifolds, i.e., with additional constraints beyond the parameter domain being a manifold. Specifically, we introduce stochastic Riemannian Frank–Wolfe (Fw) methods for nonconvex and geodesically convex problems. We present algorithms for both purely stochastic optimization and finite-sum problems. For the latter, we develop variance-reduced methods, including a Riemannian adaptation of the recently proposed Spider technique. For all settings, we recover convergence rates that are comparable to the best-known rates for their Euclidean counterparts. Finally, we discuss applications to two classic tasks: the computation of the Karcher mean of positive definite matrices and Wasserstein barycenters for multivariate normal distributions. For both tasks, stochastic Fw methods yield state-of-the-art empirical performance. 
    more » « less
  3. (, International Conference on Machine Learning)
    In modern machine learning systems, distributed algorithms are deployed across applications to ensure data privacy and optimal utilization of computational resources. This work offers a fresh perspective to model, analyze, and design distributed optimization algorithms through the lens of stochastic multi-rate feedback control. We show that a substantial class of distributed algorithms—including popular Gradient Tracking for decentralized learning, and FedPD and Scaffold for federated learning—can be modeled as a certain discrete-time stochastic feedback-control system, possibly with multiple sampling rates. This key observation allows us to develop a generic framework to analyze the convergence of the entire algorithm class. It also enables one to easily add desirable features such as differential privacy guarantees, or to deal with practical settings such as partial agent participation, communication compression, and imperfect communication in algorithm design and analysis. 
    more » « less
  4. ; ; ; ; (, Journal of machine learning research)
    Bilevel optimization is one of the fundamental problems in machine learning and optimization. Recent theoretical developments in bilevel optimization focus on finding the firstorder stationary points for nonconvex-strongly-convex cases. In this paper, we analyze algorithms that can escape saddle points in nonconvex-strongly-convex bilevel optimization. Specifically, we show that the perturbed approximate implicit differentiation (AID) with a warm start strategy finds an -approximate local minimum of bilevel optimization in ̃O(−2) iterations with high probability. Moreover, we propose an inexact NEgativecurvature-Originated-from-Noise Algorithm (iNEON), an algorithm that can escape saddle point and find local minimum of stochastic bilevel optimization. As a by-product, we provide the first nonasymptotic analysis of perturbed multi-step gradient descent ascent (GDmax) algorithm that converges to local minimax point for minimax problems. 
    more » « less
  5. ; (, ArXivorg)
    null (Ed.)
    We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire feasible set are avoided, in stark contrast to projected gradient methods or the Frank-Wolfe method, and (ii) iterates are allowed to become infeasible, which differs from active set or feasible direction methods, where the descent motion stops as soon as a new constraint is encountered. The resulting algorithmic procedure is simple to implement even when constraints are nonlinear, and is suitable for large-scale constrained optimization problems in which the feasible set fails to have a simple structure. The key underlying idea is that constraints are expressed in terms of velocities instead of positions, which has the algorithmic consequence that optimizations over feasible sets at each iteration are replaced with optimizations over local, sparse convex approximations. The result is a simplified suite of algorithms and an expanded range of possible applications in machine learning. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email