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: Byzantine-Resilient Federated PCA and Low-Rank Column-Wise Sensing
This work considers two related learning problems in a federated attack-prone setting – federated principal com- ponents analysis (PCA) and federated low rank column-wise sensing (LRCS). The node attacks are assumed to be Byzan- tine which means that the attackers are omniscient and can collude. We introduce a novel provably Byzantine-resilient communication-efficient and sample-efficient algorithm, called Subspace-Median, that solves the PCA problem and is a key part of the solution for the LRCS problem. We also study the most natural Byzantine-resilient solution for federated PCA, a geometric median based modification of the federated power method, and explain why it is not useful. Our second main contribution is a complete alternating gradient descent (GD) and minimization (altGDmin) algorithm for Byzantine-resilient horizontally federated LRCS and sample and communication complexity guarantees for it. Extensive simulation experiments are used to corroborate our theoretical guarantees. The ideas that we develop for LRCS are easily extendable to other LR recovery problems as well.  more » « less
Award ID(s):
2341359
PAR ID:
10597122
Author(s) / Creator(s):
;
Publisher / Repository:
IEEE Transactions on Information Theory
Date Published:
Journal Name:
IEEE Transactions on Information Theory
Volume:
70
Issue:
11
ISSN:
0018-9448
Page Range / eLocation ID:
8001 to 8025
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, Proceedings of the 41st International Conference on Machine Learning (ICML) 2024)
    This work introduces a Byzantine resilient so- lution for learning low-dimensional linear rep- resentation. Our main contribution is the de- velopment of a provably Byzantine-resilient Alt- GDmin algorithm for solving this problem in a federated setting. We argue that our solution is sample-efficient, fast, and communication- efficient. In solving this problem, we also intro- duce a novel secure solution to the federated sub- space learning meta-problem that occurs in many different applications. 
    more » « less
  2. ; (, Proceedings of the 41st International Conference on Machine Learning (ICML) 2024)
    This work introduces a Byzantine resilient so- lution for learning low-dimensional linear rep- resentation. Our main contribution is the de- velopment of a provably Byzantine-resilient Alt- GDmin algorithm for solving this problem in a federated setting. We argue that our solution is sample-efficient, fast, and communication- efficient. In solving this problem, we also intro- duce a novel secure solution to the federated sub- space learning meta-problem that occurs in many different applications. 
    more » « less
  3. (, Foundations and Trends® in Optimization)
    This monograph describes a novel optimization solution framework, called alternating gradient descent (GD) and minimization (AltGDmin), that is useful for many problems for which alternating minimization (AltMin) is a popular solution. AltMin is a special case of the block coordinate descent algorithm that is useful for problems in which min- imization w.r.t one subset of variables keeping the other fixed is closed form or otherwise reliably solved. Denote the two blocks/subsets of the optimization variables Z by Zslow, Zfast, i.e., Z = {Zslow, Zfast}. AltGDmin is often a faster solution than AltMin for any problem for which (i) the minimization over one set of variables, Zfast, is much quicker than that over the other set, Zslow; and (ii) the cost function is differentiable w.r.t. Zslow. Often, the reason for one minimization to be quicker is that the problem is “decou- pled” for Zfast and each of the decoupled problems is quick to solve. This decoupling is also what makes AltGDmin communication-efficient for federated settings. Important examples where this assumption holds include (a) low rank column-wise compressive sensing (LRCS), low rank matrix completion (LRMC), (b) their outlier-corrupted extensions such as robust PCA, robust LRCS and robust LRMC; (c) phase retrieval and its sparse and low-rank model based extensions; (d) tensor extensions of many of these problems such as tensor LRCS and tensor completion; and (e) many partly discrete problems where GD does not apply – such as clustering, unlabeled sensing, and mixed linear regression. LRCS finds important applications in multi-task representation learning and few shot learning, federated sketching, and accelerated dynamic MRI. LRMC and robust PCA find important applications in recommender systems, computer vision and video analytics. 
    more » « less
  4. ; ; ; (, Proceedings of the ACM on Management of Data)
    Privacy and Byzantine resilience are two indispensable requirements for a federated learning (FL) system. Although there have been extensive studies on privacy and Byzantine security in their own track, solutions that consider both remain sparse. This is due to difficulties in reconciling privacy-preserving and Byzantine-resilient algorithms. In this work, we propose a solution to such a two-fold issue. We use our version of differentially private stochastic gradient descent (DP-SGD) algorithm to preserve privacy and then apply our Byzantine-resilient algorithms. We note that while existing works follow this general approach, an in-depth analysis on the interplay between DP and Byzantine resilience has been ignored, leading to unsatisfactory performance. Specifically, for the random noise introduced by DP, previous works strive to reduce its seemingly detrimental impact on the Byzantine aggregation. In contrast, we leverage the random noise to construct a first-stage aggregation that effectively rejects many existing Byzantine attacks. Moreover, based on another property of our DP variant, we form a second-stage aggregation which provides a final sound filtering. Our protocol follows the principle of co-designing both DP and Byzantine resilience. We provide both theoretical proof and empirical experiments to show our protocol is effective: retaining high accuracy while preserving the DP guarantee and Byzantine resilience. Compared with the previous work, our protocol 1) achieves significantly higher accuracy even in a high privacy regime; 2) works well even when up to 90% distributive workers are Byzantine. 
    more » « less
  5. ; (, IEEE Transactions on Information Theory)
    In this work, we develop and analyze a novel Gradient Descent (GD) based solution, called Alternating GD and Minimization (AltGDmin), for efficiently solving the low rank matrix completion (LRMC) in a federated setting. Here “efficient” refers to communication-, computation- and sample- efficiency. LRMC involves recovering an n × q rank-r matrix X⋆ from a subset of its entries when r ≪ min(n, q). Our theoretical bounds on the sample complexity and iteration complexity of AltGDmin imply that it is the most communication-efficient solution while also been one of the most computation- and sample- efficient ones. We also extend our guarantee to the noisy LRMC setting. In addition, we show how our lemmas can be used to provide an improved sample complexity guarantee for the Alternating Minimization (AltMin) algorithm for LRMC. AltMin is one of the fastest centralized solutions for LRMC; with AltGDmin having comparable time cost even for the centralized setting. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email