Efficient Federated Optimization with Doubly Regularized Drift Correction

Core Concepts

Federated optimization can achieve communication reduction by exploiting similarities between client functions using regularized drift correction.

Abstract

The paper presents a framework called DANE+ that generalizes the DANE algorithm for distributed optimization with regularized drift correction. DANE+ allows the use of inexact local solvers and arbitrary control variates, and has more freedom to choose how to aggregate the local updates. The authors show that DANE+ can achieve deterministic communication reduction across different settings (strongly-convex, convex, non-convex) by exploiting the similarities between client functions, as measured by the Averaged Hessian Dissimilarity (δA) and Bounded Hessian Dissimilarity (δB).
The authors also propose a novel framework called FedRed that employs doubly regularized drift correction. FedRed enjoys the same communication reduction as DANE+ but has improved local computational complexity. Specifically, when using gradient descent as the local solver, FedRed may require fewer communication rounds than vanilla gradient descent without incurring additional computational overhead.
The key insights are:

Regularized drift correction is the key mechanism that allows communication reduction when the client functions exhibit certain similarities.
DANE, an established method in distributed optimization, already implicitly uses this technique and can achieve communication reduction in terms of δA.
By adding an additional regularizer, FedRed can further improve the local computational efficiency while retaining the communication reduction.

The authors provide comprehensive theoretical analysis for DANE+, FedRed, and their variants, establishing improved communication and computational complexities compared to prior work. Experiments on both synthetic and real datasets demonstrate the effectiveness of the proposed methods.

Stats

The smoothness parameter L for the client functions can be as small as the Lipschitz constant.
The Averaged Hessian Dissimilarity δA and Bounded Hessian Dissimilarity δB can be much smaller than L in practice.

Quotes

"Federated learning is a distributed optimization paradigm that allows training machine learning models across decentralized devices while keeping the data localized."
"FedAvg suffers from client drift which can hamper performance and increase communication costs over centralized methods."
"DANE can achieve the desired communication reduction under Hessian similarity constraints."
"FedRed enjoys the same communication reduction as DANE+ but has improved local computational complexity."

Key Insights Distilled From

Federated Optimization with Doubly Regularized Drift Correction

by Xiaowen Jian... at arxiv.org 04-15-2024

https://arxiv.org/pdf/2404.08447.pdf

Deeper Inquiries

How can the proposed methods be extended to handle client sampling and compression techniques to further reduce communication costs

The proposed methods can be extended to handle client sampling and compression techniques by incorporating these strategies into the optimization framework. Client sampling involves selecting a subset of clients to participate in each communication round, reducing the overall communication overhead. This can be achieved by modifying the averaging strategy to consider only a subset of client updates at each iteration. Additionally, compression techniques can be applied to reduce the size of the transmitted data between clients and the server, further decreasing communication costs. By integrating client sampling and compression into the optimization algorithms, the overall efficiency of the federated learning process can be significantly improved.

What are the potential limitations of the Hessian dissimilarity assumptions, and how can they be relaxed or generalized in future work

The Hessian dissimilarity assumptions, while useful for analyzing communication complexity in federated optimization, have certain limitations that need to be considered. One potential limitation is the strict requirement for similarity among the Hessians of individual functions, which may not always hold in practical scenarios. To address this limitation, future work could focus on relaxing the assumptions by considering more flexible measures of similarity, such as spectral properties or geometric characteristics of the Hessians. By generalizing the notion of dissimilarity, the algorithms can be applied to a wider range of scenarios where strict Hessian similarity may not be feasible.

Can the ideas of doubly regularized drift correction be applied to other distributed optimization settings beyond federated learning, such as multi-task learning or decentralized optimization

The ideas of doubly regularized drift correction can be applied to other distributed optimization settings beyond federated learning, such as multi-task learning or decentralized optimization. In multi-task learning, where multiple tasks are learned simultaneously, the concept of regularized drift correction can help mitigate the issue of task drift and improve convergence rates. By incorporating regularization terms that control the deviation of task-specific models from a shared global model, the optimization process can be stabilized and accelerated. Similarly, in decentralized optimization settings where multiple agents collaborate to solve a common objective, doubly regularized drift correction can enhance the efficiency of the optimization process by ensuring consistency among the local updates and the global model. This approach can lead to faster convergence and improved performance in decentralized optimization scenarios.