FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Data (2005.11418v3)

Abstract: Federated Learning (FL) has become a popular paradigm for learning from distributed data. To effectively utilize data at different devices without moving them to the cloud, algorithms such as the Federated Averaging (FedAvg) have adopted a "computation then aggregation" (CTA) model, in which multiple local updates are performed using local data, before sending the local models to the cloud for aggregation. However, these schemes typically require strong assumptions, such as the local data are identically independent distributed (i.i.d), or the size of the local gradients are bounded. In this paper, we first explicitly characterize the behavior of the FedAvg algorithm, and show that without strong and unrealistic assumptions on the problem structure, the algorithm can behave erratically for non-convex problems (e.g., diverge to infinity). Aiming at designing FL algorithms that are provably fast and require as few assumptions as possible, we propose a new algorithm design strategy from the primal-dual optimization perspective. Our strategy yields a family of algorithms that take the same CTA model as existing algorithms, but they can deal with the non-convex objective, achieve the best possible optimization and communication complexity while being able to deal with both the full batch and mini-batch local computation models. Most importantly, the proposed algorithms are {\it communication efficient}, in the sense that the communication pattern can be adaptive to the level of heterogeneity among the local data. To the best of our knowledge, this is the first algorithmic framework for FL that achieves all the above properties.

Federated Learning Framework: FedPD Analysis

The paper introduces FedPD, a novel federated learning framework that addresses key limitations of existing algorithms, particularly FedAvg, when handling non-IID data settings prevalent in real-world applications. Federated Learning (FL) has gained traction for its ability to perform machine learning on distributed data without requiring centralized data storage, leveraging the "computation then aggregation" (CTA) approach. However, traditional methods like FedAvg exhibit significant shortcomings, particularly in non-IID scenarios and concerning the assumptions they rely on for convergence.

Problem Definition and Challenges

FL aims to optimize a global model by aggregating locally computed updates from multiple distributed clients, thus maintaining data privacy. Central to this process is the CTA protocol, where clients perform several local updates before a global aggregation step. The paper focuses on two primary concerns: ensuring optimal convergence rates without overly stringent assumptions (like IID data distribution or bounded gradients) and enhancing communication efficiency, particularly relevant in non-homogeneous (non-IID) data environments.

FedPD Framework

FedPD tackles these challenges through a primal-dual optimization strategy, reformulating the FL problem as a global consensus optimization task. This novel approach allows for more sophisticated local update dynamics, enhanced stability, and adaptivity to data heterogeneity. The framework introduces a probability-based communication schedule that dynamically adjusts the frequency of client-server communication based on the degree of data non-IID-ness, quantified through a parameter $\delta$.

Theoretical Contributions

1. Convergence and Complexity:

• FedPD guarantees convergence for non-convex objectives with optimal rates, relying on weaker assumptions compared to FedAvg and similar methods. Specifically, it dispenses with the bounded gradient assumption essential for FedAvg's stability.
• The framework achieves state-of-the-art communication complexity, especially when data is nearly IID, by allowing communication savings proportional to $\log(\epsilon/\delta^2)$. This adaptivity ensures that communication costs reduce as the data becomes more homogeneous, which is crucial for practical scalability.

2. Addressing Erratic Behavior in FedAvg:

• The paper clearly delineates conditions under which FedAvg fails, particularly highlighting its reliance on strong assumptions like IID data for convergence. FedPD, by contrast, remains robust without these assumptions, thus broadening FL's applicability.

3. Local Gradient Update Strategy:

• FedPD employs a flexible local update mechanism, leveraging either full-batch, mini-batch, or variance-reduced SGD techniques to handle the local primal-dual subproblems. This flexibility not only enhances convergence speed but also aligns well with varied computational capacities across clients.

Practical Implications and Future Directions

FedPD's theoretical insights translate into practical implications. It forms the groundwork for developing FL solutions that are not only more communicationally efficient but also resilient in diverse data settings. By reducing the reliance on data assumptions, FedPD is positioned to impact FL's application in domains like healthcare (where privacy and data variability are paramount) and mobile networks.

Moving forward, the adaptability of FedPD in dynamic environments, where client availability and data distribution may change, opens new avenues for robust FL systems. Future research could further explore adaptive strategies within FedPD, optimizing the balance between communication saving and model convergence in real-time, heterogeneous settings. Additionally, integrating privacy-preserving mechanisms directly with FedPD's framework could offer dual benefits of efficiency and enhanced privacy, crucial for consent-driven data collaboration frameworks.

In summary, FedPD represents a significant advancement in the FL paradigm, offering a resilient, efficient, and theoretically sound framework that alleviates many practical challenges plaguing traditional FL algorithms.