[Paper Review] FLIX: A Simple and Communication-Efficient Alternative to Local Methods in Federated Learning

Elnur Gasanov, Ahmed Khaled+2 more|arXiv (Cornell University)|Nov 22, 2021

Privacy-Preserving Technologies in Data4 citations

TL;DR

FLIX proposes a communication-efficient federated learning framework that replaces local updates with a novel finite-sum optimization formulation using client-specific personalization parameters. By leveraging locally computed model states and a smart initialization, FLIX achieves performance on par with local methods while enabling standard distributed optimization and adaptive communication control, validated through extensive experiments on diverse datasets.

ABSTRACT

Federated Learning (FL) is an increasingly popular machine learning paradigm in which multiple nodes try to collaboratively learn under privacy, communication and multiple heterogeneity constraints. A persistent problem in federated learning is that it is not clear what the optimization objective should be: the standard average risk minimization of supervised learning is inadequate in handling several major constraints specific to federated learning, such as communication adaptivity and personalization control. We identify several key desiderata in frameworks for federated learning and introduce a new framework, FLIX, that takes into account the unique challenges brought by federated learning. FLIX has a standard finite-sum form, which enables practitioners to tap into the immense wealth of existing (potentially non-local) methods for distributed optimization. Through a smart initialization that does not require any communication, FLIX does not require the use of local steps but is still provably capable of performing dissimilarity regularization on par with local methods. We give several algorithms for solving the FLIX formulation efficiently under communication constraints. Finally, we corroborate our theoretical results with extensive experimentation.

Motivation & Objective

• Address the limitations of standard federated learning, where average risk minimization fails to handle communication constraints and personalization needs.
• Develop a flexible optimization framework that supports both communication efficiency and client-specific model personalization.
• Enable the use of existing non-local distributed optimization methods in federated settings without requiring local steps.
• Provide theoretical guarantees for convergence under standard smoothness and convexity assumptions.
• Demonstrate empirical superiority over local methods and meta-learning baselines in heterogeneous data settings.

Proposed method

• Formulate federated learning as a finite-sum problem: $\tilde{f}(x) = \frac{1}{n}\sum_{i=1}^{n} f_i(\alpha_i x + (1 - \alpha_i)x_i)$, where $x_i$ is the local minimizer of client $i$'s loss.
• Use $\alpha_i \in [0,1]$ as a tunable personalization parameter to control the influence of global and local models on each client’s final model.
• Compute $x_i$ locally without communication, enabling communication-efficient initialization.
• Deploy the final model on client $i$ as $T_i(x_*) = \alpha_i x_* + (1 - \alpha_i)x_i$, allowing for personalized generalization.
• Apply standard distributed optimization methods (e.g., GD, CGD, DIANA) to solve the FLIX formulation under communication constraints.
• Ensure theoretical convergence guarantees by preserving smoothness and convexity of the original $f_i$ in the transformed $\tilde{f}$.

Experimental results

Research questions

• RQ1 Can a federated learning framework be designed that avoids local updates while matching the performance of local methods?
• RQ2 How can communication efficiency and personalization be jointly optimized in federated learning?
• RQ3 Can standard distributed optimization methods be effectively applied to a new finite-sum formulation in FL?
• RQ4 What is the impact of the personalization parameter $\alpha_i$ on convergence and generalization in heterogeneous data settings?
• RQ5 How does FLIX compare empirically to FedAvg, FOMAML, and Reptile in terms of communication cost and test accuracy?

Key findings

• FLIX achieves generalization performance comparable to local methods without requiring any local optimization steps.
• The framework enables communication-efficient training: when $\alpha_i = 0$, no communication is needed to deploy the final model on client $i$.
• Grid search results show that smaller $\alpha_i$ values require larger step-sizes to achieve optimal generalization, consistent with theoretical convergence analysis.
• On EMNIST and Shakespeare datasets, FLIX with $\alpha = 0.3$ and $\alpha = 0.5$ achieved the highest test accuracy among all compared methods.
• In logistic regression experiments, FLIX outperformed GD and DIANA in terms of communication cost, especially when measured in floating-point operations.
• Theoretical analysis confirms that smoothness and convexity of $f_i$ are preserved in $\tilde{f}$, enabling fast convergence with standard optimization methods.