Cost-Effective Federated Learning Design

Abstract: Federated learning (FL) is a distributed learning paradigm that enables a large number of devices to collaboratively learn a model without sharing their raw data. Despite its practical efficiency and effectiveness, the iterative on-device learning process incurs a considerable cost in terms of learning time and energy consumption, which depends crucially on the number of selected clients and the number of local iterations in each training round. In this paper, we analyze how to design adaptive FL that optimally chooses these essential control variables to minimize the total cost while ensuring convergence. Theoretically, we analytically establish the relationship between the total cost and the control variables with the convergence upper bound. To efficiently solve the cost minimization problem, we develop a low-cost sampling-based algorithm to learn the convergence related unknown parameters. We derive important solution properties that effectively identify the design principles for different metric preferences. Practically, we evaluate our theoretical results both in a simulated environment and on a hardware prototype. Experimental evidence verifies our derived properties and demonstrates that our proposed solution achieves near-optimal performance for various datasets, different machine learning models, and heterogeneous system settings.

• The paper presents an analytical framework and sampling algorithm to minimize the total cost (time and energy) of federated learning by optimizing the number of clients and local iterations while guaranteeing model convergence.
• It formulates the cost optimization as a biconvex problem, deriving efficient closed-form solutions and learning unknown parameters with minimal overhead.
• The study identifies theoretical properties for cost-efficient FL design and validates its proposed method empirically through simulations and hardware experiments, showing near-optimal performance.

An Analytical Approach to Cost-Effective Federated Learning Design

The paper presents a comprehensive approach to designing a cost-effective federated learning (FL) process. It addresses the crucial issue of optimizing the learning process in FL by minimizing the total cost, essentially comprising learning time and energy consumption, while ensuring the convergence of the model. The primary focus is on determining the optimal values for two key control variables: the number of participating clients ($K$) and the number of local iterations ($E$).

Key Contributions

1. Analytical Formulation: The authors develop an analytical framework that describes the relationship between total cost and control variables with an upper bound on convergence. They provide an approximate solution to minimize the expected total cost, which includes time and energy metrics, under a convergence constraint.
2. Optimization Algorithm: A major contribution is a sampling-based algorithm designed to learn unknown parameters related to the convergence bound with minimal estimation overhead. The paper demonstrates that the optimization problem is biconvex with respect to $K$ and $E$; thereby, efficient solutions can be derived using closed-form expressions.
3. Theoretical Properties: The study uncovers important theoretical properties that help establish design principles for different optimization goals. For instance, a larger $K$ can expedite learning time but may increase energy consumption unless optimized. It also highlights that neither a very high nor very low $E$ is suitable for cost-efficiency, and the optimal $E$ should balance computation and communication costs.
4. Empirical Validation: The theoretical findings and proposed algorithm are evaluated using both simulations and a hardware prototype involving 20 Raspberry Pi devices. Results show that the proposed method achieves near-optimal performance across various datasets, models, and system configurations.

Methodological Framework

• Cost Analysis:

The paper dissects the total cost into components of learning time and energy consumption. For typical FL systems, the per-round time is dictated by the slowest participating client, and the total energy cost aggregates the consumption of all participating clients.

• Problem Formulation:

The authors frame the challenge as an optimization problem (P1), which aims to minimize the expected cost while satisfying a convergence condition. This is transformed into an approximate problem (P2) by utilizing an analytical relationship between cost metrics and convergence.

• Numerical Estimation:

To handle unknown convergence parameters, a sampling-based estimation approach is employed, which minimally impacts the overall system performance.

Implications and Future Directions

The insights presented in the paper have practical and theoretical implications for FL systems. Practically, the proposed approach offers a framework that can be integrated into existing FL systems to reduce operational costs. Theoretically, it provides a basis for further exploration of parameter tuning in decentralized learning environments.

As FL continues to evolve, the trade-off between time and energy consumption in heterogeneous environments will become increasingly pertinent, particularly with the proliferation of IoT and edge devices. Future developments can explore refining the understanding of convergence dynamics in highly non-i.i.d. settings, as well as extending these optimization techniques to more complex models and systems.

In conclusion, the paper contributes significantly to the body of knowledge on federated learning by offering a detailed assessment and solution framework for cost-efficient design, thereby opening avenues for optimized machine learning practices across distributed networks.