Generalization in Federated Learning: A Conditional Mutual Information Framework (2503.04091v2)

Abstract: Federated learning (FL) is a widely adopted privacy-preserving distributed learning framework, yet its generalization performance remains less explored compared to centralized learning. In FL, the generalization error consists of two components: the out-of-sample gap, which measures the gap between the empirical and true risk for participating clients, and the participation gap, which quantifies the risk difference between participating and non-participating clients. In this work, we apply an information-theoretic analysis via the conditional mutual information (CMI) framework to study FL's two-level generalization. Beyond the traditional supersample-based CMI framework, we introduce a superclient construction to accommodate the two-level generalization setting in FL. We derive multiple CMI-based bounds, including hypothesis-based CMI bounds, illustrating how privacy constraints in FL can imply generalization guarantees. Furthermore, we propose fast-rate evaluated CMI bounds that recover the best-known convergence rate for two-level FL generalization in the small empirical risk regime. For specific FL model aggregation strategies and structured loss functions, we refine our bounds to achieve improved convergence rates with respect to the number of participating clients. Empirical evaluations confirm that our evaluated CMI bounds are non-vacuous and accurately capture the generalization behavior of FL algorithms.

• The paper introduces a two-level generalization framework using Conditional Mutual Information (CMI) to analyze out-of-sample and participation gaps in Federated Learning.
• It derives novel CMI-based bounds showing that privacy constraints can enhance generalization and proposes Evaluated CMI (e-CMI) bounds for practical scenarios.
• Empirical evaluations on MNIST and CIFAR-10 datasets confirm the bounds' effectiveness and show improved generalization with specific model aggregation strategies.

Generalization in Federated Learning: A Conditional Mutual Information Framework

The paper presents a comprehensive paper on the generalization capabilities of Federated Learning (FL), with an emphasis on employing the Conditional Mutual Information (CMI) framework to achieve robust theoretical insights. Federated Learning stands as a pivotal approach for distributed machine learning, fostering model training across various clients while ensuring data privacy. This paper seeks to address the complex challenge of generalization in FL, a domain where heterogeneity in data distribution poses significant challenges.

Theoretical Contributions

The authors introduce a novel two-level generalization framework that systematically addresses both out-of-sample and participation gaps in FL. The out-of-sample gap refers to discrepancies between empirical and true risks within participating clients, while the participation gap examines the risk differences between participating and non-participating clients.

Key to the paper's contribution is the adaptation of the CMI framework to FL. This involves a superclient approach which ingeniously creates groups and utilizes Bernoulli random variables to simulate client participation. Through this, they derive refined CMI-based bounds which offer tighter generalization guarantees than traditional mutual information (MI) techniques. In particular, they highlight:

• Hypothesis-based CMI Bounds: These bounds demonstrate that privacy constraints can naturally lead to improved generalization in FL, a crucial insight given the privacy-preserving goals of FL.
• Evaluated CMI (e-CMI) Bounds: In scenarios of low empirical risk, these bounds recover optimal convergence rates, supporting theoretical assurances with practical ease of computation.
• Enhancements through Specific Model Aggregation Strategies: The paper explores Bregman loss functions and model averaging strategies, leading to improved rates for generalization bound decay.

Practical Implications and Empirical Validation

Experimentally, the paper evaluates the performance of these bounds on datasets like MNIST and CIFAR-10, confirming their non-vacuous nature and efficacy in captaining the generalization behavior of FL algorithms. The empirical results corroborate the theoretical claims, particularly in regimes where empirical risk is minimized, aligning the theoretical advancements with practical deployment scenarios.

Future Directions

The paper opens avenues for further exploration, such as investigating model aggregation frequency's impact on generalization via CMI analysis, and extending the framework to unbounded loss functions. Given the evolving landscape of FL, these insights are likely to propel subsequent research in enhancing both theoretical and practical aspects of federated learning models.

In conclusion, this paper significantly advances the understanding of generalization in federated learning, providing a robust theoretical foundation while also offering empirical evidence to support practical implementations. The use of CMI in this context showcases its potential in addressing the intricacies of learning in distributed, non-i.i.d. environments.