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Pursuing Overall Welfare in Federated Learning through Sequential Decision Making

Seok-Ju Hahn, Gi-Soo Kim, Junghye Lee

TL;DR

This work tackles client-level fairness in Federated Learning under statistical heterogeneity by recasting adaptive aggregation as an online convex optimization problem and proposing AAggFF. It introduces two practical variants, AAggFF-S for cross-silo and AAggFF-D for cross-device, and provides sublinear regret guarantees for both settings, namely $\mathcal{O}(\sqrt{T\log K})$ in cross-device and $\mathcal{O}(K\log T)$ in cross-silo. The framework unifies existing fairness-aware FL methods under the OCO/OPS lens and enhances decision making through a stateful, regularized objective (FTRL), with bounded-response transformations and gradient estimation strategies for partial observations. Empirically, AAggFF improves the worst-case client performance and fairness (lower Gini coefficients and smaller accuracy-parity gaps) while preserving competitive average accuracy, across diverse cross-silo and cross-device benchmarks, and can be plugged into existing FL pipelines without extra communication. The work thus offers a scalable, theoretically grounded pathway to improve welfare and participation motivation in federated systems, while highlighting directions for robustness, privacy, and further convergence analysis.

Abstract

In traditional federated learning, a single global model cannot perform equally well for all clients. Therefore, the need to achieve the client-level fairness in federated system has been emphasized, which can be realized by modifying the static aggregation scheme for updating the global model to an adaptive one, in response to the local signals of the participating clients. Our work reveals that existing fairness-aware aggregation strategies can be unified into an online convex optimization framework, in other words, a central server's sequential decision making process. To enhance the decision making capability, we propose simple and intuitive improvements for suboptimal designs within existing methods, presenting AAggFF. Considering practical requirements, we further subdivide our method tailored for the cross-device and the cross-silo settings, respectively. Theoretical analyses guarantee sublinear regret upper bounds for both settings: $\mathcal{O}(\sqrt{T \log{K}})$ for the cross-device setting, and $\mathcal{O}(K \log{T})$ for the cross-silo setting, with $K$ clients and $T$ federation rounds. Extensive experiments demonstrate that the federated system equipped with AAggFF achieves better degree of client-level fairness than existing methods in both practical settings. Code is available at https://github.com/vaseline555/AAggFF

Pursuing Overall Welfare in Federated Learning through Sequential Decision Making

TL;DR

This work tackles client-level fairness in Federated Learning under statistical heterogeneity by recasting adaptive aggregation as an online convex optimization problem and proposing AAggFF. It introduces two practical variants, AAggFF-S for cross-silo and AAggFF-D for cross-device, and provides sublinear regret guarantees for both settings, namely in cross-device and in cross-silo. The framework unifies existing fairness-aware FL methods under the OCO/OPS lens and enhances decision making through a stateful, regularized objective (FTRL), with bounded-response transformations and gradient estimation strategies for partial observations. Empirically, AAggFF improves the worst-case client performance and fairness (lower Gini coefficients and smaller accuracy-parity gaps) while preserving competitive average accuracy, across diverse cross-silo and cross-device benchmarks, and can be plugged into existing FL pipelines without extra communication. The work thus offers a scalable, theoretically grounded pathway to improve welfare and participation motivation in federated systems, while highlighting directions for robustness, privacy, and further convergence analysis.

Abstract

In traditional federated learning, a single global model cannot perform equally well for all clients. Therefore, the need to achieve the client-level fairness in federated system has been emphasized, which can be realized by modifying the static aggregation scheme for updating the global model to an adaptive one, in response to the local signals of the participating clients. Our work reveals that existing fairness-aware aggregation strategies can be unified into an online convex optimization framework, in other words, a central server's sequential decision making process. To enhance the decision making capability, we propose simple and intuitive improvements for suboptimal designs within existing methods, presenting AAggFF. Considering practical requirements, we further subdivide our method tailored for the cross-device and the cross-silo settings, respectively. Theoretical analyses guarantee sublinear regret upper bounds for both settings: for the cross-device setting, and for the cross-silo setting, with clients and federation rounds. Extensive experiments demonstrate that the federated system equipped with AAggFF achieves better degree of client-level fairness than existing methods in both practical settings. Code is available at https://github.com/vaseline555/AAggFF
Paper Structure (58 sections, 14 theorems, 97 equations, 1 figure, 9 tables, 3 algorithms)

This paper contains 58 sections, 14 theorems, 97 equations, 1 figure, 9 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Works
  4. Client-Level Fairness in Federated Learning
  5. Online Decision Making
  6. Backgrounds
  7. Mixing Coefficients in Federated Learning
  8. Online Convex Optimization as a Unified Language
  9. Sequential Probability Assignment
  10. Proposed Methods
  11. Improved Design for Better Decision Making
  12. AAggFF: Adaptive Aggregation for Fair Federated Learning
  13. AAggFF-S: Algorithm for the Cross-Silo Federated Learning
  14. Online Newton Step ons1ons2
  15. Necessity of Bounded Response
  16. ...and 43 more sections

Key Result

Lemma 4.1

For all $t\in[T]$, suppose each entry of a response vector $\boldsymbol{r}^{(t)}\in\mathbb{R}^K$ is bounded as $r_i^{(t)}\in[C_1,C_2]$ for some constants $C_1$ and $C_2$ satisfying $0<C_1<C_2$. Then, the decision loss $\ell^{(t)}$ defined in (eq:decision_loss) is $\frac{C_2}{1+C_1}$-Lipschitz contin

Figures (1)

  • Figure A1: Cumulative values of a global objective according to different CDFs (smaller is better). (Left) Berka dataset (cross-silo setting; $K=7, T=100$). (Right) Reddit dataset (cross-device setting; $K=817, T=300, C=0.00612$)

Theorems & Definitions (37)

  • Definition 2.1
  • Remark 3.1
  • Definition 3.2
  • Lemma 4.1
  • Definition 4.2
  • Lemma 4.3
  • Lemma 4.4
  • Remark 4.5
  • Theorem 5.1
  • Theorem 5.2
  • ...and 27 more