Rethinking the Personalized Relaxed Initialization in the Federated Learning: Consistency and Generalization
Organizations: School of Cyber Science and Technology, Shenzhen Campus of Sun Yat-sen University · School of Computer Science, Faculty of Engineering, The University of Sydney · Generative AI Lab, College of Computing and Data Science, Nanyang Technological University
Abstract
Federated learning (FL) is a distributed paradigm that coordinates massive local clients to collaboratively train a global model via stage-wise local training processes on the heterogeneous dataset. Previous works have implicitly studied that FL suffers from the client-drift'' problem, which is caused by the inconsistent optimum across local clients. However, till now it still lacks solid theoretical analysis to explain the impact of this local inconsistency. To alleviate the negative impact of client drift'' and explore its substance in FL, in this paper, we first propose an efficient FL algorithm FedInit, which allows employing the personalized relaxed initialization state at the beginning of each local training stage. Specifically, FedInit initializes the local state by moving away from the current global state towards the reverse direction of the latest local state. Moreover, to further understand how inconsistency disrupts performance in FL, we introduce the excess risk analysis and study the divergence term to investigate the test error in FL. Our studies show that optimization error is not sensitive to this local inconsistency, while it mainly affects the generalization error bound. Extensive experiments are conducted to validate its efficiency. The proposed FedInit method could achieve comparable results compared to several advanced benchmarks without any additional training or communication costs. Meanwhile, the stage-wise personalized relaxed initialization could also be incorporated into several current advanced algorithms to achieve higher generalization performance in the FL paradigm.
Figures & tables
| Symbol | Definition |
|---|---|
| set / number of active clients | |
| set / number of total clients | |
| number / index of local interval | |
| number / index of communication rounds | |
| model parameters / optimum parameters | |
| local dataset / size of local dataset |
| Assumption | Convergence bound | Convergence rate |
|---|---|---|
| 1 , 3 , 5 | ||
| 1 , 2 , 3 , 5 | ||
| 1 , 4 , 6 | ||
| 1 , 2 , 4 , 6 |
| SGD | FedAvg | |
|---|---|---|
| number of samples | ||
| number of iterations |
| Method | CIFAR-10 | |||
|---|---|---|---|---|
| -100 clients | -200 clients | |||
| Dir-0.6 | Dir-0.1 | Dir-0.6 | Dir-0.1 | |
| FedAvg | ||||
| FedAdam | ||||
| FedSAM | ||||
| SCAFFOLD | ||||
| Method | CIFAR-100 | |||
|---|---|---|---|---|
| -100 clients | -200 clients | |||
| Dir-0.6 | Dir-0.1 | Dir-0.6 | Dir-0.1 | |
| FedAvg | ||||
| FedAdam | ||||
| FedSAM | ||||
| SCAFFOLD | ||||
| Method | -100 clients | -200 clients | ||||||
|---|---|---|---|---|---|---|---|---|
| Dir-0.6 | Dir-0.1 | Dir-0.6 | Dir-0.1 | |||||
| - | +RI | - | +RI | - | +RI | - | +RI | |
| FedAvg | 78.77 | 83.11 | 72.53 | 75.95 | 74.81 | 80.58 | 70.65 | 74.92 |
| FedAdam | 76.52 | 78.33 | 70.44 | 72.55 | 73.28 | 78.33 | 68.87 | 71.34 |
| FedSAM | 79.23 | 83.36 | 72.89 | 76.34 | 75.45 | 80.66 | 71.23 | 75.08 |
| SCAFFOLD | 81.37 | 83.27 | 75.06 | 77.30 | 78.17 | 81.02 | 74.24 | 76.22 |
| FedAvg | FedAdam | FedSAM | SCAFFOLD | FedDyn | FedCM | FedInit | |
|---|---|---|---|---|---|---|---|
| 10 -100 | 19.38 | 23.22 | 30.23 | 28.61 | 23.84 | 22.63 | 20.41 |
| ratio | 1 | 1.19 | 1.56 | 1.47 | 1.23 | 1.17 | 1.05 |
| 5 -200 | 15.87 | 17.50 | 22.18 | 24.49 | 20.61 | 18.19 | 16.14 |
| ratio | 1 | 1.10 | 1.40 | 1.54 | 1.30 | 1.15 | 1.02 |
| Round | Time (s) | |||
| Speed Ratio | Speed Ratio | |||
| FedAvg | 371 | 1 | 7189 | 1 |
| FedAdam | 489 | 0.76 | 11354 | 0.63 |
| FedSAM | 377 | 0.98 | 11396 | 0.63 |
| SCAFFOLD | 248 | 1.50 | 7095 | 1.01 |
| FedDyn | 192 | 1.93 | 4577 | 1.57 |
| Method | Communication | ratio | Storage | ratio |
|---|---|---|---|---|
| FedAvg | 1 | 1 | ||
| FedAdam | 1 | 2 | ||
| FedSAM | 1 | 2 | ||
| SCAFFOLD | 2 | 2 | ||
| FedDyn | 1 | 2 | ||
| FedCM | 2 | 2 |
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
| Notation | Formulation | Description |
|---|---|---|
| - | parameters at -th iteration in round on client | |
| - | global parameters in round | |
| averaged norm of the local updates in round | ||
| norm of the global updates in round | ||
| inconsistency/divergence term in round | ||
| bias between the initialization state and optimal |
| Notation | Formulation | Description |
|---|---|---|
| - | parameters trained with set | |
| - | parameters trained with set | |
| inconsistency/divergence term in round | ||
| stability difference at -iteration on -round |
Federated Learning
Federated learning trains shared models across data holders without requiring them to pool their raw data.
See all 943 papers