Source-linked AI summary
Asynchronous Federated Optimization
Cong Xie, Sanmi Koyejo, Indranil Gupta
TL;DR
Federated learning must coordinate training across massive edge-device populations despite stragglers and heterogeneous availability. The paper proposes asynchronous federated optimization with regularized local problems and staleness-adaptive mixing, and reports fast convergence with performance that often matches or exceeds FedAvg. Its guarantees rely on bounded delays, bounded local-update imbalance, gradient bounds, and sufficiently strong regularization.
Problem
Synchronous federated learning can be slow because heterogeneous device availability, computation, and battery constraints create many stragglers.
Method
The algorithm solves regularized local problems and asynchronously updates the global model using weighted averaging with a mixing weight adapted to staleness.
Results
FedAsync performs as well as FedAvg and in most cases better; with small staleness it converges much faster, while with large staleness it achieves similar performance.
Takeaways & Limitations
The approach supports fast asynchronous federated optimization while tolerating staleness in practical settings.
Takeaways & Limitations
The guarantees assume bounded delay, bounded local-update imbalance, bounded gradients, and regularization satisfying ρ > μ.
Abstract
from arXiv · showhide
Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence to a global optimum, for both strongly convex and a restricted family of non-convex problems. Empirical results show that the proposed algorithm converges quickly and tolerates staleness in various applications.
1. Introduction
Federated learning trains global models across massive, resource-weak edge-device datasets, but synchronous coordination is vulnerable to stragglers. The paper proposes asynchronous federated optimization using regularized local problems and staleness-adaptive weighted averaging.
- Federated learning aggregates locally trained models from private, disjoint datasets across edge devices into a global model.
- Infrequent activation, communication constraints, and non-IID data complicate federated optimization across edge devices.
- Synchronous federated learning can be slow because heterogeneous availability, computation, and battery constraints create many stragglers.
- The proposed algorithm solves regularized local problems and uses staleness-adaptive weighted averaging to update the global model.
- The paper proves convergence for a restricted family of non-convex problems and reports fast convergence, staleness tolerance, and frequent empirical advantages over synchronous optimization.
2. Problem formulation
The problem formulation considers training a global model from data distributed across n devices, with each worker optimizing on its own local dataset.
- The system contains n devices, each with a worker process that trains a model on local data.
- The objective is to train a global model x ∈ R^d by minimizing the average expected local loss across devices.
- Each device samples from its own local dataset D_i, and different devices have different datasets.
3. Methodology
The method asynchronously aggregates locally trained models through weighted global updates. Regularized local optimization and staleness-dependent mixing reduce the impact of delayed models while allowing workers and servers to operate without synchronization.
- At each global epoch, the server receives a locally trained model and updates the global model by weighted averaging.The update is x_t = (1 − α)x_{t−1} + αx_new, with α ∈ (0, 1).
- Workers solve regularized local optimization problems with SGD for multiple iterations after receiving a potentially stale global model.
- The updater can adjust the mixing weight as α_t = α × s(t − τ), where s decreases as staleness increases.
- Non-blocking communication lets servers and workers update at different times, accommodating heterogeneous device conditions.
- Local parameters, sampled data, and iteration counts are indexed by the received model timestamp and local iteration.
- The scheduler and updater run asynchronously, enabling training tasks and global-model updates to proceed in parallel.
4. Convergence analysis
The convergence analysis establishes guarantees under smoothness, weak convexity, bounded delays, bounded local-update imbalance, and gradient-bound assumptions. Under these conditions, the algorithm converges to a critical point after T global updates.
- The analysis begins by introducing definitions and assumptions for its convergence results.
- The objective assumes L-smoothness and μ-weak convexity, with convexity recovered when μ = 0.
- Each worker performs between H_min and H_max local updates, with bounded delay t − τ ≤ K and imbalance ratio δ = H_max/H_min.
- The analysis assumes bounded gradients for both the original and regularized per-sample objectives and requires sufficiently large regularization ρ > μ.
- Under the stated conditions and γ < 1/L, Algorithm 1 converges to a critical point after T global updates.
5. Experiments
The experiments evaluate FedAsync on CIFAR-10 and WikiText-2 under varying staleness, comparing adaptive mixing strategies with synchronous and single-thread baselines. FedAsync converges quickly at low staleness, remains comparable to FedAvg at high staleness, and is more robust with adaptive mixing.
- Evaluation setup: Experiments use CIFAR-10 and WikiText-2 partitioned across 100 devices, with FedAvg and single-thread SGD as baselines.Each experiment is repeated 10 times and averaged; CIFAR-10 uses top-1 test accuracy, while comparisons use metrics versus applied gradients.
- Evaluation setup: FedAsync is evaluated with constant, polynomial, and hinge staleness-dependent mixing functions.The adaptive strategies use α_t = α × s(t − τ), with polynomial and hinge functions parameterized by a and b.
- Convergence: At low staleness, FedAsync converges as fast as SGD and faster than FedAvg; at high staleness, its convergence rate can become similar to FedAvg.The experiments plot convergence against the number of gradients on CNN/CIFAR-10 and an LSTM language model/WikiText-2.
- Staleness robustness: Larger staleness slows convergence, but its influence is not catastrophic, and adaptive α mitigates instability.Using adaptive α improves performance compared with constant α, while overly large α can destabilize convergence, especially for FedAsync+Const.
- Discussion: FedAsync’s convergence rate lies between single-thread SGD and FedAvg, shifting toward SGD with larger α and lower staleness.With smaller α and larger staleness, FedAsync becomes closer to FedAvg.
- Discussion: FedAsync is generally insensitive to hyperparameters; empirically, FedAsync+Hinge performs best among adaptive choices, while Poly and Hinge are similar.For large staleness, tuning α improves convergence; without adaptation, smaller α performs better.
- Discussion: Compared with FedAvg, FedAsync performs at least as well and usually better, with much faster convergence when staleness is small.At large staleness, FedAsync still achieves performance similar to FedAvg.
6. Conclusion
The paper proposes asynchronous federated optimization for non-IID data, proves convergence for a restricted family of non-convex problems, and empirically finds fast convergence with staleness tolerance.
- The proposed asynchronous federated optimization algorithm is designed for non-IID training data.
- The authors prove convergence for a restricted family of non-convex problems.
- Empirical evaluation validates fast convergence and tolerance to staleness.
Appendix A. Proofs
The proofs establish convergence under smoothness, weak convexity, bounded local-update imbalance, and bounded delay. They analyze stale model differences and derive a critical-point guarantee after T global updates.
- Assumptions: Theorem 1 assumes L-smoothness, µ-weak convexity, bounded local updates Hmin to Hmax, and delay t−τ≤K.The local-update imbalance is represented by δ = Hmax/Hmin.
- Proof strategy: The analysis uses smoothness, convexity-related assumptions, rearrangement, and telescoping to relate local progress to global objective decrease.The derivation proceeds through conditional inequalities and total expectation over global epochs.
- Proof strategy: The proof bounds the distance between stale and current server models using the delay bound and local-update quantities.These bounds scale with K, Hmax, α, γ, and variance-related terms.
- Convergence result: The convergence bound is obtained after T global epochs by telescoping and taking total expectation, with parameter choices involving α = 1/√Hmin.The displayed rate tracks objective decrease and terms involving delay, local updates, and variance.
B.1. NN architecture
This section reports the CNN architecture used in the experiments and refers to a summary of its detailed network structures.
- CNN architecture: Table 2 provides the detailed network structures of the CNN used in the experiments.The table is labeled “CNN Summary.”