Research map / Federated learning and privacy / Communication-efficient FL
Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradients
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use gradient correction with the stale global gradient and client-specific step sizes inversely proportional to local-step counts | FedLin · Strongly convex, smooth objectives with arbitrary objective and systems heterogeneity | linear convergence rate: (1-\frac{1}{6\kappa})^T | Helped |
| Add server-side error feedback to TOP-k sparsification (ablation) | FedLin with server-side sparsification · Strongly convex, smooth | convergence-rate dependence on compression: inversely proportional to \delta_s^{\frac{3}{2}} -> inversely proportional to \delta_s | Helped |
| Sparsify gradients at clients before aggregation instead of sparsifying the aggregated gradient at the server (ablation) | FedLin · Strongly convex, smooth; client-side TOP-k | convergence endpoint | Hurt |
| Increase client-side compression level (ablation) | FedLin with client-side TOP-k · Synthetic least-squares regression | convergence error | Hurt |
| Increase objective heterogeneity (ablation) | FedLin with client-side sparsification · Synthetic least-squares regression | convergence error | Hurt |
| Increase objective heterogeneity (ablation) | FedLin with server-side sparsification · Synthetic least-squares regression | convergence speed and accuracy | No clear effect |
| Use more local steps between communication rounds under objective heterogeneity (ablation) | FedLin · Strongly convex, smooth | convergence rate: The upper bound's exponent is independent of H; the lower bound is \exp(-4T) | No clear effect |
| Use constant step sizes with local updates under heterogeneous objectives | FedProx and FedNova · Deterministic strongly convex quadratics | convergence to the global minimum | Hurt |
| Add server-side gradient sparsification without error feedback (ablation) | FedLin · Strongly convex, smooth; server TOP-k | linear convergence to the global minimum: (1-\frac{1}{2\delta_s (2+\sqrt{\delta_s})\kappa})^T | Helped |
| Use a time-varying learning rate in the noisy setting, with \bar{\eta_t}=O(1/t) | FedLin · Strongly convex stochastic oracle | suboptimality rate: O(1/T) | Helped |
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