Q-LocalAdam: Memory-Efficient Client-Side Adaptive Optimization for Edge Federated Learning

Federated learning on edge devices must cope with non-IID client data and tight memory budgets. Adaptive optimizers like Adam stabilize training under data heterogeneity but require storing full-precision momentum and variance states, often tripling client memory overhead. This limits deployable model sizes and concurrent federated jobs on resource-constrained devices. We empirically observe that momentum and variance in federated Adam exhibit fundamentally different statistical properties: momentum values are symmetric and bounded, while variance spans eight orders of magnitude with log-normal structure. Motivated by this asymmetry, we propose Q-LocalAdam, which applies distribution-aware 8-bit quantization block-wise linear encoding for momentum and log-space encoding for variance while keeping model parameters in full precision. Across CIFAR-10 and CIFAR-100 under varying data heterogeneity (α ∈ 0.1, 0.5, 1.0, IID), Q-LocalAdam achieves 3.37× optimizer memory reduction with no accuracy loss under moderate heterogeneity and significant improvements under extreme heterogeneity (e.g., +5.74pp on CIFAR-100, α=0.1). Multi-seed validation confirms statistical significance (p<0.01). In contrast, naive uniform quantization degrades to random performance, demonstrating that distribution-aware design is essential. Q-LocalAdam enables larger models and more concurrent workloads on memory-constrained edge devices without modifying the federated protocol.