  Wireless federated learning (WFL) suffers from heterogeneity prevailing in
the data distributions, computing powers, and channel conditions of
participating devices. This paper presents a new Federated Learning with
Adjusted leaRning ratE (FLARE) framework to mitigate the impact of the
heterogeneity. The key idea is to allow the participating devices to adjust
their individual learning rates and local training iterations, adapting to
their instantaneous computing powers. The convergence upper bound of FLARE is
established rigorously under a general setting with non-convex models in the
presence of non-i.i.d. datasets and imbalanced computing powers. By minimizing
the upper bound, we further optimize the scheduling of FLARE to exploit the
channel heterogeneity. A nested problem structure is revealed to facilitate
iteratively allocating the bandwidth with binary search and selecting devices
with a new greedy method. A linear problem structure is also identified and a
low-complexity linear programming scheduling policy is designed when training
models have large Lipschitz constants. Experiments demonstrate that FLARE
consistently outperforms the baselines in test accuracy, and converges much
faster with the proposed scheduling policy.
