Federated Majorize-Minimization: Beyond Parameter Aggregation

This paper proposes a unified approach for designing stochastic optimization algorithms that robustly scale to the federated learning setting. Our work studies a class of Majorize-Minimization (MM) problems, which possesses a linearly parameterized family of majorizing surrogate functions. This framework encompasses (proximal) gradient-based algorithms for (regularized) smooth objectives, the Expectation Maximization algorithm, and many problems seen as variational surrogate MM. We show that our framework motivates a unifying algorithm called Stochastic Approximation Stochastic Surrogate MM (\SSMM), which includes previous stochastic MM procedures as special instances. We then extend \SSMM\ to the federated setting, while taking into consideration common bottlenecks such as data heterogeneity, partial participation, and communication constraints; this yields \QSMM. The originality of \QSMM\ is to learn locally and then aggregate information characterizing the \textit{surrogate majorizing function}, contrary to classical algorithms which learn and aggregate the \textit{original parameter}. Finally, to showcase the flexibility of this methodology beyond our theoretical setting, we use it to design an algorithm for computing optimal transport maps in the federated setting.

Compression with Exact Error Distribution for Federated Learning

Compression schemes have been extensively used in Federated Learning (FL) to reduce the communication cost of distributed learning. While most approaches rely on a bounded variance assumption of the noise produced by the compressor, this paper investigates the use of compression and aggregation schemes that produce a specific error distribution, e.g., Gaussian or Laplace, on the aggregated data. We present and analyze different aggregation schemes based on layered quantizers achieving exact error distribution. We provide different methods to leverage the proposed compression schemes to obtain compression-for-free in differential privacy applications. Our general compression methods can recover and improve standard FL schemes with Gaussian perturbations such as Langevin dynamics and randomized smoothing.