Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.

In this paper we prove a new complexity bound for a variant of Accelerated Coordinate Descent Method [7]. We show that this method often outperforms the standard Fast Gradient Methods (FGM, [3, 6]) on optimization problems with dense data. In many important situations, the computational expenses of oracle and method itself at each iteration of our scheme are perfectly balanced (both depend linearly on dimensions of the problem). As application examples, we consider unconstrained convex quadratic minimization, and the problems arising in Smoothing Technique [6]. On some special problem instances, the provable acceleration factor with respect to FGM can reach the square root of the number of variables. Our theoretical conclusions are confirmed by numerical experiments.

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Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.

We consider decentralized stochastic optimization with the objective function (e.g. data samples for machine learning task) being distributed over n machines that can only communicate to their neighbors on a fixed communication graph. To reduce the communication bottleneck, the nodes compress (e.g. quantize or sparsify) their model updates. We cover both unbiased and biased compression operators with quality denoted by ω ≤ 1 (ω = 1 meaning no compression). We (i) propose a novel gossip-based stochastic gradient descent algorithm, Choco-SGD, that converges at rate O 1/(nT ) + 1/(T δ 2 ω) 2 for strongly convex objectives, where T denotes the number of iterations and δ the eigengap of the connectivity matrix. Despite compression quality and network connectivity affecting the higher order terms, the first term in the rate, O(1/(nT )), is the same as for the centralized baseline with exact communication. We (ii) present a novel gossip algorithm, Choco-Gossip, for the average consensus problem that converges in time O(1/(δ 2 ω) log(1/ )) for accuracy > 0. This is (up to our knowledge) the first gossip algorithm that supports arbitrary compressed messages for ω > 0 and still exhibits linear convergence. We (iii) show in experiments that both of our algorithms do outperform the respective state-of-the-art baselines and Choco-SGD can reduce communication by at least two orders of magnitudes.