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We introduce a framework - Artemis - to tackle the problem of learning in adistributed or federated setting with communication constraints and devicepartial participation. Several workers (randomly sampled) perform theoptimization process using a central server to aggregate their computations. Toalleviate the communication cost, Artemis allows to compress the informationsent in both directions (from the workers to the server and conversely)combined with a memory mechanism. It improves on existing algorithms that onlyconsider unidirectional compression (to the server), or use very strongassumptions on the compression operator, and often do not take into accountdevices partial participation. We provide fast rates of convergence (linear upto a threshold) under weak assumptions on the stochastic gradients (noise'svariance bounded only at optimal point) in non-i.i.d. setting, highlight theimpact of memory for unidirectional and bidirectional compression, analyzePolyak-Ruppert averaging. We use convergence in distribution to obtain a lowerbound of the asymptotic variance that highlights practical limits ofcompression. We propose two approaches to tackle the challenging case ofdevices partial participation and provide experimental results to demonstratethe validity of our analysis.

Bidirectional compression in heterogeneous settings for distributed or federated learning with partial participation: tight convergence guarantees