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Federated sampling algorithms have recently gained great popularity in thecommunity of machine learning and statistics. This paper studies variants ofsuch algorithms called Error Feedback Langevin algorithms (ELF). In particular,we analyze the combinations of EF21 and EF21-P with the federated LangevinMonte-Carlo. We propose three algorithms: P-ELF, D-ELF, and B-ELF that use,respectively, primal, dual, and bidirectional compressors. We analyze theproposed methods under Log-Sobolev inequality and provide non-asymptoticconvergence guarantees.

ELF: Federated Langevin Algorithms with Primal, Dual and Bidirectional Compression