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Distributed optimization algorithms have emerged as a superior approaches for solving machine learning problems. To accommodate the diverse ways in which data can be stored across devices, these methods must be adaptable to a wide range of situations. As a result, two orthogonal regimes of distributed algorithms are distinguished: horizontal and vertical. During parallel training, communication between nodes can become a critical bottleneck, particularly for high-dimensional and over-parameterized models. Therefore, it is crucial to enhance current methods with strategies that minimize the amount of data transmitted during trainng while still achieving a model of similar quality. This paper introduces a new accelerated algorithm, working in the regime of vertical data division. By utilizing a momentum and variance reduction technique from the L-Katyusha algorithm and Gossip procedure for communications, we provide one of the first theoretical convergence guarantees for the vertical regime.
