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With ever growing data volume and model size, an error-tolerant,communication efficient, yet versatile distributed algorithm has become vitalfor the success of many large-scale machine learning applications. In this workwe propose m-PAPG, an implementation of the flexible proximal gradientalgorithm in model parallel systems equipped with the partially asynchronouscommunication protocol. The worker machines communicate asynchronously with acontrolled staleness bound $s$ and operate at different frequencies. Wecharacterize various convergence properties of m-PAPG: 1) Under a generalnon-smooth and non-convex setting, we prove that every limit point of thesequence generated by m-PAPG is a critical point of the objective function; 2)Under an error bound condition, we prove that the function value decayslinearly for every $s$ steps; 3) Under the Kurdyka-${\L}$ojasiewicz inequality,we prove that the sequences generated by m-PAPG converge to the same criticalpoint, provided that a proximal Lipschitz condition is satisfied.

Distributed Proximal Gradient Algorithm for Partially Asynchronous Computer Clusters