Parallel Random Coordinate Descent Method for Composite Minimization: Convergence Analysis and Error Bounds

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DJAM: Distributed Jacobi Asynchronous Method for Learning Personal Models (2018, methodology): “The methods proposed in [15] and [16] can tackle more general problems, but both require that agents communicate with all their neighbors before updating, while our method needs only communications between two agents at a time.”
GIANT: Globally Improved Approximate Newton Method for Distributed Optimization (2017, methodology): “Examples of such methods include distributed variants of stochastic gradient descent (SGD) [17, 27, 47], accelerated SGD [35], variance reduction SGD [10, 28], stochastic coordinate descent methods [5, 13, 20, 31] and dual coordinate ascent algorithms [30, 43, 46].”
Linear convergence of first order methods for non-strongly convex optimization (2015, background): “In [10,11] it has been proved that for the class of functions (43) the error bound constant κ f depends on the Hoffman constant θ as κ f = O(1/θ2), and thus the quadratic functional growth constant depends on the Hoffman constant θ as O(κ(2)f ) = O(1/θ4) (recall that the Hoffman constant θ can be ve”
L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework (2015, methodology): “Other parallel coordinate descent methods on the L1-objective have recently been analyzed in [9, 28, 21], but not in the communication-efficient or distributed setting.”