Decentralized Feature-Distributed Optimization for Generalized Linear Models

TL;DR

This paper introduces a decentralized optimization method for generalized linear models where features are distributed among agents, using a primal-dual algorithm with proven convergence rates under different loss function assumptions.

Contribution

It develops a novel decentralized feature-distributed optimization approach for generalized linear models employing the Chambolle--Pock algorithm with convergence guarantees.

Findings

Convergence rates depend on loss function properties and network topology.

The method efficiently handles feature partitioning among agents.

The approach applies to regularized empirical risk minimization.

Abstract

We consider the "all-for-one" decentralized learning problem for generalized linear models. The features of each sample are partitioned among several collaborating agents in a connected network, but only one agent observes the response variables. To solve the regularized empirical risk minimization in this distributed setting, we apply the Chambolle--Pock primal--dual algorithm to an equivalent saddle-point formulation of the problem. The primal and dual iterations are either in closed-form or reduce to coordinate-wise minimization of scalar convex functions. We establish convergence rates for the empirical risk minimization under two different assumptions on the loss function (Lipschitz and square root Lipschitz), and show how they depend on the characteristics of the design matrix and the Laplacian of the network.