Efficient Protocols for Distributed Classification and Optimization

TL;DR

This paper introduces communication-efficient protocols for distributed classification and optimization, improving upon prior models with simple, scalable algorithms that are empirically validated and applicable to various convex problems.

Contribution

Develops a new two-party multiplicative-weight-update protocol with optimal communication bounds for distributed classification and extends it to multiple nodes and convex optimization problems.

Findings

Protocol uses $O(d^2 \, \log{1/\eps})$ words for classification.

Extends to $O(kd^2 \, \log{1/\eps})$ words for $k$ nodes.

Empirically more efficient than baseline methods.

Abstract

In distributed learning, the goal is to perform a learning task over data distributed across multiple nodes with minimal (expensive) communication. Prior work (Daume III et al., 2012) proposes a general model that bounds the communication required for learning classifiers while allowing for $\eps$ training error on linearly separable data adversarially distributed across nodes. In this work, we develop key improvements and extensions to this basic model. Our first result is a two-party multiplicative-weight-update based protocol that uses $O(d^2 \log{1/\eps})$ words of communication to classify distributed data in arbitrary dimension $d$, $\eps$-optimally. This readily extends to classification over $k$ nodes with $O(kd^2 \log{1/\eps})$ words of communication. Our proposed protocol is simple to implement and is considerably more efficient than baselines compared, as demonstrated by our empirical results. In addition, we illustrate general algorithm design paradigms for doing efficient learning over distributed data. We show how to solve fixed-dimensional and high dimensional linear programming efficiently in a distributed setting where constraints may be distributed across nodes. Since many learning problems can be viewed as convex optimization problems where constraints are generated by individual points, this models many typical distributed learning scenarios. Our techniques make use of a novel connection from multipass streaming, as well as adapting the multiplicative-weight-update framework more generally to a distributed setting. As a consequence, our methods extend to the wide range of problems solvable using these techniques.