Hogwild! over Distributed Local Data Sets with Linearly Increasing Mini-Batch Sizes
This work addresses communication efficiency in distributed machine learning for heterogeneous data, representing an incremental improvement over existing methods.
The paper tackles the problem of performing asynchronous stochastic gradient descent (SGD) on distributed, heterogeneous data by proposing a method where local nodes start with small mini-batch sizes that increase over time to reduce communication costs. It achieves O(√K) communication rounds for strongly convex problems, with a tight convergence analysis proven for heterogeneous data without relying on bounded gradient assumptions.
Hogwild! implements asynchronous Stochastic Gradient Descent (SGD) where multiple threads in parallel access a common repository containing training data, perform SGD iterations and update shared state that represents a jointly learned (global) model. We consider big data analysis where training data is distributed among local data sets in a heterogeneous way -- and we wish to move SGD computations to local compute nodes where local data resides. The results of these local SGD computations are aggregated by a central "aggregator" which mimics Hogwild!. We show how local compute nodes can start choosing small mini-batch sizes which increase to larger ones in order to reduce communication cost (round interaction with the aggregator). We improve state-of-the-art literature and show $O(\sqrt{K}$) communication rounds for heterogeneous data for strongly convex problems, where $K$ is the total number of gradient computations across all local compute nodes. For our scheme, we prove a \textit{tight} and novel non-trivial convergence analysis for strongly convex problems for {\em heterogeneous} data which does not use the bounded gradient assumption as seen in many existing publications. The tightness is a consequence of our proofs for lower and upper bounds of the convergence rate, which show a constant factor difference. We show experimental results for plain convex and non-convex problems for biased (i.e., heterogeneous) and unbiased local data sets.