Rateless Codes for Near-Perfect Load Balancing in Distributed Matrix-Vector Multiplication

Large-scale machine learning and data mining applications require computer systems to perform massive matrix-vector and matrix-matrix multiplication operations that need to be parallelized across multiple nodes. The presence of straggling nodes--computing nodes that unpredictably slow down or fail--is a major bottleneck in such distributed computations. Ideal load balancing strategies that dynamically allocate more tasks to faster nodes require knowledge or monitoring of node speeds as well as the ability to quickly move data. Recently proposed fixed-rate erasure coding strategies can handle unpredictable node slowdown, but they ignore partial work done by straggling nodes, thus resulting in a lot of redundant computation. We propose a rateless fountain coding strategy that achieves the best of both worlds--we prove that its latency is asymptotically equal to ideal load balancing, and it performs asymptotically zero redundant computations. Our idea is to create linear combinations of the m rows of the matrix and assign these encoded rows to different worker nodes. The original matrix-vector product can be decoded as soon as slightly more than m row-vector products are collectively finished by the nodes. Evaluation on parallel and distributed computing yields as much as three times speedup over uncoded schemes. Matrix-vector multiplications form the core of a plethora of scientific computing and machine learning applications that include solving partial differential equations, forward and back propagation in neural networks, computing the PageRank of graphs, etcetera. In the age of Big Data, most of these applications involve multiplying extremely large matrices and vectors and the computations cannot be performed efficiently on a single machine. This has motivated the development of several algorithms that seek to speed up matrix-vector multiplication by distributing the computation across multiple computing nodes.