Miguel A Carreira-Perpinan, Mehdi Alizadeh
Many powerful machine learning models are based on the composition of multiple processing layers, such as deep nets, which gives rise to nonconvex objective functions. A general, recent approach to optimise such "nested" functions is the method of auxiliary coordinates (MAC). MAC introduces an auxiliary coordinate for each data point in order to decouple the nested model into independent submodels. This decomposes the optimisation into steps that alternate between training single layers and updating the coordinates. It has the advantage that it reuses existing single-layer algorithms, introduces parallelism, and does not need to use chain-rule gradients, so it works with nondifferentiable layers. We describe ParMAC, a distributed-computation model for MAC. This trains on a dataset distributed across machines while limiting the amount of communication so it does not obliterate the benefit of parallelism. ParMAC works on a cluster of machines with a circular topology and alternates two steps until convergence: one step trains the submodels in parallel using stochastic updates, and the other trains the coordinates in parallel. Only submodel parameters, no data or coordinates, are ever communicated between machines. ParMAC exhibits high parallelism, low communication overhead, and facilitates data shuffling, load balancing, fault tolerance and streaming data processing. We study the convergence of ParMAC and its parallel speedup, and implement ParMAC using MPI to learn binary autoencoders for fast image retrieval, achieving nearly perfect speedups in a 128-processor cluster with a training set of 100 million images.