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We consider learning problems over training sets in which both, the number oftraining examples and the dimension of the feature vectors, are large. To solvethese problems we propose the random parallel stochastic algorithm (RAPSA). Wecall the algorithm random parallel because it utilizes multiple processors tooperate in a randomly chosen subset of blocks of the feature vector. We callthe algorithm parallel stochastic because processors choose elements of thetraining set randomly and independently. Algorithms that are parallel in eitherof these dimensions exist, but RAPSA is the first attempt at a methodology thatis parallel in both, the selection of blocks and the selection of elements ofthe training set. In RAPSA, processors utilize the randomly chosen functions tocompute the stochastic gradient component associated with a randomly chosenblock. The technical contribution of this paper is to show that this minimallycoordinated algorithm converges to the optimal classifier when the trainingobjective is convex. In particular, we show that: (i) When using decreasingstepsizes, RAPSA converges almost surely over the random choice of blocks andfunctions. (ii) When using constant stepsizes, convergence is to a neighborhoodof optimality with a rate that is linear in expectation. RAPSA is numericallyevaluated on the MNIST digit recognition problem.

Doubly Random Parallel Stochastic Methods for Large Scale Learning