Parallel Optimization

This work generalizes 1D s-step SGD and 1D Federated SGD with Averaging (FedAvg) to yield a 2D parallel SGD method (HybridSGD) that attains a continuous performance trade-off between the two baseline algorithms. We present theoretical analysis of the convergence, computation, communication, and memory trade-offs, and a C++/MPI implementation that achieves speedups of up to 5.3x over s-step SGD and up to 121x over FedAvg on a Cray EX system.

This work introduces Communication-Avoiding SGD (CA-SGD) for distributed-memory logistic regression. CA-SGD reorganizes stochastic gradient computations to communicate every $s$ iterations instead of every iteration and achieves speedups of up to 4.97x over SGD on a high-performance InfiniBand cluster without altering convergence behavior or accuracy.

This work develops communication-avoiding variants of primal and dual block coordinate descent for regularized least-squares problems. The variants communicate every $s$ iterations instead of every iteration and attain strong-scaling speedups up to 6.1x on a Cray XC30 supercomputer.