Graph Oracle Models, Lower Bounds, and Gaps for Parallel Stochastic Optimization [article]

Blake Woodworth, Jialei Wang, Adam Smith, Brendan McMahan, Nathan Srebro
2019 arXiv   pre-print
We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed updates and parallel processing with intermittent communication. We highlight gaps between lower and upper bounds on the oracle complexity, and cases where the "natural" algorithms are not known to be optimal.
arXiv:1805.10222v3 fatcat:islrouwldjdarbl64qmrkt2wli