  We consider distributed optimization problems where forming the Hessian is
computationally challenging and communication is a significant bottleneck. We
develop unbiased parameter averaging methods for randomized second order
optimization that employ sampling and sketching of the Hessian. Existing works
do not take the bias of the estimators into consideration, which limits their
application to massively parallel computation. We provide closed-form formulas
for regularization parameters and step sizes that provably minimize the bias
for sketched Newton directions. We also extend the framework of second order
averaging methods to introduce an unbiased distributed optimization framework
for heterogeneous computing systems with varying worker resources.
Additionally, we demonstrate the implications of our theoretical findings via
large scale experiments performed on a serverless computing platform.
