AdaBatch: Efficient Gradient Aggregation Rules for Sequential and Parallel Stochastic Gradient Methods

We study a new aggregation operator for gradients coming from a mini-batch for stochastic gradient (SG) methods that allows a significant speed-up in the case of sparse optimization problems. We call this method AdaBatch and it only requires a few lines of code change compared to regular mini-batch SGD algorithms. We provide a theoretical insight to understand how this new class of algorithms is performing and show that it is equivalent to an implicit per-coordinate rescaling of the gradients, similarly to what Adagrad methods can do. In theory and in practice, this new aggregation allows to keep the same sample efficiency of SG methods while increasing the batch size. Experimentally, we also show that in the case of smooth convex optimization, our procedure can even obtain a better loss when increasing the batch size for a fixed number of samples. We then apply this new algorithm to obtain a parallelizable stochastic gradient method that is synchronous but allows speed-up on par with Hogwild! methods as convergence does not deteriorate with the increase of the batch size. The same approach can be used to make mini-batch provably efficient for variance-reduced SG methods such as SVRG

Numerically Computing QCD Laplace Sum-Rules Using pySecDec

pySecDec is a program that numerically calculates dimensionally regularized integrals. We use pySecDec to compute QCD Laplace sum-rules for pseudoscalar (i.e., $J^{PC}=0^{-+}$) charmonium hybrids, and compare the results to sum-rules computed using analytic results for dimensionally regularized integrals. We find that the errors due to the use of numerical integration methods is negligible compared to the uncertainties in the sum-rules stemming from the uncertainties in the parameters of QCD, e.g., the coupling constant, quark masses, and condensate values. Also, we demonstrate that numerical integration methods can be used to calculate finite-energy and Gaussian sum-rules in addition to Laplace sum-rules.Comment: 10 pages, 5 figure