On Constructing Cost Models for Online Automatic Tuning Using ATMathCoreLib: Case Studies through the SVD Computation on a Multicore Processor

We consider the problem of online automatic tuning. In this setting, we execute the target program with some tuning parameters N times, where N is given, while optimizing the parameters to minimize some objective function such as the total execution time. Thus we have to choose the parameters for each execution by taking into account the trade-off between exploration and exploitation. The ATMathCoreLib library developed by Suda is a set of software that solves this problem. To model the performance of the target software, ATMathCoreLib uses a linear statistical model, and its basis functions must be provided by the user. In this paper, we investigate how to choose the basis functions appropriately, using the singular value decomposition of a square matrix as an example. We consider three cases, namely, (I) when the performance characteristics of the target problem are well understood by the user, (II) when the tuning parameter has a complicated structure, as occurs in the case of simultaneous selection of an algorithm and its parameter, and (III) when the performance characteristics of the target problem are not known to the user. The results of using ATMathCoreLib with different basis functions for each case are given. They help one understand the tuning by ATMathCoreLib and contribute to the progress of ATMathCoreLib.