Reinforcement learning for automated performance tuning: Initial evaluation for sparse matrix format selection

Abstract

The field of reinforcement learning has developed techniques for choosing beneficial actions within a dynamic environment. Such techniques learn from experience and do not require teaching. This paper explores how reinforcement learning techniques might be used to determine efficient storage formats for sparse matrices. Three different storage formats are considered: coordinate, compressed sparse row, and blocked compressed sparse row. Which format performs best depends heavily on the nature of the matrix and the computer system being used. To test the above a program has been written to generate a series of sparse matrices, where any given matrix performs optimally using one of the three different storage types. For each matrix several sparse matrix vector products are performed. The goal of the learning agent is to predict the optimal sparse matrix storage format for that matrix. The proposed agent uses five attributes of the sparse matrix: the number of rows, the number of columns, the number of non-zero elements, the standard deviation of non-zeroes per row and the mean number of neighbours. The agent is characterized by two parameters: an exploration rate and a parameter that determines how the state space is partitioned. The ability of the agent to successfully predict the optimal storage format is analyzed for a series of 1,000 automatically generated test matrices.