Lattice-search runtime distributions may be heavy-tailed

  • Authors:
  • Filip Železny;Ashwin Srinivasan;David Page

  • Affiliations:
  • Dept. of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Czech Republic;Oxford University Computing Laboratory, Oxford, UK;Dept. of Biostatistics and Medical Informatics and Dept. of Computer Science, University of Wisconsin, Madison, WI

  • Venue:
  • ILP'02 Proceedings of the 12th international conference on Inductive logic programming
  • Year:
  • 2002

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Abstract

Recent empirical studies show that runtime distributions of backtrack procedures for solving hard combinatorial problems often have intriguing properties. Unlike standard distributions (such as the normal), such distributions decay slower than exponentially and have "heavy tails". Procedures characterized by heavy-tailed runtime distributions exhibit large variability in efficiency, but a very straightforward method called rapid randomized restarts has been designed to essentially improve their average performance. We show on two experimental domains that heavy-tailed phenomena can be observed in ILP, namely in the search for a clause in the subsumption lattice. We also reformulate the technique of randomized rapid restarts to make it applicable in ILP and show that it can reduce the average search-time.