Algorithm selection as a bandit problem with unbounded losses

  • Authors:

  • Matteo Gagliolo;Jürgen Schmidhuber

  • Affiliations:

  • IDSIA, Manno, Lugano, Switzerland and University of Lugano, Faculty of Informatics, Lugano, Switzerland;IDSIA, Manno, Lugano, Switzerland and University of Lugano, Faculty of Informatics, Lugano, Switzerland

  • Venue:
  • LION'10 Proceedings of the 4th international conference on Learning and intelligent optimization
  • Year:
  • 2010

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Abstract

Algorithm selection is typically based on models of algorithm performance learned during a separate offline training sequence, which can be prohibitively expensive. In recent work, we adopted an online approach, in which a performance model is iteratively updated and used to guide selection on a sequence of problem instances. The resulting exploration-exploitation trade-off was represented as a bandit problem with expert advice, using an existing solver for this game, but this required the setting of an arbitrary bound on algorithm runtimes, thus invalidating the optimal regret of the solver. In this paper, we propose a simpler framework for representing algorithm selection as a bandit problem, with partial information, and an unknown bound on losses. We adapt an existing solver to this game, proving a bound on its expected regret, which holds also for the resulting algorithm selection technique. We present experiments with a set of SAT solvers on a mixed SAT-UNSAT benchmark.