New Error Bounds for Approximations from Projected Linear Equations

  • Authors:
  • Huizhen Yu;Dimitri P. Bertsekas

  • Affiliations:
  • Helsinki Institute for Information Technology (HIIT), University of Helsinki, Finland;Laboratory for Information and Decision Systems (LIDS), M.I.T., Cambridge, USA MA 02139

  • Venue:
  • Recent Advances in Reinforcement Learning
  • Year:
  • 2008

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Abstract

We consider linear fixed point equations and their approximations by projection on a low dimensional subspace. We derive new bounds on the approximation error of the solution, which are expressed in terms of low dimensional matrices and can be computed by simulation. When the fixed point mapping is a contraction, as is typically the case in Markovian decision processes (MDP), one of our bounds is always sharper than the standard worst case bounds, and another one is often sharper. Our bounds also apply to the non-contraction case, including policy evaluation in MDP with nonstandard projections that enhance exploration. There are no error bounds currently available for this case to our knowledge.