Error bounds for approximations from projected linear equations

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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 ixed point mapping is a contraction, as is typically the case in Markov decision processes (MDP), one of our bounds is always sharper than the standard contraction-based bounds, and another one is often sharper. The former bound is also tight in a worst-case sense. Our bounds also apply to the noncontraction 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.

Original languageEnglish (US)
Pages (from-to)306-329
Number of pages24
JournalMathematics of Operations Research
Issue number2
StatePublished - May 2010
Externally publishedYes


  • Dynamic programming
  • Error bounds
  • Function approximation
  • Galerkin methods
  • Projected linear equations
  • Temporal difference methods

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research


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