New Error Bounds for Approximations from Projected Linear Equations

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. Joint Technical Report of U.H. and M.I.T. Technical Report C-2008-43 Dept. Computer Science University of Helsinki and LIDS Report 2797 Dept. EECS M.I.T. July 2008 Huizhen Yu is with HIIT and Dept. Computer Science, University of Helsinki, Finland. Dimitri Bertsekas is with the Laboratory for ...

• Type: Conference
• Year: 2008
• Where: EWRL
• Authors: Huizhen Yu, Dimitri P. Bertsekas
• Keywords: EWRL 2008, Low Dimensional Matrices, Low Dimensional Subspace, Machine Learning, Worst Case Bounds