Error Bounds for Approximations from Projected Linear Equations

• 成果类型: Article
• 署名作者: Yu, Huizhen; Bertsekas, Dimitri P.
• 署名单位: University of Helsinki; Massachusetts Institute of Technology (MIT)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1100.0441
• 发表日期: 2010
• 页码: 306-329
• 关键词: algorithms

摘要

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 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.