TY - GEN
T1 - New error bounds for approximations from projected linear equations
AU - Yu, Huizhen
AU - Bertsekas, Dimitri P.
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=64549107571&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=64549107571&partnerID=8YFLogxK
U2 - 10.1109/ALLERTON.2008.4797685
DO - 10.1109/ALLERTON.2008.4797685
M3 - Conference contribution
AN - SCOPUS:64549107571
SN - 9781424429264
T3 - 46th Annual Allerton Conference on Communication, Control, and Computing
SP - 1116
EP - 1123
BT - 46th Annual Allerton Conference on Communication, Control, and Computing
T2 - 46th Annual Allerton Conference on Communication, Control, and Computing
Y2 - 24 September 2008 through 26 September 2008
ER -