Download Dynamic Programming and its Applications. Proceedings of the by M.L. Puterman PDF
By M.L. Puterman
Read or Download Dynamic Programming and its Applications. Proceedings of the International Conference on Dynamic Programming and its Applications, University of British Columbia, Vancouver, British Columbia, Canada, April 14–16, 1977 PDF
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Additional info for Dynamic Programming and its Applications. Proceedings of the International Conference on Dynamic Programming and its Applications, University of British Columbia, Vancouver, British Columbia, Canada, April 14–16, 1977
Example text
2) that the T-operator never has a unique fixed point and hence is never a contraction operator on E N (and neither is any of its powers). 3) J sp[x] rL J = x - x . max min as a quasi-norm ( c f . Bather [ 2 ] ) . However, Example 1 i n [13] shows t h a t T (or any of i t s powers) i s n o t n e c e s s a r i l y contracting with r e s p e c t t o t h e sp-norm e i t h e r . That i s , only under s p e c i a l c o n d i t i o n s with r e s p e c t t o t h e ( c h a i n and p e r i o d i c t y ) s t r u c t u r e of t h e problem, ( c f .
V . ] , 1 X keL(i) X j 1J 3 3 , i = 1, * · · , Ν i = 1, ,N where L(i) = { k e K ( i ) | g = I Pk j J g } , J i = 1, . . 6) always have a s o l u t i o n p a i r ( cf. Howard [22]) and each s o l u t i o n p a i r (g,v) has g = g , so t h a t t h e s e t s L ( i ) a r e u n i q u e l y determined as w e l l . However, u n l i k e t h e d i s counted c a s e , v i s not u n i q u e l y determined by ( 4 . 6 ) . Note e . g . , t h a t i f v s a t i s f i e s ( 4 . _ f o r any s c a l a r c. A c h a r a c t e r i z a t i o n of t h e s e t V = { v | v s a t i s f i e s ( 4 .
4. of * v , v as a r e l a t i v e value vector for any policy in S(n), i . e . , S(n) Ç S (v*) , as well as on the length of the t a i l of an i n i t i a l l y stationary (periodic) ε-optimal strategy. All of the bounds in ( l ) - ( 4 ) vary logarithmically with ε~ sp[Tx-x] where in (2), ε has to be taken < minig* - g \keS, * AT AI g > g } and in (3), ε has to be taken < min{sp[v* - v ] |Αε5, * A sp[v - v ] > 0 } . Except for the case where every policy is Discounted and Undiscounted Value-Iteration 43 unichained ( cf.