LEADER 03547nam 22006255 450 001 9911031571803321 005 20251001130645.0 010 $a3-032-00854-9 024 7 $a10.1007/978-3-032-00854-1 035 $a(CKB)41520856700041 035 $a(MiAaPQ)EBC32323412 035 $a(Au-PeEL)EBL32323412 035 $a(DE-He213)978-3-032-00854-1 035 $a(EXLCZ)9941520856700041 100 $a20251001d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTurnpike Phenomenon for Markov Decision Processes /$fby Alexander J. Zaslavski 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (183 pages) 225 1 $aSpringerBriefs in Mathematics,$x2191-8201 311 08$a3-032-00853-0 327 $a1. Introduction -- 2. Uniqueness and stability of optimal policies -- 3. Existence of an overtaking optimal policy -- 4. A weak turnpike property -- 5. Convex Markov decision processes -- 6. Turnpike properties for MDPs with perturbations -- 7. Controllability properties -- 8. Optimal control problems with singleton-turnpikes -- 9. Conclusions. 330 $aThis book provides a comprehensive examination of the structure of approximate optimal policies in Markov decision processes (MDPs) with finite state spaces, as well as approximate optimal solutions for deterministic discrete-time optimal control problems. At its core, the monograph delves into the turnpike property, a concept introduced by P. Samuelson, which suggests that optimal solutions are largely determined by the objective function, independent of interval length or endpoint conditions. Key concepts include the uniqueness and stability of minimizing Markov actions, the existence of overtaking optimal policies, and the asymptotic and weak turnpike properties. The authors meticulously examine these phenomena across various classes of MDPs, employing a Baire category approach to demonstrate the generic nature of these properties. The book also addresses the impact of perturbations on cost functions, ensuring the stability of turnpike properties. This monograph is an essential resource for researchers and scholars in the fields of operations research, applied mathematics, and control theory. It provides valuable insights into the intricate dynamics of MDPs and optimal control systems, making it a must-read for anyone seeking to deepen their understanding of these complex topics. 410 0$aSpringerBriefs in Mathematics,$x2191-8201 606 $aMathematical optimization 606 $aCalculus of variations 606 $aProbabilities 606 $aSystem theory 606 $aControl theory 606 $aCalculus of Variations and Optimization 606 $aProbability Theory 606 $aSystems Theory, Control 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aProbabilities. 615 0$aSystem theory. 615 0$aControl theory. 615 14$aCalculus of Variations and Optimization. 615 24$aProbability Theory. 615 24$aSystems Theory, Control. 676 $a519.6 676 $a515.64 700 $aZaslavski$b Alexander J$0721713 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911031571803321 996 $aTurnpike Phenomenon for Markov Decision Processes$94443320 997 $aUNINA