2004 Fiscal Year Final Research Report Summary
Studios on theory of optimization with utility in stochastic model
| Project/Area Number |
14540125
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kochi University |
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Principal Investigator |
OHTSUBO Yoshio Kochi University, Faculty of Science, Professor, 理学部, 教授 (20136360)
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| Co-Investigator(Kenkyū-buntansha) |
YASUDA Masami Chiba University, Faculty of Science, Professor, 理学部, 教授 (00041244)
IWAMOTO Seiiti Kyushu University, Faculty of Economics, Professor, 大学院・経済学研究院, 教授 (90037284)
NIIZEKI Shozo Kochi University, Faculty of Science, Professor, 理学部, 教授 (60036572)
NOMAKUCHI Kentaro Kochi University, Faculty of Science, Professor, 理学部, 教授 (60124806)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Markov decision process / threshold probability / optimal value and optimal policy / equivalence class / Fuzzy measure / stochastic optimization / finite intersection family / EM algorithm |
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| Research Abstract |
The summary of research results is as follows.
1.We consider risk minimizing problems in undiscounted Markov decisions processes with a target set. We formulate the problem as an infinite horizon case with a recurrent class. We show that an optimal value function is a unique solution to an optimality equation and there exists an stationary optimal policy. Also we give several value iteration methods and a policy improvement method. We also consider eight problems in which we maximize or minimize threshold probabilities in discounted Markov decision processes with bounded reward set. We show that such problems are classified to two equivalence classes and give a relationship between optimal values and optimal policies of problems in each equivalence class. We also give two sufficient conditions for the existence of an optimal policy. Finally we give a relationship of optimal values between first and second equivalence classes.
2.We solves a finite horizon stochastic optimization problem with forward recursive criterion through dynamic programming. The basic idea is to apply invariant imbedding method for stochastic programming.
3.We show that weakly null-additive fuzzy measures on metric spaces posses regularity Lusin's theorem is generalized to fuzzy measure space by using the regularity and weakly null-additivity
4.We introduce an idea of finite intersection family into a topological space, characterize several concepts in a topological space by mean of finite intersection family and illustrate some applications of finite intersection family.
5.EM-algorithm users believe that the conditions of Wu(1983) assure the convergence of GEM sequence, but this paper gives a brief counter example which satisfies Wu's conditions but not converge to MILE or any optimal solutions. It also gives a correction of his proof for the convergence of EM sequence.
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