This article explores controllable Borel spaces, stationary, homogeneous Markov processes, discrete time with infinite horizon, with bounded cost functions and using the expected total discounted cost criterion. The p...This article explores controllable Borel spaces, stationary, homogeneous Markov processes, discrete time with infinite horizon, with bounded cost functions and using the expected total discounted cost criterion. The problem of the estimation of stability for this type of process is set. The central objective is to obtain a bounded stability index expressed in terms of the Lévy-Prokhorov metric;likewise, sufficient conditions are provided for the existence of such inequalities.展开更多
In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary poli...In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary policies and for the value functions, the stability index is explicitly calculated and through statistical techniques its asymptotic behavior is investigated (using numerical experiments) when the discount coefficient approaches 1. The results obtained define the conditions under which an approximate optimal stationary policy can be used to control the original process.展开更多
Due to various advantages in storage and implementation, simple strategies are usually preferred than complex strategies when the performances are close. Strategy optimization for controlled Markov process with descri...Due to various advantages in storage and implementation, simple strategies are usually preferred than complex strategies when the performances are close. Strategy optimization for controlled Markov process with descriptive complexity constraint provides a general framework for many such problems. In this paper, we first show by examples that the descriptive complexity and the performance of a strategy could be independent, and use the F-matrix in the No-Free-Lunch Theorem to show the risk that approximating complex strategies may lead to simple strategies that are unboundedly worse in cardinal performance than the original complex strategies. We then develop a method that handles the descriptive complexity constraint directly, which describes simple strategies exactly and only approximates complex strategies during the optimization. The ordinal performance difference between the resulting strategies of this selective approximation method and the global optimum is quantified. Numerical examples on an engine maintenance problem show how this method improves the solution quality. We hope this work sheds some insights to solving general strategy optimization for controlled Markov process with descriptive complexity constraint.展开更多
文摘This article explores controllable Borel spaces, stationary, homogeneous Markov processes, discrete time with infinite horizon, with bounded cost functions and using the expected total discounted cost criterion. The problem of the estimation of stability for this type of process is set. The central objective is to obtain a bounded stability index expressed in terms of the Lévy-Prokhorov metric;likewise, sufficient conditions are provided for the existence of such inequalities.
文摘In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary policies and for the value functions, the stability index is explicitly calculated and through statistical techniques its asymptotic behavior is investigated (using numerical experiments) when the discount coefficient approaches 1. The results obtained define the conditions under which an approximate optimal stationary policy can be used to control the original process.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60274011, 60574067, 60704008, 60736027, 60721003, 90924001)the New Century Excellent Talents in University (Grant No. NCET-04-0094)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20070003110)the Programme of Introducing Talents of Discipline to Universities (the National 111 International Collaboration Projects) (Grant No. B06002)
文摘Due to various advantages in storage and implementation, simple strategies are usually preferred than complex strategies when the performances are close. Strategy optimization for controlled Markov process with descriptive complexity constraint provides a general framework for many such problems. In this paper, we first show by examples that the descriptive complexity and the performance of a strategy could be independent, and use the F-matrix in the No-Free-Lunch Theorem to show the risk that approximating complex strategies may lead to simple strategies that are unboundedly worse in cardinal performance than the original complex strategies. We then develop a method that handles the descriptive complexity constraint directly, which describes simple strategies exactly and only approximates complex strategies during the optimization. The ordinal performance difference between the resulting strategies of this selective approximation method and the global optimum is quantified. Numerical examples on an engine maintenance problem show how this method improves the solution quality. We hope this work sheds some insights to solving general strategy optimization for controlled Markov process with descriptive complexity constraint.
