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An average-value-at-risk criterion for markov decision processes with unbounded costs

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Frontiers of Mathematics in China 2022年第4期17卷 673-687页

作者： Qiuli LIU Wai-Ki CHING Junyu ZHANG Hongchu WANG School of Mathematical Sciences South China Normal UniversityGuangzhou510631China Advanced Modeling and Applied Computing Laboratory Department of MathematicsThe University of Hong KongHong KongChina School of Mathematics Sun Yat-Sen UniversityGuangzhou510275China

We study the markov decision processes under the average-value-at-risk *** state space and the action space are Borel spaces,the costs are admitted to be unbounded from above,and the discount factors are state-action *** suitable conditions,we establish the existence of optimal deterministic stationary ***,we apply our main results to a cash-balance model.

关键词： markov decision processes average-value-at-risk(AVaR) state-action dependent discount factors optimal policy

Solving markov decision processes with Downside Risk Adjustment

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International Journal of Automation and computing 2016年第3期13卷 235-245页

作者： Abhijit Gosavi Anish Parulekar 219 Engineering Management Building Department of Engineering Management and Systems Engineering Missouri University of Science and Technology Rolla MO 65409 USA Axis Bank Mumbai India

markov decision processes （MDPs） and their variants are widely studied in the theory of controls for stochastic discrete- event systems driven by markov chains. Much of the literature focusses on the risk-neutral criterion in which the expected rewards, either average or discounted, are maximized. There exists some literature on MDPs that takes risks into account. Much of this addresses the exponential utility （EU） function and mechanisms to penalize different forms of variance of the rewards. EU functions have some numerical deficiencies, while variance measures variability both above and below the mean rewards; the variability above mean rewards is usually beneficial and should not be penalized/avoided. As such, risk metrics that account for pre-specified targets （thresholds） for rewards have been considered in the literature, where the goal is to penalize the risks of revenues falling below those targets. Existing work on MDPs that takes targets into account seeks to minimize risks of this nature. Minimizing risks can lead to poor solutions where the risk is zero or near zero, but the average rewards are also rather low. In this paper, hence, we study a risk-averse criterion, in particular the so-called downside risk, which equals the probability of the revenues falling below a given target, where, in contrast to minimizing such risks, we only reduce this risk at the cost of slightly lowered average rewards. A solution where the risk is low and the average reward is quite high, although not at its maximum attainable value, is very attractive in practice. To be more specific, in our formulation, the objective function is the expected value of the rewards minus a scalar times the downside risk. In this setting, we analyze the infinite horizon MDP, the finite horizon MDP, and the infinite horizon semi-MDP （SMDP）. We develop dynamic programming and reinforcement learning algorithms for the finite and infinite horizon. The algorithms are tested in numerical studies an

关键词： Downside risk markov decision processes reinforcement learning dynamic programming targets thresholds.

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WEIGHTED DISCOUNTED markov decision processes WITH PERTURBATION

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Acta Mathematicae Applicatae Sinica 1999年第2期15卷 183-189页

作者：刘克 Institute of Applied Mathematics the Chinese Academy of Sciences Beijing China

In this paper we consider the weighted reward discounted markov decision processes orMDP's, for short, with perturbation. We give the proof of existence of an optimal simple ulti-mately deterministic policy for process We also prove that there exists a -optimalsimple ultimately deterministic policy in the perturbed weighted MDP, for all Finally weprove the following result: If is an optimal policy of then for any >0 there existsan -neighborhood B(D) such that when D1 B(D), is a -optimal policy of

关键词： markov decision processes perturbation optimal policy

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CONTINUOUS TIME markov decision processes (CTMDP) WITH NON-UNIFORMLY BOUNDED TRANSITION RATES

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中国科学A辑(英文版) 1988年第11期 1281-1291页

作者：宋京生 Institute of Applied Mathematics Academia Sinica Beijing

CTMDP are considered in the situation of denumerable state space, finite action sets and bounded rewards. The distinction of this paper from others is that the transition rate matrices need not to be uniformly bounded as they used to be required. Under a new but a much weaker assumption, which is also a sufficient condition for the uniqueness of Q-process. We have proved all the former results (of. [4, 5]). Some new and excellent properties about optimal policies are given. The general class of policies is the class of all stochastic markov policies.

关键词： markov decision processes transition rate optimal stationary policy denumerable state.

Potential-based sensitivity estimation for markov decision processes with general state space

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Potential-based sensitivity estimation for Markov decision p...

ENTROPIC MEASUREMENTS OF COMPLEXITY FOR FULLY OBSERVABLE markov decision processes

第二十一届中国控制会议

作者： FANG Hai-tao , CAO Xi-ren ( Institute of Systems Science, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing, 100080, China Department of EEE, Hong Kong University of Science and TechnologyClear Water Bay, Kowloon, Hongkong)

＜正＞We propose a unified formulation for the performance sensitivity analysis of markov chain and MDPs in general state space with both infinite horizon average-cost and discounted performance criteria. And the sens... 详细信息

关键词： markov decision processes Poisson equations potentials sensitivity analysis W-factors

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ENTROPIC MEASUREMENTS OF COMPLEXITY FOR FULLY OBSERVABLE MAR...

Service Migration Algorithm Based on markov decision Process with Multiple Service Types and Multiple System Factors

The Fourth International Conference on Systems Science and Systems Engineering(ICSSSE’03)

作者： Hongwei Wang Chen Li Huixin LiuInstitute of Systems Engineering Huazhong University of Science and Technology Wuhan 430074 P.R.China

＜正＞ Complex dynamic systems are an active topic,and how to measure the complexity of dynamic decisions still remains to be an unresolved *** this paper,we apply Shannon’s entropy as well as other entropy indices to measure the complexity for fully observable markov decision processes,and extend the measurements of the complexity,uncertainty and unpredictability for markov Chains to the measurements for markov decision *** develop a methodology of information-theoretic complexity measurements for fully observable markov decision processes.

关键词： Entropic Measurement Complexity markov Chain markov decision processes

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Chinese Journal of Electronics 2024年第6期33卷 1515-1525页

作者： Anhua MA Su PAN Weiwei ZHOU Broadband Wireless Communication College Nanjing University of Posts and Telecommunications School of Computer Science and Technology Nanjing Tech University

This paper proposes a markov decision process based service migration algorithm to satisfy quality of service(QoS) requirements when the terminals leave the original server. Services were divided into real-time services and non-real-time services, each type of them has different requirements on transmission bandwidth and latency,which were considered in the revenue function. Different values were assigned to the weight coefficients of QoS parameters for different service types in the revenue and cost functions so as to distinguish the differences between the two service types. The overall revenue was used for migration decisions, rather than fixed threshold or instant *** markov decision process was used to maximize the overall revenue of the system. Simulation results show that the proposed algorithm obtained more revenue compared with the existing works.

关键词： Energy consumption Costs markov decision processes Simulation Quality of service Market research Cost function Real-time systems Energy efficiency Servers

Model Checking Computation Tree Logic over Multi-Valued decision processes and Its Reduction Techniques

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Chinese Journal of Electronics 2024年第6期33卷 1399-1411页

作者： Wuniu LIU Junmei WANG Qing HE Yongming LI School of Mathematics and Statistics Shaanxi Normal University School of Computer Science Shaanxi Normal University

Model checking computation tree logic based on multi-valued possibility measures has been studied by Li et al. on Information Sciences in 2019. However, the previous work did not consider the nondeterministic choices inherent in systems represented by multi-valued Kripke structures(MvKSs). This nondeterminism is crucial for accurate system modeling, decision making, and control capabilities. To address this limitation, we draw inspiration from the generalization of markov chains to markov decision processes in probabilistic systems. By integrating nondeterminism into MvKS, we introduce multi-valued decision processes(MvDPs) as a framework for modeling MvKSs with nondeterministic choices. We investigate the problems of model checking over MvDPs. Verifying properties are expressed by using multi-valued computation tree logic based on schedulers. Our primary objective is to leverage fixpoint techniques to determine the maximum and minimum possibilities of the system satisfying temporal *** allows us to identify the optimal or worst-case schedulers for decision making or control purposes. We aim to develop reduction techniques that enhance the efficiency of model checking, thereby reducing the associated time complexity. We mathematically demonstrate three reduction techniques that improve model checking performance in most scenarios.

关键词： Statistical analysis Computational modeling Scalability markov decision processes decision making Model checking Systems modeling Probabilistic logic Mathematical models Time complexity

Inspection strategies for quality products withrewards in a multi-stage production

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Journal of Control and decision 2023年第4期10卷 596-609页

作者： R.Satheesh Kumar A.Nagarajan Department of Mathematics PSNA College of Engineering and TechnologyDindigulIndia

In a multi-stage manufacturing system,defective components are generated due to deteriorating machine parts and failure to install the feed *** these circumstances,the system requires inspection counters to distinguish imperfect items and takes a few discreet decisions to produce impeccable *** the prioritisation of employee appreciation and working on reward is one of the important policies to improve *** we look at the multistage manufacturing system as an M/PH/1 queue model and rewards are given for using certain inspection strategies to produce the quality items.A matrix analytical method is proposed to explain a continuous-time markov process in which the reward points are given to the strategy of inspection in each state of the *** constructing the value functions of this dynamic programming model,we derive the optimal policy and the optimal average reward of the entire system in the long *** addition,we obtain the percentage of time spent on each system state for the probability of conformity and non-conformity of the product over the long *** results of our computational experiments and case study suggest that the average reward increases due to the actions are taken at each decision epoch for rework and disposal of the non-conformity items.

关键词： Sequential process infinitesimal operator markov decision processes value function optimal policy optimal average reward