Variance minimization for continuous-time Markov decision processes: two approaches

This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.

Variance Optimization for Continuous-Time Markov Decision Processes

This paper considers the variance optimization problem of average reward in continuous-time Markov decision process (MDP). It is assumed that the state space is countable and the action space is Borel measurable space. The main purpose of this paper is to find the policy with the minimal variance in the deterministic stationary policy space. Unlike the traditional Markov decision process, the cost function in the variance criterion will be affected by future actions. To this end, we convert the variance minimization problem into a standard (MDP) by introducing a concept called pseudo-variance. Further, by giving the policy iterative algorithm of pseudo-variance optimization problem, the optimal policy of the original variance optimization problem is derived, and a sufficient condition for the variance optimal policy is given. Finally, we use an example to illustrate the conclusion of this paper.

CONVERGENCE OF CONTROLLED MODELS FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES WITH CONSTRAINED AVERAGE CRITERIA

This paper attempts to study the convergence of optimal values and optimal policies of continuous-time Markov decision processes(CTMDP for short)under the constrained average criteria. For a given original model M_∞of CTMDP with denumerable states and a sequence {M_n} of CTMDP with finite states, we give a new convergence condition to ensure that the optimal values and optimal policies of {M_n} converge to the optimal value and optimal policy of M_∞as the state space Snof Mnconverges to the state space S_∞of M_∞, respectively. The transition rates and cost/reward functions of M_∞are allowed to be unbounded. Our approach can be viewed as a combination method of linear program and Lagrange multipliers.

STRONG N-DISCOUNT AND FINITE-HORIZON OPTIMALITY FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES

This paper studies the strong n(n =—1,0)-discount and finite horizon criteria for continuoustime Markov decision processes in Polish spaces.The corresponding transition rates are allowed to be unbounded,and the reward rates may have neither upper nor lower bounds.Under mild conditions,the authors prove the existence of strong n(n =—1,0)-discount optimal stationary policies by developing two equivalence relations:One is between the standard expected average reward and strong—1-discount optimality,and the other is between the bias and strong 0-discount optimality.The authors also prove the existence of an optimal policy for a finite horizon control problem by developing an interesting characterization of a canonical triplet.

Average Sample-path Optimality for Continuous-time Markov Decision Processes in Polish Spaces

In this paper we study the average sample-path cost （ASPC） problem for continuous-time Markov decision processes in Polish spaces. To the best of our knowledge, this paper is a first attempt to study the ASPC criterion on continuous-time MDPs with Polish state and action spaces. The corresponding transition rates are allowed to be unbounded, and the cost rates may have neither upper nor lower bounds. Under some mild hypotheses, we prove the existence of （ε〉 0）-ASPC optimal stationary policies based on two different approaches： one is the ＂optimality equation＂ approach and the other is the ＂two optimality inequalities＂ approach.

TOTAL REWARD CRITERIA FOR UNCONSTRAINED/CONSTRAINED CONTINUOUS-TIME MARKOV DECISION PROCESSES

This paper studies denumerable continuous-time Markov decision processes with expected total reward criteria. The authors first study the unconstrained model with possible unbounded transition rates, and give suitable conditions on the controlled system＇s primitive data under which the authors show the existence of a solution to the total reward optimality equation and also the existence of an optimal stationary policy. Then, the authors impose a constraint on an expected total cost, and consider the associated constrained model. Basing on the results about the unconstrained model and using the Lagrange multipliers approach, the authors prove the existence of constrained-optimal policies under some additional conditions. Finally, the authors apply the results to controlled queueing systems.

Modeling and Design of Real-Time Pricing Systems Based on Markov Decision Processes

A real-time pricing system of electricity is a system that charges different electricity prices for different hours of the day and for different days, and is effective for reducing the peak and flattening the load curve. In this paper, using a Markov decision process (MDP), we propose a modeling method and an optimal control method for real-time pricing systems. First, the outline of real-time pricing systems is explained. Next, a model of a set of customers is derived as a multi-agent MDP. Furthermore, the optimal control problem is formulated, and is reduced to a quadratic programming problem. Finally, a numerical simulation is presented.

Robust analysis of discounted Markov decision processes with uncertain transition probabilities

Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.

Adaptive Strategies for Accelerating the Convergence of Average Cost Markov Decision Processes Using a Moving Average Digital Filter

This paper proposes a technique to accelerate the convergence of the value iteration algorithm applied to discrete average cost Markov decision processes. An adaptive partial information value iteration algorithm is proposed that updates an increasingly accurate approximate version of the original problem with a view to saving computations at the early iterations, when one is typically far from the optimal solution. The proposed algorithm is compared to classical value iteration for a broad set of adaptive parameters and the results suggest that significant computational savings can be obtained, while also ensuring a robust performance with respect to the parameters.

Conditional Value-at-Risk for Random Immediate Reward Variables in Markov Decision Processes

We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equations for the discounted or average case. As an application, the inventory models are considered.

Development of Optimal Maintenance Policies for Offshore Wind Turbine Gearboxes Based on the Non-homogeneous Continuous-Time Markov Process

Gearbox in offshore wind turbines is a component with the highest failure rates during operation. Analysis of gearbox repair policy that includes economic considerations is important for the effective operation of offshore wind farms. From their initial perfect working states, gearboxes degrade with time, which leads to decreased working efficiency. Thus, offshore wind turbine gearboxes can be considered to be multi-state systems with the various levels of productivity for different working states. To efficiently compute the time-dependent distribution of this multi-state system and analyze its reliability, application of the nonhomogeneous continuous-time Markov process(NHCTMP) is appropriate for this type of object. To determine the relationship between operation time and maintenance cost, many factors must be taken into account, including maintenance processes and vessel requirements. Finally, an optimal repair policy can be formulated based on this relationship.

Seeking for Passenger under Dynamic Prices: A Markov Decision Process Approach

In recent years, ride-on-demand (RoD) services such as Uber and Didi are becoming increasingly popular. Different from traditional taxi services, RoD services adopt dynamic pricing mechanisms to manipulate the supply and demand on the road, and such mechanisms improve service capacity and quality. Seeking route recommendation has been widely studied in taxi service. In RoD services, the dynamic price is a new and accurate indicator that represents the supply and demand condition, but it is yet rarely studied in providing clues for drivers to seek for passengers. In this paper, we proposed to incorporate the impacts of dynamic prices as a key factor in recommending seeking routes to drivers. We first showed the importance and need to do that by analyzing real service data. We then designed a Markov Decision Process (MDP) model based on passenger order and car GPS trajectories datasets, and took into account dynamic prices in designing rewards. Results show that our model not only guides drivers to locations with higher prices, but also significantly improves driver revenue. Compared with things with the drivers before using the model, the maximum yield after using it can be increased to 28%.

Heterogeneous Network Selection Optimization Algorithm Based on a Markov Decision Model

A network selection optimization algorithm based on the Markov decision process(MDP)is proposed so that mobile terminals can always connect to the best wireless network in a heterogeneous network environment.Considering the different types of service requirements,the MDP model and its reward function are constructed based on the quality of service(QoS)attribute parameters of the mobile users,and the network attribute weights are calculated by using the analytic hierarchy process(AHP).The network handoff decision condition is designed according to the different types of user services and the time-varying characteristics of the network,and the MDP model is solved by using the genetic algorithm and simulated annealing(GA-SA),thus,users can seamlessly switch to the network with the best long-term expected reward value.Simulation results show that the proposed algorithm has good convergence performance,and can guarantee that users with different service types will obtain satisfactory expected total reward values and have low numbers of network handoffs.

A dynamical neural network approach for distributionally robust chance-constrained Markov decision process

In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.

An Optimized Vertical Handoff Algorithm Based on Markov Process in Vehicle Heterogeneous Network

In order to solve the problem the existing vertical handoff algorithms of vehicle heterogeneous wireless network do not consider the diversification of network's status, an optimized vertical handoff algorithm based on markov process is proposed and discussed in this paper. This algorithm takes into account that the status transformation of available network will affect the quality of service(Qo S) of vehicle terminal's communication service. Firstly, Markov process is used to predict the transformation of wireless network's status after the decision via transition probability. Then the weights of evaluating parameters will be determined by fuzzy logic method. Finally, by comparing the total incomes of each wireless network, including handoff decision incomes, handoff execution incomes and communication service incomes after handoff, the optimal network to handoff will be selected. Simulation results show that: the algorithm proposed, compared to the existing algorithm, is able to receive a higher level of load balancing and effectively improves the average blocking rate, packet loss rate and ping-pang effect.

Probabilistic Analysis and Multicriteria Decision for Machine Assignment Problem with General Service Times

In this paper we carried out a probabilistic analysis for a machine repair system with a general service-time distribution by means of generalized Markov renewal processes. Some formulas for the steady-state performance measures. such as the distribution of queue sizes, average queue length, degree of repairman utilization and so on. are then derived. Finally, the machine repair model and a multiple critcria decision-making method are applied to study machine assignment problem with a general service-time distribution to determine the optimum number of machines being serviced by one repairman.

A Novel Dynamic Decision Model in 2-player Symmetric Repeated Games

Considering the dynamic character of repeated games and Markov process, this paper presented a novel dynamic decision model for symmetric repeated games. In this model, players＇ actions were mapped to a Markov decision process with payoffs, and the Boltzmann distribution was intousluced. Our dynamic model is different from others＇ , we used this dynamic model to study the iterated prisoner＇ s dilemma, and the results show that this decision model can successfully be used in symmetric repeated games and has an ability of adaptive learning.

考虑光伏电源可靠性的新能源配电网数据驱动无功电压优化控制

充分挖掘分布式光伏电源的无功支撑能力,有助于解决光伏高比例接入带来的配电网电压波动、电压越限以及新能源消纳等问题,但光伏电源无功输出会造成其功率器件结温越限或剧烈波动,严重威胁到光伏电源的可靠运行。为此,提出考虑光伏电源可靠性的新能源配电网数据驱动无功电压优化控制策略。首先,提出一种基于数据驱动的光伏电源可靠性评估方法,该方法采用XGBoost机器学习模型计算IGBT结温,提高了IGBT结温计算效率,避免了评估精度对IGBT参数的依赖;进而建立考虑光伏电源可靠性的配电网无功电压优化模型,将IGBT结温均值和结温波动引入模型优化目标;然后,将该模型进行马尔可夫决策过程转化,并基于深度确定性策略梯度强化学习算法完成智能体训练;最后,通过IEEE33节点系统验证所提策略在无功电压快速优化和光伏电源可靠性提升方面的优势。

基于深度强化学习的多自动导引车运动规划

为解决移动机器人仓储系统中的多自动导引车(AGV)无冲突运动规划问题,建立了Markov决策过程模型,提出一种新的基于深度Q网络(DQN)的求解方法。将AGV的位置作为输入信息,利用DQN估计该状态下采取每个动作所能获得的最大期望累计奖励,并采用经典的深度Q学习算法进行训练。算例计算结果表明,该方法可以有效克服AGV车队在运动中的碰撞问题,使AGV车队能够在无冲突的情况下完成货架搬运任务。与已有启发式算法相比,该方法求得的AGV运动规划方案所需要的平均最大完工时间更短。

支持无线采能及簇间负载均衡的无人机辅助数据调度及轨迹优化算法

该文研究了无人机(UAV)辅助无线传感器网络的数据收集问题。首先提出基于均值漂移算法的传感器节点(SN)初始分簇策略,进而以簇间负载均衡为目标,设计SN切换算法。基于所得成簇策略,将UAV数据收集及轨迹规划问题建模为系统能耗最小化问题。由于该问题是一个非凸问题,难以直接求解,将其分为两个子问题,即数据调度子问题及UAV轨迹规划子问题。针对数据调度子问题,提出一种基于多时隙库恩-蒙克雷斯算法的时频资源调度策略。针对UAV轨迹规划子问题,将其建模为马尔可夫决策过程,并提出一种基于深度Q网络的UAV轨迹规划算法。仿真结果验证了所提算法的有效性。