In this study, by starting from Maximum entropy (MaxEnt) distribution of time series, we introduce a measure that quantifies information worth of a set of autocovariances. The information worth of autocovariences is m...In this study, by starting from Maximum entropy (MaxEnt) distribution of time series, we introduce a measure that quantifies information worth of a set of autocovariances. The information worth of autocovariences is measured in terms of entropy difference of MaxEnt distributions subject to different autocovariance sets due to the fact that the information discrepancy between two distributions is measured in terms of their entropy difference in MaxEnt modeling. However, MinMaxEnt distributions (models) are obtained on the basis of MaxEnt distributions dependent on parameters according to autocovariances for time series. This distribution is the one which has minimum entropy and maximum information out of all MaxEnt distributions for family of time series constructed by considering one or several values as parameters. Furthermore, it is shown that as the number of autocovariances increases, the entropy of approximating distribution goes on decreasing. In addition, it is proved that information worth of each model defined on the basis of MinMaxEnt modeling about stationary time series is equal to sum of all possible information increments corresponding to each model with respect to preceding model starting with first model in the sequence of models. The fulfillment of obtained results is demonstrated on an example by using a program written in Matlab.展开更多
Obtaining the accurate value estimation and reducing the estimation bias are the key issues in reinforcement learning.However,current methods that address the overestimation problem tend to introduce underestimation,w...Obtaining the accurate value estimation and reducing the estimation bias are the key issues in reinforcement learning.However,current methods that address the overestimation problem tend to introduce underestimation,which face a challenge of precise decision-making in many fields.To address this issue,we conduct a theoretical analysis of the underestimation bias and propose the minmax operation,which allow for flexible control of the estimation bias.Specifically,we select the maximum value of each action from multiple parallel state-action networks to create a new state-action value sequence.Then,a minimum value is selected to obtain more accurate value estimations.Moreover,based on the minmax operation,we propose two novel algorithms by combining Deep Q-Network(DQN)and Double DQN(DDQN),named minmax-DQN and minmax-DDQN.Meanwhile,we conduct theoretical analyses of the estimation bias and variance caused by our proposed minmax operation,which show that this operation significantly improves both underestimation and overestimation biases and leads to the unbiased estimation.Furthermore,the variance is also reduced,which is helpful to improve the network training stability.Finally,we conduct numerous comparative experiments in various environments,which empirically demonstrate the superiority of our method.展开更多
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research t...A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.展开更多
In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the ...This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the necessary and sufficient optimality conditions for a class of nonsmooth semi-infinite minmax programming problems, where set of restrictions are indexed in a compact set. Utilizing the sufficient optimality conditions, the authors formulate three types of dual models and establish weak and strong duality results. The results of the paper extend and unify naturally some earlier results from the literature.展开更多
基于虚拟力的无线传感器网络覆盖算法易陷入局部最优,导致覆盖率低、收敛速度慢。针对上述问题,提出一种基于虚拟力和泰森多边形划分的分布式覆盖(virtual force Voronoi partition,VFVP)优化算法。通过虚拟力方案尽可能分散节点,提高...基于虚拟力的无线传感器网络覆盖算法易陷入局部最优,导致覆盖率低、收敛速度慢。针对上述问题,提出一种基于虚拟力和泰森多边形划分的分布式覆盖(virtual force Voronoi partition,VFVP)优化算法。通过虚拟力方案尽可能分散节点,提高监测区域的覆盖率,采用集合划分泰森多边形方案和Minmax算法减少虚拟力末端中覆盖率下降的情况,使用质心算法提高虚拟力算法的收敛速度。相比基于虚拟力的网络覆盖算法,VFVP算法提高了5%左右的覆盖率。展开更多
文摘In this study, by starting from Maximum entropy (MaxEnt) distribution of time series, we introduce a measure that quantifies information worth of a set of autocovariances. The information worth of autocovariences is measured in terms of entropy difference of MaxEnt distributions subject to different autocovariance sets due to the fact that the information discrepancy between two distributions is measured in terms of their entropy difference in MaxEnt modeling. However, MinMaxEnt distributions (models) are obtained on the basis of MaxEnt distributions dependent on parameters according to autocovariances for time series. This distribution is the one which has minimum entropy and maximum information out of all MaxEnt distributions for family of time series constructed by considering one or several values as parameters. Furthermore, it is shown that as the number of autocovariances increases, the entropy of approximating distribution goes on decreasing. In addition, it is proved that information worth of each model defined on the basis of MinMaxEnt modeling about stationary time series is equal to sum of all possible information increments corresponding to each model with respect to preceding model starting with first model in the sequence of models. The fulfillment of obtained results is demonstrated on an example by using a program written in Matlab.
基金supported by the National Natural Science Foundation of China(No.62173272).
文摘Obtaining the accurate value estimation and reducing the estimation bias are the key issues in reinforcement learning.However,current methods that address the overestimation problem tend to introduce underestimation,which face a challenge of precise decision-making in many fields.To address this issue,we conduct a theoretical analysis of the underestimation bias and propose the minmax operation,which allow for flexible control of the estimation bias.Specifically,we select the maximum value of each action from multiple parallel state-action networks to create a new state-action value sequence.Then,a minimum value is selected to obtain more accurate value estimations.Moreover,based on the minmax operation,we propose two novel algorithms by combining Deep Q-Network(DQN)and Double DQN(DDQN),named minmax-DQN and minmax-DDQN.Meanwhile,we conduct theoretical analyses of the estimation bias and variance caused by our proposed minmax operation,which show that this operation significantly improves both underestimation and overestimation biases and leads to the unbiased estimation.Furthermore,the variance is also reduced,which is helpful to improve the network training stability.Finally,we conduct numerous comparative experiments in various environments,which empirically demonstrate the superiority of our method.
文摘A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
文摘In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
基金supported by the National Board of Higher Mathematics(NBHM)Department of Atomic Energy,India,under Grant No.2/40(12)/2014/R&D-II/10054
文摘This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the necessary and sufficient optimality conditions for a class of nonsmooth semi-infinite minmax programming problems, where set of restrictions are indexed in a compact set. Utilizing the sufficient optimality conditions, the authors formulate three types of dual models and establish weak and strong duality results. The results of the paper extend and unify naturally some earlier results from the literature.
文摘基于虚拟力的无线传感器网络覆盖算法易陷入局部最优,导致覆盖率低、收敛速度慢。针对上述问题,提出一种基于虚拟力和泰森多边形划分的分布式覆盖(virtual force Voronoi partition,VFVP)优化算法。通过虚拟力方案尽可能分散节点,提高监测区域的覆盖率,采用集合划分泰森多边形方案和Minmax算法减少虚拟力末端中覆盖率下降的情况,使用质心算法提高虚拟力算法的收敛速度。相比基于虚拟力的网络覆盖算法,VFVP算法提高了5%左右的覆盖率。
