The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are ...The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.展开更多
To strengthen border patrol measures, unmanned aerial vehicles(UAVs) are gradually used in many countries to detect illegal entries on borders. However, how to efficiently deploy limited UAVs to patrol on borders of l...To strengthen border patrol measures, unmanned aerial vehicles(UAVs) are gradually used in many countries to detect illegal entries on borders. However, how to efficiently deploy limited UAVs to patrol on borders of large areas remains challenging. In this paper, we first model the problem of deploying UAVs for border patrol as a Stackelberg game. Two players are considered in this game: The border patrol agency is the leader,who optimizes the patrol path of UAVs to detect the illegal immigrant. The illegal immigrant is the follower, who selects a certain area of the border to pass through at a certain time after observing the leader’s strategy. Second, a compact linear programming problem is proposed to tackle the exponential growth of the number of leader’s strategies. Third, a method is proposed to reduce the size of the strategy space of the follower. Then, we provide some theoretic results to present the effect of parameters of the model on leader’s utilities. Experimental results demonstrate the positive effect of limited starting and ending areas of UAV’s patrolling conditions and multiple patrolling altitudes on the leader ’s utility, and show that the proposed solution outperforms two conventional patrol strategies and has strong robustness.展开更多
随着电网中新能源渗透率的增加,传统火电机组调频已无法满足电能质量需求。针对多源场景中传统自动发电控制系统区域控制误差较大的问题,提出一种基于Stackelberg博弈与改进深度神经网络(Stackelberg game and improved deep neural net...随着电网中新能源渗透率的增加,传统火电机组调频已无法满足电能质量需求。针对多源场景中传统自动发电控制系统区域控制误差较大的问题,提出一种基于Stackelberg博弈与改进深度神经网络(Stackelberg game and improved deep neural network,S-DNN)的多源调频协调策略。首先,设计一种改进多层次深度神经网络(deep neural network,DNN),由DNN层、自然梯度提升层、最小二乘支持向量机层顺序递进完成预测、评价、执行动作,输出总调频功率指令。该多层次总调频功率输出模型考虑新能源渗透率对调频系统的动态影响,充分学习历史信息与实时状态中更多的特征,提高了时序调频指令精度。然后基于Stackelberg博弈理论,考虑多源调频特征与协同作用,优化各调频源间的功率分配,提高系统二次调频的经济性。最后,通过算例分析验证了提出的多源调频协调策略的有效性。与传统调频方法相比,所提出的S-DNN多源调频协调策略可有效降低区域控制误差与频率偏差,并降低调频成本。展开更多
文摘The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.
基金supported by the National Natural Science Foundation of China (71971075,71871079)the National Key Research and Development Program of China (2019YFE0110300)+1 种基金the Anhui Provincial Natural Science Foundation (1808085MG213)the Fundamental R esearch Funds for the Central Universities (PA2019GDPK0082)。
文摘To strengthen border patrol measures, unmanned aerial vehicles(UAVs) are gradually used in many countries to detect illegal entries on borders. However, how to efficiently deploy limited UAVs to patrol on borders of large areas remains challenging. In this paper, we first model the problem of deploying UAVs for border patrol as a Stackelberg game. Two players are considered in this game: The border patrol agency is the leader,who optimizes the patrol path of UAVs to detect the illegal immigrant. The illegal immigrant is the follower, who selects a certain area of the border to pass through at a certain time after observing the leader’s strategy. Second, a compact linear programming problem is proposed to tackle the exponential growth of the number of leader’s strategies. Third, a method is proposed to reduce the size of the strategy space of the follower. Then, we provide some theoretic results to present the effect of parameters of the model on leader’s utilities. Experimental results demonstrate the positive effect of limited starting and ending areas of UAV’s patrolling conditions and multiple patrolling altitudes on the leader ’s utility, and show that the proposed solution outperforms two conventional patrol strategies and has strong robustness.
文摘随着电网中新能源渗透率的增加,传统火电机组调频已无法满足电能质量需求。针对多源场景中传统自动发电控制系统区域控制误差较大的问题,提出一种基于Stackelberg博弈与改进深度神经网络(Stackelberg game and improved deep neural network,S-DNN)的多源调频协调策略。首先,设计一种改进多层次深度神经网络(deep neural network,DNN),由DNN层、自然梯度提升层、最小二乘支持向量机层顺序递进完成预测、评价、执行动作,输出总调频功率指令。该多层次总调频功率输出模型考虑新能源渗透率对调频系统的动态影响,充分学习历史信息与实时状态中更多的特征,提高了时序调频指令精度。然后基于Stackelberg博弈理论,考虑多源调频特征与协同作用,优化各调频源间的功率分配,提高系统二次调频的经济性。最后,通过算例分析验证了提出的多源调频协调策略的有效性。与传统调频方法相比,所提出的S-DNN多源调频协调策略可有效降低区域控制误差与频率偏差,并降低调频成本。
