Comparison of two kinds of approximate proximal point algorithms for monotone variational inequalities

This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ＂Error bounds for proximal point subproblems and associated inexact proximal point algorithms＂ published in 2000. They are both prediction- correction methods which use the same inexactness restriction; the only difference is that they use different search directions in the correction steps. This paper also chooses an optimal step size in the two versions of the APPA to improve the profit at each iteration. Analysis also shows that the two APPAs are globally convergent under appropriate assumptions, and we can expect algorithm 2 to get more progress in every iteration than algorithm 1. Numerical experiments indicate that algorithm 2 is more efficient than algorithm 1 with the same correction step size,

PROXIMAL POINT ALGORITHM WITH ERRORS FOR GENERALIZED STRONGLY NONLINEARQUASIVARIATIONAL INCLUSIONS

In this paper, a class of generalized strongly nonlinear quasivariational inclusions are studied. By using the properties of the resolvent operator associated with a maximal monotone; mapping in Hilbert space, an existence theorem of solutions for generalized strongly nonlinear quasivariational inclusion is established and a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly, nonlinear quasivariational inclusion. As special cases, some known results in this field are also discussed.

Comparison of two approximal proximal point algorithms for monotone variational inequalities

Proximal point algorithms （PPA） are attractive methods for solving monotone variational inequalities （MVI）. Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions ofPPA （APPA） are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm Ⅰ; in the same way, Algorithm Ⅱ is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm Ⅱ usually outperforms Algorithm Ⅰ. For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm Ⅱ to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration. And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some numerical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm II is feasible and easy to implement with relatively low computation load.

MODIFIED APPROXIMATE PROXIMAL POINT ALGORITHMS FOR FINDING ROOTS OF MAXIMAL MONOTONE OPERATORS

In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.

On Over-Relaxed Proximal Point Algorithms for Generalized Nonlinear Operator Equation with (A,η,m)-Monotonicity Framework

In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion

In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor set.Moreover,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost.Meanwhile,the convergence of the new algorithm is discussed under some reasonable conditions.Finally,the numerical experiments show the effectiveness of the proposed algorithm.

山区应急供水装备路径规划系统设计与应用

灾后救援保障中,应急供水扮演着至关重要的角色.然而,由于山区地形和地貌条件复杂多变,现场指挥调度尤为关键,关系着救援人员能否迅速展开保障装备进行应急供水作业.文中基于多智能体强化学习(multi-agent proximal policy optimization,MAPPO)算法进行了路径规划系统的设计,并进行了试验仿真验证,根据奖励图结果确认该路径规划系统的可行性,并实现系统运行可视化,证明该路径规划系统可以初步满足山区应急供水装备路径规划需求.在此基础上,结合Mask2Former图像分割模型优化山区应急供水装备路径规划系统,将地物信息输出结果和路径规划结果相结合,有效避免了单一路径规划算法在受到环境影响时结果波动较大的问题,提高了路径规划的鲁棒性和可靠性.将该路径规划系统集成至山区应急供水装备指挥平台,以解决山区应急供水路径规划问题,为山区应急供水装备的实际运行提供了有力支持.

基于EMSDBO算法的无人机三维航迹规划

针对无人机(unmanned aerial vehicle,UAV)三维航迹规划问题,提出一种增强型多策略蜣螂算法的UAV航迹规划方法。首先,将飞行接近率和响应时间的动态约束添加到威胁成本代价中,并考虑UAV转弯性能的影响,建立三维任务空间模型与航迹代价函数。其次,在蜣螂算法中引入偏移估计策略、变螺旋搜索策略、准反向学习策略和逐维变异策略,提高算法的全局寻优能力和收敛速度。最后,给出了改进算法在三维环境下航迹规划的仿真结果。结果表明:综合考虑UAV机动性能和转弯性能,规划出的路径可以更加安全有效地避开危险源。相比其他算法,改进算法的寻优能力更好,规划的航迹质量更优。

基于自注意力PPO算法的智能配电网多设备协同无功优化控制策略

针对智能配电网无功可调控资源多样化场景下的快速趋优难题,提出了一种基于多头自注意力近端策略优化算法的多设备协同无功优化控制方法。首先,将无功优化问题建模为马尔可夫决策过程;然后,在深度强化学习框架下使用多头自注意力改进近端策略优化(PPO)算法对策略网络进行优化训练,算法采用多头自注意力网络获取配电网的实时状态特征,并通过剪切策略梯度法动态控制策略网络的更新幅度;最后,在改进IEEE69节点系统进行仿真验证。结果表明,所提算法的控制性能优于现有先进强化学习算法。

基于样本优化的PPO算法在单路口信号控制的应用

优化交通信号的控制策略可以提高道路车辆通行效率,缓解交通拥堵.针对基于值函数的深度强化学习算法难以高效优化单路口信号控制策略的问题,构建了一种基于样本优化的近端策略优化(MPPO)算法的单路口信号控制方法,通过对传统PPO算法中代理目标函数进行最大化提取,有效提高了模型选择样本的质量,采用多维交通状态向量作为模型观测值的输入方法,以及时跟踪并利用道路交通状态的动态变化过程.为了验证MPPO算法模型的准确性和有效性,在城市交通微观模拟软件(SUMO)上与值函数强化学习控制方法进行对比.仿真实验表明,相比于值函数强化学习控制方法,该方法更贴近真实的交通场景,显著加快了车辆累计等待时间的收敛速度,车辆的平均队列长度和平均等待时间明显缩短,有效提高了单路口车辆的通行效率.

一种求解低秩矩阵补全的修正加速近端梯度算法

设计适应大规模数据的快速算法是求解低秩矩阵补全的重点。文章改变了加速近端梯度算法的步长,对近似函数的近端最优点和上一迭代点增加了一个仿射组合。通过控制仿射系数,能够使得到的新迭代点有靠近原函数的趋势,进而能在保持算法精度的同时提高算法效率。最后通过相应的数值实验证明了算法的有效性和稳定性。

基于注意力的循环PPO算法及其应用

针对深度强化学习算法在部分可观测环境中面临信息掌握不足、存在随机因素等问题,提出了一种融合注意力机制与循环神经网络的近端策略优化算法(ARPPO算法)。该算法首先通过卷积网络层提取特征;其次采用注意力机制突出状态中重要的关键信息;再次通过LSTM网络提取数据的时域特性;最后基于Actor-Critic结构的PPO算法进行策略学习与训练提升。基于Gym-Minigrid环境设计了两项探索任务的消融与对比实验,实验结果表明ARPPO算法较已有的A2C算法、PPO算法、RPPO算法具有更快的收敛速度,且ARPPO算法在收敛之后具有很强的稳定性,并对存在随机因素的未知环境具备更强的适应力。

基于局部性原理的高效软聚类联邦学习

软聚类常用于解决多任务联邦学习(federated learning,FL)场景下存在非独立同分布(non-independent and identically distributed,non-IID)数据时的模型精度下降问题。然而,使用软聚类需上传和下载更多的模型参数。为了应对这一挑战,提出了基于局部性原理的联邦学习(federated learning with principle of locality,FedPol)算法。采用近端局部更新机制以确保客户端的本地更新在一定范围内波动;利用客户端本地数据分布的局部特性,整合历史数据分布信息至模型训练过程,加速了模型收敛,减少了需要传输的参数量。仿真实验证明,针对non-IID数据,FedPol算法可以在保持模型精度的前提下比其他算法减少约10%的迭代轮次,有效降低了通信成本。

基于混合启发式算法的中小学布局优化研究

以就近入学和均衡化发展为目标,提出中小学空间优化方法。从各区域学生平均上学距离与中小学空间分布的角度出发,建立武汉市中小学空间优化模型。基于ArcGIS分析和TS-SA混合启发式算法构建空间优化模型。经过学区优化调整,中小学可达规范服务半径内的能力得到提升,校际差异缩小,较好实现了就近入学、均衡教育和提升服务覆盖的目标。

基于强化学习的动目标协同观测任务自主规划方法

随着空间目标的数量逐渐增多、空中目标动态性日趋提升,对目标的观测定位问题变得愈发重要.由于需同时观测的目标多且目标动态性强,而星座观测资源有限,为了更高效地调用星座观测资源,需要动态调整多目标协同观测方案,使各目标均具有较好的定位精度,因此需解决星座协同观测多目标的任务规划问题.建立星座姿态轨道模型、目标飞行模型、目标协同探测及定位模型,提出基于几何精度衰减因子(geometric dilution of precision, GDOP)的目标观测定位误差预估模型及目标观测优先级模型,建立基于强化学习的协同观测任务规划框架,采用多头自注意力机制建立策略网络,以及近端策略优化算法开展任务规划算法训练.仿真验证论文提出的方法相比传统启发式方法提升了多目标观测精度和有效跟踪时间,相比遗传算法具有更快的计算速度.

信息年龄约束下的无人机数据采集能耗优化路径规划算法

信息年龄(AoI)是评价无线传感器网络(WSN)数据时效性的重要指标,无人机辅助WSN数据采集过程中采用优化飞行轨迹、提升速度等运动策略保障卸载至基站的数据满足各节点AoI限制。然而,不合理的运动策略易导致无人机因飞行距离过长、速度过快产生非必要能耗,造成数据采集任务失败。针对该问题,该文首先提出信息年龄约束的无人机数据采集能耗优化路径规划问题并进行数学建模;其次,设计一种协同混合近端策略优化(CH-PPO)强化学习算法,同时规划无人机对传感器节点或基站的访问次序、悬停位置和飞行速度,在满足各传感器节点信息年龄约束的同时,最大限度地减少无人机能量消耗。再次,设计一种融合离散和连续策略的损失函数,增强CH-PPO算法动作的合理性,提升其训练效果。仿真实验结果显示,CH-PPO算法在无人机能量消耗以及影响该指标因素的比较中均优于对比的3种强化学习算法,并具有良好的收敛性、稳定性和鲁棒性。

A Mini-Batch Proximal Stochastic Recursive Gradient Algorithm with Diagonal Barzilai–Borwein Stepsize

Many machine learning problems can be formulated as minimizing the sum of a function and a non-smooth regularization term.Proximal stochastic gradient methods are popular for solving such composite optimization problems.We propose a minibatch proximal stochastic recursive gradient algorithm SRG-DBB,which incorporates the diagonal Barzilai–Borwein(DBB)stepsize strategy to capture the local geometry of the problem.The linear convergence and complexity of SRG-DBB are analyzed for strongly convex functions.We further establish the linear convergence of SRGDBB under the non-strong convexity condition.Moreover,it is proved that SRG-DBB converges sublinearly in the convex case.Numerical experiments on standard data sets indicate that the performance of SRG-DBB is better than or comparable to the proximal stochastic recursive gradient algorithm with best-tuned scalar stepsizes or BB stepsizes.Furthermore,SRG-DBB is superior to some advanced mini-batch proximal stochastic gradient methods.

异构编队卫星近距离操作轨迹规划方法

针对编队卫星的空间在轨服务任务,提出一种多类载荷异构星群的协同操作方案。首先,考虑星间自主通信,建立了由一颗主故障识别的观测卫星和多颗主维修补给的操作卫星构成的编队系统。其次,提出一种基于循环交替策略的多星协同轨迹规划方法,并基于差分进化算法优化了星群轨迹。最后,结合算例仿真,分析了系统内各成员卫星在编队控制过程中所需的脉冲大小以及编队系统整体的安全性能。仿真结果表明,异构编队系统可快速规划出安全性较高、鲁棒性较强的在轨服务轨迹,具有一定的工程应用价值。

基于Edge-TB的联邦学习中客户端选择策略和数据集划分研究

联邦学习是分布式机器学习在现实中的应用之一。针对联邦学习中的异构性,基于FedProx算法,提出优先选择近端项较大的客户端选择策略,效果优于常见的选择局部损失值较大的客户端选择策略,可以有效提高FedProx算法在异构数据和系统下的收敛速度,提高有限聚合次数内的准确率。针对联邦学习数据异构的假设,设计了一套异构数据划分流程,得到了基于真实图像数据集的异构联邦数据集作为实验数据集。使用开源的分布式机器学习框架Edge-TB作为实验测试平台,以异构划分后的Cifar10作为数据集,实验表明,采用新的客户端选择策略的改进FedProx算法较原算法在有限的聚合轮数内准确率提升14.96%,通信开销减小6.3%;与SCAFFOLD算法相比,准确率提升3.6%,通信开销减小51.7%,训练时间减少15.4%。