学习优化（L2O）最近被出现为通过利用神经网络的强预测力来解决优化问题的有希望的方法，并提供比传统求解器更低的运行时复杂性。虽然L2O已经应用于各种问题，但对于Minimax优化形式的一个至关重要的且挑战性的问题 - 稳健的组合优化 - 在很大程度上仍然存在。除了指数大的决策空间之外，对于鲁棒组合优化的关键挑战在于内部优化问题，其通常是非凸出的并且缠绕在外的优化中。在本文中，我们研究了强大的组合优化，并提出了一种新的基于学习的优化器，称为LRCO（用于鲁棒组合优化的学习），其在存在不确定上下文存在下快速输出鲁棒解决方案。 LRCO利用一对基于学习的优化器 - 一个用于最小化器，另一个用于最大化器 - 使用它们各自的目标函数作为损失，并且可以培训而无需标签训练问题实例。为了评估LRCO的性能，我们对车辆边缘计算中的任务卸载问题进行仿真。我们的结果突出显示LRCO可以大大降低最坏情况的成本并提高鲁棒性，同时具有非常低的运行时复杂性。

组合优化是运营研究和计算机科学领域的一个公认领域。直到最近，它的方法一直集中在孤立地解决问题实例，而忽略了它们通常源于实践中的相关数据分布。但是，近年来，人们对使用机器学习，尤其是图形神经网络（GNN）的兴趣激增，作为组合任务的关键构件，直接作为求解器或通过增强确切的求解器。GNN的电感偏差有效地编码了组合和关系输入，因为它们对排列和对输入稀疏性的意识的不变性。本文介绍了对这个新兴领域的最新主要进步的概念回顾，旨在优化和机器学习研究人员。

This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems, state-of-the-art algorithms rely on handcrafted heuristics for making decisions that are otherwise too expensive to compute or mathematically not well defined. Thus, machine learning looks like a natural candidate to make such decisions in a more principled and optimized way. We advocate for pushing further the integration of machine learning and combinatorial optimization and detail a methodology to do so. A main point of the paper is seeing generic optimization problems as data points and inquiring what is the relevant distribution of problems to use for learning on a given task.

未来的互联网涉及几种新兴技术，例如5G和5G网络，车辆网络，无人机（UAV）网络和物联网（IOT）。此外，未来的互联网变得异质并分散了许多相关网络实体。每个实体可能需要做出本地决定，以在动态和不确定的网络环境下改善网络性能。最近使用标准学习算法，例如单药强化学习（RL）或深入强化学习（DRL），以使每个网络实体作为代理人通过与未知环境进行互动来自适应地学习最佳决策策略。但是，这种算法未能对网络实体之间的合作或竞争进行建模，而只是将其他实体视为可能导致非平稳性问题的环境的一部分。多机构增强学习（MARL）允许每个网络实体不仅观察环境，还可以观察其他实体的政策来学习其最佳政策。结果，MAL可以显着提高网络实体的学习效率，并且最近已用于解决新兴网络中的各种问题。在本文中，我们因此回顾了MAL在新兴网络中的应用。特别是，我们提供了MARL的教程，以及对MARL在下一代互联网中的应用进行全面调查。特别是，我们首先介绍单代机Agent RL和MARL。然后，我们回顾了MAL在未来互联网中解决新兴问题的许多应用程序。这些问题包括网络访问，传输电源控制，计算卸载，内容缓存，数据包路由，无人机网络的轨迹设计以及网络安全问题。

Connected and automated vehicles (CAVs) are viewed as a special kind of robots that have the potential to significantly improve the safety and efficiency of traffic. In contrast to many swarm robotics studies that are demonstrated in labs by employing a small number of robots, CAV studies aims to achieve cooperative driving of unceasing robot swarm flows. However, how to get the optimal passing order of such robot swarm flows even for a signal-free intersection is an NP-hard problem (specifically, enumerating based algorithm takes days to find the optimal solution to a 20-CAV scenario). Here, we introduce a novel cooperative driving algorithm (AlphaOrder) that combines offline deep learning and online tree searching to find a near-optimal passing order in real-time. AlphaOrder builds a pointer network model from solved scenarios and generates near-optimal passing orders instantaneously for new scenarios. Furthermore, our approach provides a general approach to managing preemptive resource sharing between swarm robotics (e.g., scheduling multiple automated guided vehicles (AGVs) and unmanned aerial vehicles (UAVs) at conflicting areas

在线算法是算法设计中的重要分支。设计具有有界竞争比率的在线算法（在最坏情况性能方面）可能是艰难的并且通常依赖于特定于问题的假设。由生成对抗净净净（GAN）的对抗训练的启发和在线算法的竞争比率基于最坏情况的输入，我们采用深度神经网络来学习从头开始进行资源分配和定价问题的在线算法对于最坏情况的输入，可以最小化离线最佳和学习的在线算法之间的性能差距的目标。具体而言，我们分别利用两个神经网络作为算法和对手，让他们播放零和游戏，而对验证负责产生最坏情况的输入，而算法基于对手提供的输入学习最佳策略。为了确保算法网络的更好收敛（到所需的在线算法），我们提出了一种新颖的每轮更新方法来处理顺序决策，以便在不同的回合中断复杂依赖性，以便可以为每种可能的动作完成更新，而不是只有采样的行动。据我们所知，我们的作品是首次使用深度神经网络来设计一个在最坏情况性能保证的角度的在线算法。实证研究表明，我们的更新方法确保了纳什均衡的融合，并且学习算法在各种设置下优于最先进的在线算法。

随着数据生成越来越多地在没有连接连接的设备上进行，因此与机器学习（ML）相关的流量将在无线网络中无处不在。许多研究表明，传统的无线协议高效或不可持续以支持ML，这创造了对新的无线通信方法的需求。在这项调查中，我们对最先进的无线方法进行了详尽的审查，这些方法是专门设计用于支持分布式数据集的ML服务的。当前，文献中有两个明确的主题，模拟的无线计算和针对ML优化的数字无线电资源管理。这项调查对这些方法进行了全面的介绍，回顾了最重要的作品，突出了开放问题并讨论了应用程序方案。

分支机构是一种用于组合优化的系统枚举方法，在该方法中，性能高度依赖于可变选择策略。最先进的手工启发式策略的推理时间相对较慢，而当前的机器学习方法需要大量的标记数据。我们提出了一种新方法，以根据使用强化学习（RL）范式来解决组合优化中的数据标记和推理潜伏期问题。我们使用模仿学习来引导RL代理，然后使用近端策略优化（PPO）进一步探索全球最佳动作。然后，一个值网络用于运行蒙特卡洛树搜索（MCT）以增强策略网络。我们评估了我们在四个不同类别的组合优化问题上的方法的性能，并表明我们的方法与最先进的机器学习和基于启发式方法的方法相比表现强劲。

Influence Maximization (IM) is a classical combinatorial optimization problem, which can be widely used in mobile networks, social computing, and recommendation systems. It aims at selecting a small number of users such that maximizing the influence spread across the online social network. Because of its potential commercial and academic value, there are a lot of researchers focusing on studying the IM problem from different perspectives. The main challenge comes from the NP-hardness of the IM problem and \#P-hardness of estimating the influence spread, thus traditional algorithms for overcoming them can be categorized into two classes: heuristic algorithms and approximation algorithms. However, there is no theoretical guarantee for heuristic algorithms, and the theoretical design is close to the limit. Therefore, it is almost impossible to further optimize and improve their performance. With the rapid development of artificial intelligence, the technology based on Machine Learning (ML) has achieved remarkable achievements in many fields. In view of this, in recent years, a number of new methods have emerged to solve combinatorial optimization problems by using ML-based techniques. These methods have the advantages of fast solving speed and strong generalization ability to unknown graphs, which provide a brand-new direction for solving combinatorial optimization problems. Therefore, we abandon the traditional algorithms based on iterative search and review the recent development of ML-based methods, especially Deep Reinforcement Learning, to solve the IM problem and other variants in social networks. We focus on summarizing the relevant background knowledge, basic principles, common methods, and applied research. Finally, the challenges that need to be solved urgently in future IM research are pointed out.

Integrated space-air-ground networks promise to offer a valuable solution space for empowering the sixth generation of communication networks (6G), particularly in the context of connecting the unconnected and ultraconnecting the connected. Such digital inclusion thrive makes resource management problems, especially those accounting for load-balancing considerations, of particular interest. The conventional model-based optimization methods, however, often fail to meet the real-time processing and quality-of-service needs, due to the high heterogeneity of the space-air-ground networks, and the typical complexity of the classical algorithms. Given the premises of artificial intelligence at automating wireless networks design and the large-scale heterogeneity of non-terrestrial networks, this paper focuses on showcasing the prospects of machine learning in the context of user scheduling in integrated space-air-ground communications. The paper first overviews the most relevant state-of-the art in the context of machine learning applications to the resource allocation problems, with a dedicated attention to space-air-ground networks. The paper then proposes, and shows the benefit of, one specific use case that uses ensembling deep neural networks for optimizing the user scheduling policies in integrated space-high altitude platform station (HAPS)-ground networks. Finally, the paper sheds light on the challenges and open issues that promise to spur the integration of machine learning in space-air-ground networks, namely, online HAPS power adaptation, learning-based channel sensing, data-driven multi-HAPSs resource management, and intelligent flying taxis-empowered systems.

与传统机器学习（ML）相比，联邦学习（FL）被认为是解决移动设备的数据隐私问题的吸引力框架。使用Edge Server（ESS）作为中间人在接近度执行模型聚合可以减少传输开销，并且它能够在低延迟FL中实现很大的潜力，其中FL（HFL）的分层体系结构被吸引更多地关注。设计适当的客户选择策略可以显着提高培训性能，并且已广泛用于FL研究。然而，据我们所知，没有专注于HFL的研究。此外，HFL的客户选择面临的挑战比传统的FL更多，例如，客户端 - es对的时变连接和网络运营商的有限预算（否）。在本文中，我们调查了HFL的客户选择问题，其中no no学习成功参与客户的数量以改善培训性能（即，在每轮中选择多个客户端）以及每个ES的有限预算。基于上下文组合多武装强盗（CC-MAB）开发了一个称为上下文知识的在线客户选择（COCS）的在线策略。 COCs观察局部计算和客户端对传输的侧信息（上下文），并使客户选择决策最大化没有给出有限预算的实用程序。理论上，与强凸和非凸HFL上的Oracle策略相比，COCS遗憾地实现了载体遗憾。仿真结果还支持拟议的COCS政策对现实世界数据集的效率。

我们为处理顺序决策和外在不确定性的应用程序开发了增强学习（RL）框架，例如资源分配和库存管理。在这些应用中，不确定性仅由于未来需求等外源变量所致。一种流行的方法是使用历史数据预测外源变量，然后对预测进行计划。但是，这种间接方法需要对外源过程进行高保真模型，以确保良好的下游决策，当外源性过程复杂时，这可能是不切实际的。在这项工作中，我们提出了一种基于事后观察学习的替代方法，该方法避开了对外源过程进行建模的建模。我们的主要见解是，与Sim2real RL不同，我们可以在历史数据中重新审视过去的决定，并在这些应用程序中对其他动作产生反事实后果。我们的框架将事后最佳的行动用作政策培训信号，并在决策绩效方面具有强大的理论保证。我们使用框架开发了一种算法，以分配计算资源，以用于现实世界中的Microsoft Azure工作负载。结果表明，我们的方法比域特异性的启发式方法和SIM2REAL RL基准学习更好的政策。

In many domains such as transportation and logistics, search and rescue, or cooperative surveillance, tasks are pending to be allocated with the consideration of possible execution uncertainties. Existing task coordination algorithms either ignore the stochastic process or suffer from the computational intensity. Taking advantage of the weakly coupled feature of the problem and the opportunity for coordination in advance, we propose a decentralized auction-based coordination strategy using a newly formulated score function which is generated by forming the problem into task-constrained Markov decision processes (MDPs). The proposed method guarantees convergence and at least 50% optimality in the premise of a submodular reward function. Furthermore, for the implementation on large-scale applications, an approximate variant of the proposed method, namely Deep Auction, is also suggested with the use of neural networks, which is evasive of the troublesome for constructing MDPs. Inspired by the well-known actor-critic architecture, two Transformers are used to map observations to action probabilities and cumulative rewards respectively. Finally, we demonstrate the performance of the two proposed approaches in the context of drone deliveries, where the stochastic planning for the drone league is cast into a stochastic price-collecting Vehicle Routing Problem (VRP) with time windows. Simulation results are compared with state-of-the-art methods in terms of solution quality, planning efficiency and scalability.

Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying decision-making process in the form of a mathematical optimization model. This statistical learning problem is referred to as data-driven inverse optimization. We focus on problems where the underlying decision-making process is modeled as a convex optimization problem whose parameters are unknown. We formulate the inverse optimization problem as a bilevel program and propose an efficient block coordinate descent-based algorithm to solve large problem instances. Numerical experiments on synthetic datasets demonstrate the computational advantage of our method compared to standard commercial solvers. Moreover, the real-world utility of the proposed approach is highlighted through two realistic case studies in which we consider estimating risk preferences and learning local constraint parameters of agents in a multiplayer Nash bargaining game.

In recent years, mobile devices are equipped with increasingly advanced sensing and computing capabilities. Coupled with advancements in Deep Learning (DL), this opens up countless possibilities for meaningful applications, e.g., for medical purposes and in vehicular networks. Traditional cloudbased Machine Learning (ML) approaches require the data to be centralized in a cloud server or data center. However, this results in critical issues related to unacceptable latency and communication inefficiency. To this end, Mobile Edge Computing (MEC) has been proposed to bring intelligence closer to the edge, where data is produced. However, conventional enabling technologies for ML at mobile edge networks still require personal data to be shared with external parties, e.g., edge servers. Recently, in light of increasingly stringent data privacy legislations and growing privacy concerns, the concept of Federated Learning (FL) has been introduced. In FL, end devices use their local data to train an ML model required by the server. The end devices then send the model updates rather than raw data to the server for aggregation. FL can serve as an enabling technology in mobile edge networks since it enables the collaborative training of an ML model and also enables DL for mobile edge network optimization. However, in a large-scale and complex mobile edge network, heterogeneous devices with varying constraints are involved. This raises challenges of communication costs, resource allocation, and privacy and security in the implementation of FL at scale. In this survey, we begin with an introduction to the background and fundamentals of FL. Then, we highlight the aforementioned challenges of FL implementation and review existing solutions. Furthermore, we present the applications of FL for mobile edge network optimization. Finally, we discuss the important challenges and future research directions in FL.

在过去的十年中，由于分散控制应用程序的趋势和网络物理系统应用的出现，网络控制系统在过去十年中引起了广泛的关注。但是，由于无线网络的复杂性质，现实世界中无线网络控制系统的通信带宽，可靠性问题以及对网络动态的认识不足。将机器学习和事件触发的控制结合起来有可能减轻其中一些问题。例如，可以使用机器学习来克服缺乏网络模型的问题，通过学习系统行为或通过不断学习模型动态来适应动态变化的模型。事件触发的控制可以通过仅在必要时或可用资源时传输控制信息来帮助保护通信带宽。本文的目的是对有关机器学习的使用与事件触发的控制的使用进行综述。机器学习技术，例如统计学习，神经网络和基于强化的学习方法，例如深入强化学习，并结合事件触发的控制。我们讨论如何根据机器学习使用的目的将这些学习算法用于不同的应用程序。在对文献的审查和讨论之后，我们重点介绍了与基于机器学习的事件触发的控制并提出潜在解决方案相关的开放研究问题和挑战。

事件处理是动态和响应互联网（物联网）的基石。该领域的最近方法基于代表性状态转移（REST）原则，其允许将事件处理任务放置在遵循相同原理的任何设备上。但是，任务应在边缘设备之间正确分布，以确保公平资源利用率和保证无缝执行。本文调查了深入学习的使用，以公平分配任务。提出了一种基于关注的神经网络模型，在不同场景下产生有效的负载平衡解决方案。所提出的模型基于变压器和指针网络架构，并通过Advantage演员批评批评学习算法训练。该模型旨在缩放到事件处理任务的数量和边缘设备的数量，不需要重新调整甚至再刷新。广泛的实验结果表明，拟议的模型在许多关键绩效指标中优于传统的启发式。通用设计和所获得的结果表明，所提出的模型可能适用于几个其他负载平衡问题变化，这使得该提案是由于其可扩展性和效率而在现实世界场景中使用的有吸引力的选择。

我们考虑使用一组并行代理和参数服务器分发在线MIN-MAX资源分配。我们的目标是最大限度地减少一组时变的凸起和降低成本函数的点最大值，而无需先验信息。我们提出了一种新的在线算法，称为分布式在线资源重新分配（DORA），其中非贸易人员学会通过陷入拖放者释放资源和共享资源。与大多数现有的在线优化策略不同，Dora的一个值得注意的特征是它不需要梯度计算或投影操作。这允许它基本上减少大规模和分布式网络中的计算开销。我们表明，所提出的算法的动态遗憾是由$ o lex的上限（t ^ {\ frac {3} {4}}（1 + p_t）^ {\ frac {1} {4} \右） $，$ t $是轮次的总数，$ p_t $是瞬时最小化器的路径长度。我们进一步考虑在分布式在线机器学习中的带宽分配问题的应用程序。我们的数值研究证明了所提出的解决方案及其性能优势在减少壁钟时间的基于梯度和/或投影的资源分配算法中的功效。

在确定性优化中，通常假定问题的所有参数都是固定和已知的。但是，实际上，某些参数可能是未知的先验参数，但可以从历史数据中估算。典型的预测 - 优化方法将预测和优化分为两个阶段。最近，端到端的预测到优化已成为有吸引力的替代方法。在这项工作中，我们介绍了PYEPO软件包，这是一个基于Pytorch的端到端预测，然后在Python中进行了优化的库。据我们所知，PYEPO（发音为“带有静音” n“”的“菠萝”）是线性和整数编程的第一个通用工具，具有预测的目标函数系数。它提供了两种基本算法：第一种基于Elmachtoub＆Grigas（2021）的开创性工作的凸替代损失函数，第二个基于Vlastelica等人的可区分黑盒求解器方法。 （2019）。 PYEPO提供了一个简单的接口，用于定义新的优化问题，最先进的预测 - 优化训练算法，自定义神经网络体系结构的使用以及端到端方法与端到端方法与与端到端方法的比较两阶段的方法。 PYEPO使我们能够进行一系列全面的实验，以比较沿轴上的多种端到端和两阶段方法，例如预测准确性，决策质量和运行时间，例如最短路径，多个背包和旅行等问题销售人员问题。我们讨论了这些实验中的一些经验见解，这些见解可以指导未来的研究。 PYEPO及其文档可在https://github.com/khalil-research/pyepo上找到。

Online optimization with multiple budget constraints is challenging since the online decisions over a short time horizon are coupled together by strict inventory constraints. The existing manually-designed algorithms cannot achieve satisfactory average performance for this setting because they often need a large number of time steps for convergence and/or may violate the inventory constraints. In this paper, we propose a new machine learning (ML) assisted unrolling approach, called LAAU (Learning-Assisted Algorithm Unrolling), which unrolls the online decision pipeline and leverages an ML model for updating the Lagrangian multiplier online. For efficient training via backpropagation, we derive gradients of the decision pipeline over time. We also provide the average cost bounds for two cases when training data is available offline and collected online, respectively. Finally, we present numerical results to highlight that LAAU can outperform the existing baselines.