Allowing non-submodular score functions in distributed task allocation

Submodularity is a powerful property that can be exploited for provable performance and convergence guarantees in distributed task allocation algorithms. However, some mission scenarios cannot easily be approximated as submodular a priori. This paper introduces an algorithmic extension for distributed multi-agent multi-task assignment algorithms which provides guaranteed convergence using non-submodular score functions. This algorithm utilizes non-submodular ranking of tasks within each agent's internal decision making process, while externally enforcing that shared bids appear as if they were created using submodular score functions. Provided proofs demonstrate that all convergence and performance guarantees hold with respect to this apparent submodular score function. The algorithm allows significant improvements over heuristic approaches that approximate truly non-submodular score functions.United States. Air Force Office of Scientific Research (Grant FA9550-11-1-0134

An Auction-based Coordination Strategy for Task-Constrained Multi-Agent Stochastic Planning with Submodular Rewards

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.Comment: 17 pages, 5 figure

On distributed virtual network embedding with guarantees

To provide wide-area network services, resources from different infrastructure providers are needed. Leveraging the consensus-based resource allocation literature, we propose a general distributed auction mechanism for the (NP-hard) virtual network (VNET) embedding problem. Under reasonable assumptions on the bidding scheme, the proposed mechanism is proven to converge, and it is shown that the solutions guarantee a worst case efficiency of (?????) relative to the optimal solution, and that this bound is optimal, that is, no better approximation exists. Using extensive simulations, we confirm superior convergence properties and resource utilization when compared with existing distributed VNET embedding solutions, and we show how byappropriate policy design, our mechanism can be instantiated to accommodate the embedding goals of different service and infrastructure providers, resulting in an attractive and flexible resource allocation solution.This work is supported in part by the National Science Foundation under grant CNS-0963974

On distributed virtual network embedding with guarantees

To provide wide-area network services, resources from different infrastructure providers are needed. Leveraging the consensus-based resource allocation literature, we propose a general distributed auction mechanism for the (NP-hard) virtual network (VNET) embedding problem. Under reasonable assumptions on the bidding scheme, the proposed mechanism is proven to converge, and it is shown that the solutions guarantee a worst case efficiency of (?????) relative to the optimal solution, and that this bound is optimal, that is, no better approximation exists. Using extensive simulations, we confirm superior convergence properties and resource utilization when compared with existing distributed VNET embedding solutions, and we show how byappropriate policy design, our mechanism can be instantiated to accommodate the embedding goals of different service and infrastructure providers, resulting in an attractive and flexible resource allocation solution.This work is supported in part by the National Science Foundation under grant CNS-0963974

Submodularity in Action: From Machine Learning to Signal Processing Applications

Submodularity is a discrete domain functional property that can be interpreted as mimicking the role of the well-known convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to efficient optimization algorithms with provable near-optimality guarantees. These characteristics, namely, efficiency and provable performance bounds, are of particular interest for signal processing (SP) and machine learning (ML) practitioners as a variety of discrete optimization problems are encountered in a wide range of applications. Conventionally, two general approaches exist to solve discrete problems: $(i)$ relaxation into the continuous domain to obtain an approximate solution, or $(ii)$ development of a tailored algorithm that applies directly in the discrete domain. In both approaches, worst-case performance guarantees are often hard to establish. Furthermore, they are often complex, thus not practical for large-scale problems. In this paper, we show how certain scenarios lend themselves to exploiting submodularity so as to construct scalable solutions with provable worst-case performance guarantees. We introduce a variety of submodular-friendly applications, and elucidate the relation of submodularity to convexity and concavity which enables efficient optimization. With a mixture of theory and practice, we present different flavors of submodularity accompanying illustrative real-world case studies from modern SP and ML. In all cases, optimization algorithms are presented, along with hints on how optimality guarantees can be established

On distributed virtual network embedding with guarantees

To provide wide-area network services, resources from different infrastructure providers are needed. Leveraging the consensus-based resource allocation literature, we propose a general distributed auction mechanism for the (NP-hard) virtual network (VNET) embedding problem. Under reasonable assumptions on the bidding scheme, the proposed mechanism is proven to converge, and it is shown that the solutions guarantee a worst-case efficiency of (1-(1/e)) relative to the optimal node embedding, or VNET embedding if virtual links are mapped to exactly one physical link. This bound is optimal, that is, no better polynomial-time approximation algorithm exists, unless P=NP. Using extensive simulations, we confirm superior convergence properties and resource utilization when compared to existing distributed VNET embedding solutions, and we show how by appropriate policy design, our mechanism can be instantiated to accommodate the embedding goals of different service and infrastructure providers, resulting in an attractive and flexible resource allocation solution.CNS-0963974 - National Science Foundationhttp://www.cs.bu.edu/fac/matta/Papers/ToN-CAD.pdfAccepted manuscrip

Routing optimization algorithms in integrated fronthaul/backhaul networks supporting multitenancy

Mención Internacional en el título de doctorEsta tesis pretende ayudar en la definición y el diseño de la quinta generación de redes de telecomunicaciones (5G) a través del modelado matemático de las diferentes cualidades que las caracterizan. En general, la ambición de estos modelos es realizar una optimización de las redes, ensalzando sus capacidades recientemente adquiridas para mejorar la eficiencia de los futuros despliegues tanto para los usuarios como para los operadores. El periodo de realización de esta tesis se corresponde con el periodo de investigación y definición de las redes 5G, y, por lo tanto, en paralelo y en el contexto de varios proyectos europeos del programa H2020. Por lo tanto, las diferentes partes del trabajo presentado en este documento cuadran y ofrecen una solución a diferentes retos que han ido apareciendo durante la definición del 5G y dentro del ámbito de estos proyectos, considerando los comentarios y problemas desde el punto de vista de todos los usuarios finales, operadores y proveedores. Así, el primer reto a considerar se centra en el núcleo de la red, en particular en cómo integrar tráfico fronthaul y backhaul en el mismo estrato de transporte. La solución propuesta es un marco de optimización para el enrutado y la colocación de recursos que ha sido desarrollado teniendo en cuenta restricciones de retardo, capacidad y caminos, maximizando el grado de despliegue de Unidades Distribuidas (DU) mientras se minimizan los agregados de las Unidades Centrales (CU) que las soportan. El marco y los algoritmos heurísticos desarrollados (para reducir la complexidad computacional) son validados y aplicados a redes tanto a pequeña como a gran (nivel de producción) escala. Esto los hace útiles para los operadores de redes tanto para la planificación de la red como para el ajuste dinámico de las operaciones de red en su infraestructura (virtualizada). Moviéndonos más cerca de los usuarios, el segundo reto considerado se centra en la colocación de servicios en entornos de nube y borde (cloud/edge). En particular, el problema considerado consiste en seleccionar la mejor localización para cada función de red virtual (VNF) que compone un servicio en entornos de robots en la nube, que implica restricciones estrictas en las cotas de retardo y fiabilidad. Los robots, vehículos y otros dispositivos finales proveen competencias significativas como impulsores, sensores y computación local que son esenciales para algunos servicios. Por contra, estos dispositivos están en continuo movimiento y pueden perder la conexión con la red o quedarse sin batería, cosa que reta aún más la entrega de servicios en este entorno dinámico. Así, el análisis realizado y la solución propuesta abordan las restricciones de movilidad y batería. Además, también se necesita tener en cuenta los aspectos temporales y los objetivos conflictivos de fiabilidad y baja latencia en el despliegue de servicios en una red volátil, donde los nodos de cómputo móviles actúan como una extensión de la infraestructura de cómputo de la nube y el borde. El problema se formula como un problema de optimización para colocación de VNFs minimizando el coste y también se propone un heurístico eficiente. Los algoritmos son evaluados de forma extensiva desde varios aspectos por simulación en escenarios que reflejan la realidad de forma detallada. Finalmente, el último reto analizado se centra en dar soporte a servicios basados en el borde, en particular, aprendizaje automático (ML) en escenarios del Internet de las Cosas (IoT) distribuidos. El enfoque tradicional al ML distribuido se centra en adaptar los algoritmos de aprendizaje a la red, por ejemplo, reduciendo las actualizaciones para frenar la sobrecarga. Las redes basadas en el borde inteligente, en cambio, hacen posible seguir un enfoque opuesto, es decir, definir la topología de red lógica alrededor de la tarea de aprendizaje a realizar, para así alcanzar el resultado de aprendizaje deseado. La solución propuesta incluye un modelo de sistema que captura dichos aspectos en el contexto de ML supervisado, teniendo en cuenta tanto nodos de aprendizaje (que realizan las computaciones) como nodos de información (que proveen datos). El problema se formula para seleccionar (i) qué nodos de aprendizaje e información deben cooperar para completar la tarea de aprendizaje, y (ii) el número de iteraciones a realizar, para minimizar el coste de aprendizaje mientras se garantizan los objetivos de error predictivo y tiempo de ejecución. La solución también incluye un algoritmo heurístico que es evaluado ensalzando una topología de red real y considerando tanto las tareas de clasificación como de regresión, y cuya solución se acerca mucho al óptimo, superando las soluciones alternativas encontradas en la literatura.This thesis aims to help in the definition and design of the 5th generation of telecommunications networks (5G) by modelling the different features that characterize them through several mathematical models. Overall, the aim of these models is to perform a wide optimization of the network elements, leveraging their newly-acquired capabilities in order to improve the efficiency of the future deployments both for the users and the operators. The timeline of this thesis corresponds to the timeline of the research and definition of 5G networks, and thus in parallel and in the context of several European H2020 programs. Hence, the different parts of the work presented in this document match and provide a solution to different challenges that have been appearing during the definition of 5G and within the scope of those projects, considering the feedback and problems from the point of view of all the end users, operators and providers. Thus, the first challenge to be considered focuses on the core network, in particular on how to integrate fronthaul and backhaul traffic over the same transport stratum. The solution proposed is an optimization framework for routing and resource placement that has been developed taking into account delay, capacity and path constraints, maximizing the degree of Distributed Unit (DU) deployment while minimizing the supporting Central Unit (CU) pools. The framework and the developed heuristics (to reduce the computational complexity) are validated and applied to both small and largescale (production-level) networks. They can be useful to network operators for both network planning as well as network operation adjusting their (virtualized) infrastructure dynamically. Moving closer to the user side, the second challenge considered focuses on the allocation of services in cloud/edge environments. In particular, the problem tackled consists of selecting the best the location of each Virtual Network Function (VNF) that compose a service in cloud robotics environments, that imply strict delay bounds and reliability constraints. Robots, vehicles and other end-devices provide significant capabilities such as actuators, sensors and local computation which are essential for some services. On the negative side, these devices are continuously on the move and might lose network connection or run out of battery, which further challenge service delivery in this dynamic environment. Thus, the performed analysis and proposed solution tackle the mobility and battery restrictions. We further need to account for the temporal aspects and conflicting goals of reliable, low latency service deployment over a volatile network, where mobile compute nodes act as an extension of the cloud and edge computing infrastructure. The problem is formulated as a cost-minimizing VNF placement optimization and an efficient heuristic is proposed. The algorithms are extensively evaluated from various aspects by simulation on detailed real-world scenarios. Finally, the last challenge analyzed focuses on supporting edge-based services, in particular, Machine Learning (ML) in distributed Internet of Things (IoT) scenarios. The traditional approach to distributed ML is to adapt learning algorithms to the network, e.g., reducing updates to curb overhead. Networks based on intelligent edge, instead, make it possible to follow the opposite approach, i.e., to define the logical network topology around the learning task to perform, so as to meet the desired learning performance. The proposed solution includes a system model that captures such aspects in the context of supervised ML, accounting for both learning nodes (that perform computations) and information nodes (that provide data). The problem is formulated to select (i) which learning and information nodes should cooperate to complete the learning task, and (ii) the number of iterations to perform, in order to minimize the learning cost while meeting the target prediction error and execution time. The solution also includes an heuristic algorithm that is evaluated leveraging a real-world network topology and considering both classification and regression tasks, and closely matches the optimum, outperforming state-of-the-art alternatives.This work has been supported by IMDEA Networks InstitutePrograma de Doctorado en Ingeniería Telemática por la Universidad Carlos III de MadridPresidente: Pablo Serrano Yáñez-Mingot.- Secretario: Andrés García Saavedra.- Vocal: Luca Valcarengh

Partial Replanning for Decentralized Dynamic Task Allocation

In time-sensitive and dynamic missions, multi-UAV teams must respond quickly to new information and objectives. This paper presents a dynamic decentralized task allocation algorithm for allocating new tasks that appear online during the solving of the task allocation problem. Our algorithm extends the Consensus-Based Bundle Algorithm (CBBA), a decentralized task allocation algorithm, allowing for the fast allocation of new tasks without a full reallocation of existing tasks. CBBA with Partial Replanning (CBBA-PR) enables the team to trade-off between convergence time and increased coordination by resetting a portion of their previous allocation at every round of bidding on tasks. By resetting the last tasks allocated by each agent, we are able to ensure the convergence of the team to a conflict-free solution. CBBA-PR can be further improved by reducing the team size involved in the replanning, further reducing the communication burden of the team and runtime of CBBA-PR. Finally, we validate the faster convergence and improved solution quality of CBBA-PR in multi-UAV simulations.Comment: 11 pages, Accepted to AIAA GNC 201

Distributed strategy adaptation with a prediction function in multi-agent task allocation

Coordinating multiple agents to complete a set of tasks under time constraints is a complex problem. Distributed consensus-based task allocation algorithms address this problem without the need for human supervision. With such algorithms, agents add tasks to their own schedule according to specified allocation strategies. Various factors, such as the available resources and number of tasks, may affect the efficiency of a particular allocation strategy. The novel idea we suggest is that each individual agent can predict locally the best task inclusion strategy, based on the limited task assignment information communicated among networked agents. Using supervised classification learning, a function is trained to predict the most appropriate strategy between two well known insertion heuristics. Using the proposed method, agents are shown to correctly predict and select the optimal insertion heuristic to achieve the overall highest number of task allocations. The adaptive agents consistently match the performances of the best non-adaptive agents across a variety of scenarios. This study aims to demonstrate the possibility and potential performance benefits of giving agents greater decision making capabilities to independently adapt the task allocation process in line with the problem of interest