Virtual Network Embedding (VNE) is a key enabler of network slicing, yet most formulations assume that each Virtual Network Request (VNR) has a fixed topology. Recently, VNE with Alternative topologies (VNEAP) was introduced to capture malleable VNRs, where each request can be instantiated using one of several functionally equivalent topologies that trade resources differently. While this flexibility enlarges the feasible space, it also introduces an additional decision layer, making dynamic embedding more challenging. This paper proposes HRL-VNEAP, a hierarchical reinforcement learning approach for VNEAP under dynamic arrivals. A high-level policy selects the most suitable alternative topology (or rejects the request), and a low-level policy embeds the chosen topology onto the substrate network. Experiments on realistic substrate topologies under multiple traffic loads show that naive exploitation strategies provide only modest gains, whereas HRL-VNEAP consistently achieves the best performance across all metrics. Compared to the strongest tested baselines, HRL-VNEAP improves acceptance ratio by up to \textbf{20.7\%}, total revenue by up to \textbf{36.2\%}, and revenue-over-cost by up to \textbf{22.1\%}. Finally, we benchmark against an MILP formulation on tractable instances to quantify the remaining gap to optimality and motivate future work on learning- and optimization-based VNEAP solutions.

Resource allocation (RA) is critical to efficient service deployment in Network Function Virtualization (NFV), a transformative networking paradigm. Recently, deep Reinforcement Learning (RL)-based methods have been showing promising potential to address this complexity. However, the lack of a systematic benchmarking framework and thorough analysis hinders the exploration of emerging networks and the development of more robust algorithms while causing inconsistent evaluation. In this paper, we introduce Virne, a comprehensive benchmarking framework for the NFV-RA problem, with a focus on supporting deep RL-based methods. Virne provides customizable simulations for diverse network scenarios, including cloud, edge, and 5G environments. It also features a modular and extensible implementation pipeline that supports over 30 methods of various types, and includes practical evaluation perspectives beyond effectiveness, such as scalability, generalization, and scalability. Furthermore, we conduct in-depth analysis through extensive experiments to provide valuable insights into performance trade-offs for efficient implementation and offer actionable guidance for future research directions. Overall, with its diverse simulations, rich implementations, and extensive evaluation capabilities, Virne could serve as a comprehensive benchmark for advancing NFV-RA methods and deep RL applications. The code is publicly available at https://github.com/GeminiLight/virne.

We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an objective function that combines a data-fidelity term, a Tikhonov-type regularization term, and a potentially nonsmooth convex penalty. The robustness of this inversion method to input perturbations is analyzed theoretically. Ensuring robustness complies with the principles of inverse problem theory, as it ensures both the continuity of the inversion method and the resilience to small noise - a critical property given the known vulnerability of deep neural networks to adversarial perturbations. A key novelty of our work lies in examining the robustness of the proposed network to perturbations in its bias, which represents the observed data in the inverse problem. Additionally, we provide numerical illustrations of the analytical Lipschitz bounds derived in our analysis.

We propose a model for the virtual function placement problem and several novel algorithms using ideas based on multi-armed bandits. We prove that these algorithms learn the optimal placement policy rapidly, and their regret grows at a rate at most $O( N M \sqrt{T\ln T} )$ while respecting the feasibility constraints with high probability. We show through numerical experiments that those algorithms both have good practical performance and modest computational complexity. Using the proposed acceleration technique, they can be used to learn in large networks where computational power is limited. Our experiments are fully reproducible, and the code is publicly available.

As an essential resource management problem in network virtualization, virtual network embedding (VNE) aims to allocate the finite resources of physical network to sequentially arriving virtual network requests (VNRs) with different resource demands. Since this is an NP-hard combinatorial optimization problem, many efforts have been made to provide viable solutions. However, most existing approaches have either ignored the admission control of VNRs, which has a potential impact on long-term performances, or not fully exploited the temporal and topological features of the physical network and VNRs. In this paper, we propose a deep Hierarchical Reinforcement Learning approach to learn a joint Admission Control and Resource Allocation policy for VNE, named HRL-ACRA. Specifically, the whole VNE process is decomposed into an upper-level policy for deciding whether to admit the arriving VNR or not and a lower-level policy for allocating resources of the physical network to meet the requirement of VNR through the HRL approach. Considering the proximal policy optimization as the basic training algorithm, we also adopt the average reward method to address the infinite horizon problem of the upper-level agent and design a customized multi-objective intrinsic reward to alleviate the sparse reward issue of the lower-level agent. Moreover, we develop a deep feature-aware graph neural network to capture the features of VNR and physical network and exploit a sequence-to-sequence model to generate embedding actions iteratively. Finally, extensive experiments are conducted in various settings, and show that HRL-ACRA outperforms state-of-the-art baselines in terms of both the acceptance ratio and long-term average revenue. Our code is available at \url{https://github.com/GeminiLight/hrl-acra}.

Virtual network embedding (VNE) is an essential resource allocation task in network virtualization, aiming to map virtual network requests (VNRs) onto physical infrastructure. Reinforcement learning (RL) has recently emerged as a promising solution to this problem. However, existing RL-based VNE methods are limited by the unidirectional action design and one-size-fits-all training strategy, resulting in restricted searchability and generalizability. In this paper, we propose a FLexible And Generalizable RL framework for VNE, named FlagVNE. Specifically, we design a bidirectional action-based Markov decision process model that enables the joint selection of virtual and physical nodes, thus improving the exploration flexibility of solution space. To tackle the expansive and dynamic action space, we design a hierarchical decoder to generate adaptive action probability distributions and ensure high training efficiency. Furthermore, to overcome the generalization issue for varying VNR sizes, we propose a meta-RL-based training method with a curriculum scheduling strategy, facilitating specialized policy training for each VNR size. Finally, extensive experimental results show the effectiveness of FlagVNE across multiple key metrics. Our code is available at GitHub (https://github.com/GeminiLight/flag-vne).

Network slicing is a crucial enabler to support the composition and deployment of virtual network infrastructures required by the dynamic behavior of networks like 5G/6G mobile networks, IoT-aware networks, e-health systems, and industry verticals like the internet of vehicles (IoV) and industry 4.0. The communication slices and their allocated communication resources are essential in slicing architectures for resource orchestration and allocation, virtual network function (VNF) deployment, and slice operation functionalities. The communication slices provide the communications capabilities required to support slice operation, SLA guarantees, and QoS/ QoE application requirements. Therefore, this contribution proposes a networking slicing conceptual model to formulate the optimization problem related to the sharing of communication resources among communication slices. First, we present a conceptual model of network slicing, we then formulate analytically some aspects of the model and the optimization problem to address. Next, we proposed to use a SARSA agent to solve the problem and implement a proof of concept prototype. Finally, we present the obtained results and discuss them.

Virtual network embedding is one of the key problems of network virtualization. Since virtual network mapping is an NP-hard problem, a lot of research has focused on the evolutionary algorithm's masterpiece genetic algorithm. However, the parameter setting in the traditional method is too dependent on experience, and its low flexibility makes it unable to adapt to increasingly complex network environments. In addition, link-mapping strategies that do not consider load balancing can easily cause link blocking in high-traffic environments. In the IoT environment involving medical, disaster relief, life support and other equipment, network performance and stability are particularly important. Therefore, how to provide a more flexible virtual network mapping service in a heterogeneous network environment with large traffic is an urgent problem. Aiming at this problem, a virtual network mapping strategy based on hybrid genetic algorithm is proposed. This strategy uses a dynamically calculated cross-probability and pheromone-based mutation gene selection strategy to improve the flexibility of the algorithm. In addition, a weight update mechanism based on load balancing is introduced to reduce the probability of mapping failure while balancing the load. Simulation results show that the proposed method performs well in a number of performance metrics including mapping average quotation, link load balancing, mapping cost-benefit ratio, acceptance rate and running time.

Virtual network embedding (VNE) is an crucial part of network virtualization (NV), which aims to map the virtual networks (VNs) to a shared substrate network (SN). With the emergence of various delay-sensitive applications, how to improve the delay performance of the system has become a hot topic in academic circles. Based on extensive research, we proposed a multi-domain virtual network embedding algorithm based on delay prediction (DP-VNE). Firstly, the candidate physical nodes are selected by estimating the delay of virtual requests, then particle swarm optimization (PSO) algorithm is used to optimize the mapping process, so as to reduce the delay of the system. The simulation results show that compared with the other three advanced algorithms, the proposed algorithm can significantly reduce the system delay while keeping other indicators unaffected.

The wireless network communication mode represented by the Internet of vehicles (IoV) has been widely used. However, due to the limitations of traditional network architecture, resource scheduling in wireless network environment is still facing great challenges. This paper focuses on the allocation of bandwidth resources in the virtual network environment. This paper proposes a bandwidth aware multi domain virtual network embedding algorithm (BA-VNE). The algorithm is mainly aimed at the problem that users need a lot of bandwidth in wireless communication mode, and solves the problem of bandwidth resource allocation from the perspective of virtual network embedding (VNE). In order to improve the performance of the algorithm, we introduce particle swarm optimization (PSO) algorithm to optimize the performance of the algorithm. In order to verify the effectiveness of the algorithm, we have carried out simulation experiments from link bandwidth, mapping cost and virtual network request (VNR) acceptance rate. The final results show that the proposed algorithm is better than other representative algorithms in the above indicators.