DeepPR: Progressive Recovery for Interdependent VNFs with Deep Reinforcement Learning

The increasing reliance upon cloud services entails more flexible networks that are realized by virtualized network equipment and functions. When such advanced network systems face a massive failure by natural disasters or attacks, the recovery of the entire system may be conducted in a progressive way due to limited repair resources. The prioritization of network equipment in the recovery phase influences the interim computation and communication capability of systems, since the systems are operated under partial functionality. Hence, finding the best recovery order is a critical problem, which is further complicated by virtualization due to dependency among network nodes and layers. This paper deals with a progressive recovery problem under limited resources in networks with VNFs, where some dependent network layers exist. We prove the NP-hardness of the progressive recovery problem and approach the optimum solution by introducing DeepPR, a progressive recovery technique based on Deep Reinforcement Learning (Deep RL). Our simulation results indicate that DeepPR can achieve the near-optimal solutions in certain networks and is more robust to adversarial failures, compared to a baseline heuristic algorithm.Comment: Technical Report, 12 page

The edge-disjoint path problem on random graphs by message-passing

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an exponential computational cost in the number of paths. To overcome this obstacle we propose an efficient implementation by mapping the equations onto a weighted combinatorial matching problem over an auxiliary graph. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behaviour of both the number of paths to be accommodated and their minimum total length.Comment: 14 pages, 8 figure

Reinforcement Learning for Racecar Control

This thesis investigates the use of reinforcement learning to learn to drive a racecar in the simulated environment of the Robot Automobile Racing Simulator. Real-life race driving is known to be difficult for humans, and expert human drivers use complex sequences of actions. There are a large number of variables, some of which change stochastically and all of which may affect the outcome. This makes driving a promising domain for testing and developing Machine Learning techniques that have the potential to be robust enough to work in the real world. Therefore the principles of the algorithms from this work may be applicable to a range of problems. The investigation starts by finding a suitable data structure to represent the information learnt. This is tested using supervised learning. Reinforcement learning is added and roughly tuned, and the supervised learning is then removed. A simple tabular representation is found satisfactory, and this avoids difficulties with more complex methods and allows the investigation to concentrate on the essentials of learning. Various reward sources are tested and a combination of three are found to produce the best performance. Exploration of the problem space is investigated. Results show exploration is essential but controlling how much is done is also important. It turns out the learning episodes need to be very long and because of this the task needs to be treated as continuous by using discounting to limit the size of the variables stored. Eligibility traces are used with success to make the learning more efficient. The tabular representation is made more compact by hashing and more accurate by using smaller buckets. This slows the learning but produces better driving. The improvement given by a rough form of generalisation indicates the replacement of the tabular method by a function approximator is warranted. These results show reinforcement learning can work within the Robot Automobile Racing Simulator, and lay the foundations for building a more efficient and competitive agent

The Algorithmic Complexity of Bondage and Reinforcement Problems in bipartite graphs

Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. The domination number of $G$, denoted by $\gamma(G)$, is the smallest cardinality of a dominating set of $G$. The bondage number of a nonempty graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with domination number larger than $\gamma(G)$. The reinforcement number of $G$ is the smallest number of edges whose addition to $G$ results in a graph with smaller domination number than $\gamma(G)$. In 2012, Hu and Xu proved that the decision problems for the bondage, the total bondage, the reinforcement and the total reinforcement numbers are all NP-hard in general graphs. In this paper, we improve these results to bipartite graphs.Comment: 13 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1109.1657; and text overlap with arXiv:1204.4010 by other author