On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Optimization

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine learning tasks. However, it has not been analyzed for non-convex minimization and there still remains a gap between the theory and the practice. In this paper, we analyze gradient descent and stochastic gradient descent with extrapolation for finding an approximate first-order stationary point in smooth non-convex optimization problems. Our convergence upper bounds show that the algorithms with extrapolation can be accelerated than without extrapolation

A Deep Learning-based Approach to Identifying and Mitigating Network Attacks Within SDN Environments Using Non-standard Data Sources

Modern society is increasingly dependent on computer networks, which are essential to delivering an increasing number of key services. With this increasing dependence, comes a corresponding increase in global traffic and users. One of the tools administrators are using to deal with this growth is Software Defined Networking (SDN). SDN changes the traditional distributed networking design to a more programmable centralised solution, based around the SDN controller. This allows administrators to respond more quickly to changing network conditions. However, this change in paradigm, along with the growing use of encryption can cause other issues. For many years, security administrators have used techniques such as deep packet inspection and signature analysis to detect malicious activity. These methods are becoming less common as artificial intelligence (AI) and deep learning technologies mature. AI and deep learning have advantages in being able to cope with 0-day attacks and being able to detect malicious activity despite the use of encryption and obfuscation techniques. However, SDN reduces the volume of data that is available for analysis with these machine learning techniques. Rather than packet information, SDN relies on flows, which are abstract representations of network activity. Security researchers have been slow to move to this new method of networking, in part because of this reduction in data, however doing so could have advantages in responding quickly to malicious activity. This research project seeks to provide a way to reconcile the contradiction apparent, by building a deep learning model that can achieve comparable results to other state-of-the-art models, while using 70% fewer features. This is achieved through the creation of new data from logs, as well as creation of a new risk-based sampling method to prioritise suspect flows for analysis, which can successfully prioritise over 90% of malicious flows from leading datasets. Additionally, provided is a mitigation method that can work with a SDN solution to automatically mitigate attacks after they are found, showcasing the advantages of closer integration with SDN