Nils Müller

Nils Müller

We study the optimization of functions with $n>2$ arguments that have a representation as a sum of several functions that have only $2$ of the $n$ arguments each, termed sums of bivariates, on finite domains. The complexity of optimizing sums of bivariates is shown to be NP-equivalent and it is shown that there exists free lunch in the optimization of sums of bivariates. Based on measure-valued extensions of the objective function, so-called relaxations, $\ell^2$-approximation, and entropy-regularization, we derive several tractable problem formulations solvable with linear programming, coordinate ascent as well as with closed-form solutions. The limits of applying tractable versions of such relaxations to sums of bivariates are investigated using general results for reconstructing measures from their bivariate marginals. Experiments in which the derived algorithms are applied to random functions, vertex coloring, and signal reconstruction problems provide insights into qualitatively different function classes that can be modeled as sums of bivariates.

Nils Müller, Charalampos Ziras, Kai Heussen

The increasing interaction of industrial control systems (ICSs) with public networks and digital devices introduces new cyber threats to power systems and other critical infrastructure. Recent cyber-physical attacks such as Stuxnet and Irongate revealed unexpected ICS vulnerabilities and a need for improved security measures. Intrusion detection systems constitute a key security technology, which typically monitors cyber network data for detecting malicious activities. However, a central characteristic of modern ICSs is the increasing interdependency of physical and cyber network processes. Thus, the integration of network and physical process data is seen as a promising approach to improve predictability in real-time intrusion detection for ICSs by accounting for physical constraints and underlying process patterns. This work systematically assesses machine learning-based cyber-physical intrusion detection and multi-class classification through a comparison to its purely network data-based counterpart and evaluation of misclassifications and detection delay. Multiple supervised detection and classification pipelines are applied on a recent cyber-physical dataset, which describes various cyber attacks and physical faults on a generic ICS. A key finding is that the integration of physical process data improves detection and classification of all considered attack types. In addition, it enables simultaneous processing of attacks and faults, paving the way for holistic cross-domain root cause identification.

Nils Müller, Carsten Heinrich, Kai Heussen et al.

The continuous electrification of the mobility and heating sectors adds much-needed flexibility to the power system. However, flexibility utilization also introduces new challenges to distribution system operators (DSOs), who need mechanisms to supervise flexibility activations and monitor their effect on distribution network operation. Flexibility activations can be broadly categorized to those originating from electricity markets and those initiated by the DSO to avoid constraint violations. Simultaneous electricity market driven flexibility activations may cause voltage quality or temporary overloading issues, and the failure of flexibility activations initiated by the DSO might leave critical grid states unresolved. This work proposes a novel data processing pipeline for automated real-time identification of fast-ramped flexibility activation events. Its practical value is twofold: i) potentially critical flexibility activations originating from electricity markets can be detected by the DSO at an early stage, and ii) successful activation of DSO-requested flexibility can be verified by the operator. In both cases the increased awareness would allow the DSO to take counteractions to avoid potentially critical grid situations. The proposed pipeline combines techniques from unsupervised detection and open-set classification. For both building blocks feasibility is systematically evaluated and proofed on real load and flexibility activation data.

Nils Müller, Tobias Glasmachers

In stochastic optimization, particularly in evolutionary computation and reinforcement learning, the optimization of a function $f: Ω\to \mathbb{R}$ is often addressed through optimizing a so-called relaxation $θ\in Θ\mapsto \mathbb{E}_θ(f)$ of $f$, where $Θ$ resembles the parameters of a family of probability measures on $Ω$. We investigate the structure of such relaxations by means of measure theory and Fourier analysis, enabling us to shed light on the success of many associated stochastic optimization methods. The main structural traits we derive and that allow fast and reliable optimization of relaxations are the consistency of optimal values of $f$, Lipschitzness of gradients, and convexity. We emphasize settings where $f$ itself is not differentiable or convex, e.g., in the presence of (stochastic) disturbance.

Nils Müller, Tobias Glasmachers

Evolution Strategies (ESs) have recently become popular for training deep neural networks, in particular on reinforcement learning tasks, a special form of controller design. Compared to classic problems in continuous direct search, deep networks pose extremely high-dimensional optimization problems, with many thousands or even millions of variables. In addition, many control problems give rise to a stochastic fitness function. Considering the relevance of the application, we study the suitability of evolution strategies for high-dimensional, stochastic problems. Our results give insights into which algorithmic mechanisms of modern ES are of value for the class of problems at hand, and they reveal principled limitations of the approach. They are in line with our theoretical understanding of ESs. We show that combining ESs that offer reduced internal algorithm cost with uncertainty handling techniques yields promising methods for this class of problems.