We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare these results with conventional derivative-free global search algorithms, such as (single-fidelity) Gaussian Processes optimization scheme, and Particle Swarm Optimization---a commonly used method in nanophotonics community, which is implemented in Lumerical commercial photonics software. We demonstrate the performance of various numerical optimization approaches on several pre-collected real-world datasets and show that by properly trading off expensive information sources with cheap simulations, one can more effectively optimize the transmission properties with a fixed budget.

Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide guarantees for application scenarios. Gaussian process regression represents one approach which provides such an indicator for the model confidence. However, this measure is only valid if the covariance function and its hyperparameters fit the underlying data generating process. In this paper, we derive an upper bound for the mean square prediction error of misspecified Gaussian process models based on a pseudo-concave optimization problem. We present application scenarios and a simulation to compare the derived upper bound with the true mean square error.

Current newspapers are full of horrific tales of "cyber-attackers" threatening our energy systems. And, if not for the notorious "evil state"-actor, it is the ongoing digitization necessary to enable increasing renewable and volatile energy generation that threatens our energy supply and thus the stability of our society. And while the main approach seems to be to patch-up the detected vulnerabilities of protocols, software and controller devices, our approach is to research and develop the means to systematically design and test systems that are structurally resilient against failures and attackers alike. Security in cyber-systems mostly should be concerned with establishing asymetric control in favour of the operator of a system. In order to achieve this on a structural level at design time, reproducible benchmark tests are required.

Recently, considerable research attention has been paid to network embedding, a popular approach to construct feature vectors of vertices. Due to the curse of dimensionality and sparsity in graphical datasets, this approach has become indispensable for machine learning tasks over large networks. The majority of existing literature has considered this technique under the assumption that the network is static. However, networks in many applications, nodes and edges accrue to a growing network as a streaming. A small number of very recent results have addressed the problem of embedding for dynamic networks. However, they either rely on knowledge of vertex attributes, suffer high-time complexity or need to be re-trained without closed-form expression. Thus the approach of adapting the existing methods to the streaming environment faces non-trivial technical challenges. These challenges motivate developing new approaches to the problems of streaming network embedding. In this paper, We propose a new framework that is able to generate latent features for new vertices with high efficiency and low complexity under specified iteration rounds. We formulate a constrained optimization problem for the modification of the representation resulting from a stream arrival. We show this problem has no closed-form solution and instead develop an online approximation solution. Our solution follows three steps: (1) identify vertices affected by new vertices, (2) generate latent features for new vertices, and (3) update the latent features of the most affected vertices. The generated representations are provably feasible and not far from the optimal ones in terms of expectation. Multi-class classification and clustering on five real-world networks demonstrate that our model can efficiently update vertex representations and simultaneously achieve comparable or even better performance.

We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard variant. With line search, we show that FW can converge to the global optimum, even for smooth functions that are not convex, but are quasi-convex and locally-Lipschitz. We also show that, for the general case of (smooth) non-convex functions, FW with line search converges with high probability to a stationary point at a rate of $O\left(\frac{1}{t}\right)$, as long as the constraint set is strongly convex -- one of the fastest convergence rates in non-convex optimization.

This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems, state-of-the-art methodologies involve algorithmic decisions that either require too much computing time or are not mathematically well defined. Thus, machine learning looks like a promising candidate to effectively deal with those decisions. We advocate for pushing further the integration of machine learning and combinatorial optimization and detail methodology to do so. A main point of the paper is seeing generic optimization problems as data points and inquiring what is the relevant distribution of problems to use for learning on a given task.

Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various probability measures, as in the Wasserstein barycenter problem, or to carry out parametric inference and density fitting, where the loss is measured in terms of an optimal transport cost to the measure of observations. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities (Wasserstein distances) that are themselves hard to compute. Entropic regularization has recently emerged as an efficient tool to approximate the solution of such variational Wasserstein problems. In this paper, we give a thorough duality tour of these regularization techniques. In particular, we show how important concepts from classical OT such as c-transforms and semi-discrete approaches translate into similar ideas in a regularized setting. These dual formulations lead to smooth variational problems, which can be solved using smooth, differentiable and convex optimization problems that are simpler to implement and numerically more stable that their un-regularized counterparts. We illustrate the versatility of this approach by applying it to the computation of Wasserstein barycenters and gradient flows of spatial regularization functionals.

Mathematical optimization offers highly-effective tools for finding solutions for problems with well-defined goals, notably scheduling. However, optimization solvers are often unexplainable black boxes whose solutions are inaccessible to users and which users cannot interact with. We define a novel paradigm using argumentation to empower the interaction between optimization solvers and users, supported by tractable explanations which certify or refute solutions. A solution can be from a solver or of interest to a user (in the context of 'what-if' scenarios). Specifically, we define argumentative and natural language explanations for why a schedule is (not) feasible, (not) efficient or (not) satisfying fixed user decisions, based on models of the fundamental makespan scheduling problem in terms of abstract argumentation frameworks (AFs). We define three types of AFs, whose stable extensions are in one-to-one correspondence with schedules that are feasible, efficient and satisfying fixed decisions, respectively. We extract the argumentative explanations from these AFs and the natural language explanations from the argumentative ones.

ABSTRACT The problem to deal with in this project is the problem of routing electric vehicles, which consists of finding the best routes for this type of vehicle, so that they reach their destination, without running out of power and optimizing to the maximum transportation costs. The importance of this problem is mainly in the sector of shipments in the recent future, when obsolete energy sources are replaced with renewable sources, where each vehicle contains a number of packages that must be delivered at specific points in the city, but, being electric, they do not have an optimal battery life, so having the ideal routes traced is a vital aspect for the proper functioning of these. Now days you can see applications of this problem in the cleaning sector, specifically with the trucks responsible for collecting garbage, which aims to travel the entire city in the most efficient way, without letting excessive garbage accumulate. PAGE SIZE All material on each page should fit within a rectangle of 18 23.5 cm (7" 9.25"), centered on the page, beginning 1.9 cm (0.75") from the top of the page and ending with 2.54 cm (1") from the bottom. The right and left margins should be 1.9 cm (.75"). The text should be in two 8.45 cm (3.33") columns with a .83

We introduce the variational filtering EM algorithm, a simple, general-purpose method for performing variational inference in dynamical latent variable models using information from only past and present variables, i.e. filtering. The algorithm is derived from the variational objective in the filtering setting and consists of an optimization procedure at each time step. By performing each inference optimization procedure with an iterative amortized inference model, we obtain a computationally efficient implementation of the algorithm, which we call amortized variational filtering. We present experiments demonstrating that this general-purpose method improves performance across several deep dynamical latent variable models.