Optimal Transport in the Face of Noisy Data

Optimal transport distances are popular and theoretically well understood in the context of data-driven prediction. A flurry of recent work has popularized these distances for data-driven decision-making as well although their merits in this context are far less well understood. This in contrast to the more classical entropic distances which are known to enjoy optimal statistical properties. This begs the question when, if ever, optimal transport distances enjoy similar statistical guarantees. Optimal transport methods are shown here to enjoy optimal statistical guarantees for decision problems faced with noisy data

Optimal Learning for Structured Bandits

We study structured multi-armed bandits, which is the problem of online decision-making under uncertainty in the presence of structural information. In this problem, the decision-maker needs to discover the best course of action despite observing only uncertain rewards over time. The decision-maker is aware of certain structural information regarding the reward distributions and would like to minimize their regret by exploiting this information, where the regret is its performance difference against a benchmark policy that knows the best action ahead of time. In the absence of structural information, the classical upper confidence bound (UCB) and Thomson sampling algorithms are well known to suffer only minimal regret. As recently pointed out, neither algorithms are, however, capable of exploiting structural information that is commonly available in practice. We propose a novel learning algorithm that we call DUSA whose worst-case regret matches the information-theoretic regret lower bound up to a constant factor and can handle a wide range of structural information. Our algorithm DUSA solves a dual counterpart of the regret lower bound at the empirical reward distribution and follows its suggested play. Our proposed algorithm is the first computationally viable learning policy for structured bandit problems that has asymptotic minimal regret

Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions

We study the problem of designing optimal learning and decision-making formulations when only historical data is available. Prior work typically commits to a particular class of data-driven formulation and subsequently tries to establish out-of-sample performance guarantees. We take here the opposite approach. We define first a sensible yard stick with which to measure the quality of any data-driven formulation and subsequently seek to find an optimal such formulation. Informally, any data-driven formulation can be seen to balance a measure of proximity of the estimated cost to the actual cost while guaranteeing a level of out-of-sample performance. Given an acceptable level of out-of-sample performance, we construct explicitly a data-driven formulation that is uniformly closer to the true cost than any other formulation enjoying the same out-of-sample performance. We show the existence of three distinct out-of-sample performance regimes (a superexponential regime, an exponential regime and a subexponential regime) between which the nature of the optimal data-driven formulation experiences a phase transition. The optimal data-driven formulations can be interpreted as a classically robust formulation in the superexponential regime, an entropic distributionally robust formulation in the exponential regime and finally a variance penalized formulation in the subexponential regime. This final observation unveils a surprising connection between these three, at first glance seemingly unrelated, data-driven formulations which until now remained hidden

Growing up with a mother with depression: an interpretative phenomenological analysis

The aim of this study was to explore the childhood experience of living with a parent with depression from a retrospective point of view. Five women between 39 and 47 years of age, who grew up with a mother with depression, were interviewed about their current perspectives on their childhood experiences. Interviews were semi-structured and the data were analyzed using interpretative phenomenological analysis. Data analysis led to a narrative organized in two parts. The first part (retrospective understanding of childhood experiences) reports on feelings of desolation contrasted to exceptional support, context-related dwelling on own experiences, and growing into a caring role as a way to keep standing. The second part (towards an integration of childhood experiences in adult realities) evidences ongoing processes of growing understanding of the situation at home, coping with own vulnerabilities, making the difference in their current family life and finding balance in the continued bond with the parents. This retrospective investigation of adults’ perspectives on their childhood experiences gave access to aspects of their experience that remain underexposed in research based on data from children and adolescents

A General Framework for Optimal Data-Driven Optimization

We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be expressed as the minimizer of a surrogate optimization model constructed from the data. The quality of a data-driven decision is measured by its out-of-sample risk. An additional quality measure is its out-of-sample disappointment, which we define as the probability that the out-of-sample risk exceeds the optimal value of the surrogate optimization model. An ideal data-driven decision should minimize the out-of-sample risk simultaneously with respect to every conceivable probability measure as the true measure is unkown. Unfortunately, such ideal data-driven decisions are generally unavailable. This prompts us to seek data-driven decisions that minimize the out-of-sample risk subject to an upper bound on the out-of-sample disappointment. We prove that such Pareto-dominant data-driven decisions exist under conditions that allow for interesting applications: the unknown data-generating probability measure must belong to a parametric ambiguity set, and the corresponding parameters must admit a sufficient statistic that satisfies a large deviation principle. We can further prove that the surrogate optimization model must be a distributionally robust optimization problem constructed from the sufficient statistic and the rate function of its large deviation principle. Hence the optimal method for mapping data to decisions is to solve a distributionally robust optimization model. Maybe surprisingly, this result holds even when the training data is non-i.i.d. Our analysis reveals how the structural properties of the data-generating stochastic process impact the shape of the ambiguity set underlying the optimal distributionally robust model.Comment: 52 page

Design and optimization of a monolithically integratable InP-based optical waveguide isolator

The optimization design of the layer structure for a novel type of a 1.3 m monolithically integrated InP-based optical waveguide isolator is presented. The concept of this component is based on introducing a nonreciprocal loss–gain behavior in a standard semiconductor optical amplifier (SOA) structure by contacting the SOA with a transversely magnetized ferromagnetic metal contact, sufficiently close to the guiding and amplifying core of the SOA. The thus induced nonreciprocal complex transverse Kerr shift on the effective index of the guided TM modes, combined with a proper current injection, allows for forward transparency and backward optical ex-tinction. We introduce two different optimization criteria for finding the optimal SOA layer structure, using two different figure-of-merit functions (FoM) for the device performance. The device performance is also com-pared for three different compositions of the CoxFe1−x x=0,50,90 ferromagnetic transition metal alloy sys-tem. It is found that equiatomic (or quasi-equiatomic) CoFe alloys are the most suitable for this application. Depending on the used FoM, two technologically practical designs are proposed for a truly monolithically in-tegrated optical waveguide isolator. It is also shown that these designs are robust with respect to variations in layer thicknesses and wavelength. Finally, we have derived an analytical expression that gives a better insight in the limit performance of a ferromagnetic metal-clad SOA–isolator in terms of metal parameters. © 200

Exterior-point Optimization for Nonconvex Learning

In this paper we present the nonconvex exterior-point optimization solver (NExOS) -- a novel first-order algorithm tailored to constrained nonconvex learning problems. We consider the problem of minimizing a convex function over nonconvex constraints, where the projection onto the constraint set is single-valued around local minima. A wide range of nonconvex learning problems have this structure including (but not limited to) sparse and low-rank optimization problems. By exploiting the underlying geometry of the constraint set, NExOS finds a locally optimal point by solving a sequence of penalized problems with strictly decreasing penalty parameters. NExOS solves each penalized problem by applying a first-order algorithm, which converges linearly to a local minimum of the corresponding penalized formulation under regularity conditions. Furthermore, the local minima of the penalized problems converge to a local minimum of the original problem as the penalty parameter goes to zero. We implement NExOS in the open-source Julia package NExOS.jl, which has been extensively tested on many instances from a wide variety of learning problems. We demonstrate that our algorithm, in spite of being general purpose, outperforms specialized methods on several examples of well-known nonconvex learning problems involving sparse and low-rank optimization. For sparse regression problems, NExOS finds locally optimal solutions which dominate glmnet in terms of support recovery, yet its training loss is smaller by an order of magnitude. For low-rank optimization with real-world data, NExOS recovers solutions with 3 fold training loss reduction, but with a proportion of explained variance that is 2 times better compared to the nuclear norm heuristic.Comment: 40 pages, 6 figure

Energy-optimal Timetable Design for Sustainable Metro Railway Networks

We present our collaboration with Thales Canada Inc, the largest provider of communication-based train control (CBTC) systems worldwide. We study the problem of designing energy-optimal timetables in metro railway networks to minimize the effective energy consumption of the network, which corresponds to simultaneously minimizing total energy consumed by all the trains and maximizing the transfer of regenerative braking energy from suitable braking trains to accelerating trains. We propose a novel data-driven linear programming model that minimizes the total effective energy consumption in a metro railway network, capable of computing the optimal timetable in real-time, even for some of the largest CBTC systems in the world. In contrast with existing works, which are either NP-hard or involve multiple stages requiring extensive simulation, our model is a single linear programming model capable of computing the energy-optimal timetable subject to the constraints present in the railway network. Furthermore, our model can predict the total energy consumption of the network without requiring time-consuming simulations, making it suitable for widespread use in managerial settings. We apply our model to Shanghai Railway Network's Metro Line 8 -- one of the largest and busiest railway services in the world -- and empirically demonstrate that our model computes energy-optimal timetables for thousands of active trains spanning an entire service period of one day in real-time (solution time less than one second on a standard desktop), achieving energy savings between approximately 20.93% and 28.68%. Given the compelling advantages, our model is in the process of being integrated into Thales Canada Inc's industrial timetable compiler.Comment: 28 pages, 8 figures, 2 table

Self-consistent multi-component simulation of plasma turbulence and neutrals in detached conditions

Simulations of high-density deuterium plasmas in a lower single-null magnetic configuration based on a TCV discharge are presented. We evolve the dynamics of three charged species (electrons, D$^{+}$ and D$_{2}^{+}$), interacting with two neutrals species (D and D$_2$) through ionization, charge-exchange, recombination and molecular dissociation processes. The plasma is modelled by using the drift-reduced fluid Braginskii equations, while the neutral dynamics is described by a kinetic model. To control the divertor conditions, a D$_2$ puffing is used and the effect of increasing the puffing strength is investigated. The increase in fuelling leads to an increase of density in the scrape-off layer and a decrease of the plasma temperature. At the same time, the particle and heat fluxes to the divertor target decrease and the detachment of the inner target is observed. The analysis of particle and transport balance in the divertor volume shows that the decrease of the particle flux is caused by a decrease of the local neutral ionization together with a decrease of the parallel velocity, both caused by the lower plasma temperature. The relative importance of the different collision terms is assessed, showing the crucial role of molecular interactions, as they are responsible for increasing the atomic neutral density and temperature, since most of the D neutrals are produced by molecular activated recombination and D$_2$ dissociation. The presence of strong electric fields in high-density plasmas is also shown, revealing the role of the $E \times B$ drift in setting the asymmetry between the divertor targets. Simulation results are in agreement with experimental observations of increased density decay length, attributed to a decrease of parallel transport, together with an increase of plasma blob size and radial velocity