395 research outputs found
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
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), interacting with
two neutrals species (D and D) 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
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 dissociation. The
presence of strong electric fields in high-density plasmas is also shown,
revealing the role of the 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
Optimization of a monolithically integrated ferromagnetic-metal-clad InP-based optical waveguide isolator
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