122,081 research outputs found
Polynomial algorithms for p-dispersion problems in a 2d Pareto Front
Having many best compromise solutions for bi-objective optimization problems,
this paper studies p-dispersion problems to select
representative points in the Pareto Front(PF). Four standard variants of
p-dispersion are considered. A novel variant, denoted Max-Sum-Neighbor
p-dispersion, is introduced for the specific case of a 2d PF. Firstly, it is
proven that -dispersion and -dispersion problems are solvable in
time in a 2d PF. Secondly, dynamic programming algorithms are designed for
three p-dispersion variants, proving polynomial complexities in a 2d PF. The
Max-Min p-dispersion problem is proven solvable in time and
memory space. The Max-Sum-Min p-dispersion problem is proven solvable in
time and space. The Max-Sum-Neighbor p-dispersion problem
is proven solvable in time and space. Complexity results and
parallelization issues are discussed in regards to practical implementation
Min Max Generalization for Two-stage Deterministic Batch Mode Reinforcement Learning: Relaxation Schemes
We study the minmax optimization problem introduced in [22] for computing
policies for batch mode reinforcement learning in a deterministic setting.
First, we show that this problem is NP-hard. In the two-stage case, we provide
two relaxation schemes. The first relaxation scheme works by dropping some
constraints in order to obtain a problem that is solvable in polynomial time.
The second relaxation scheme, based on a Lagrangian relaxation where all
constraints are dualized, leads to a conic quadratic programming problem. We
also theoretically prove and empirically illustrate that both relaxation
schemes provide better results than those given in [22]
On central tendency and dispersion measures for intervals and hypercubes
The uncertainty or the variability of the data may be treated by considering,
rather than a single value for each data, the interval of values in which it
may fall. This paper studies the derivation of basic description statistics for
interval-valued datasets. We propose a geometrical approach in the
determination of summary statistics (central tendency and dispersion measures)
for interval-valued variables
Dispersion for Data-Driven Algorithm Design, Online Learning, and Private Optimization
Data-driven algorithm design, that is, choosing the best algorithm for a
specific application, is a crucial problem in modern data science.
Practitioners often optimize over a parameterized algorithm family, tuning
parameters based on problems from their domain. These procedures have
historically come with no guarantees, though a recent line of work studies
algorithm selection from a theoretical perspective. We advance the foundations
of this field in several directions: we analyze online algorithm selection,
where problems arrive one-by-one and the goal is to minimize regret, and
private algorithm selection, where the goal is to find good parameters over a
set of problems without revealing sensitive information contained therein. We
study important algorithm families, including SDP-rounding schemes for problems
formulated as integer quadratic programs, and greedy techniques for canonical
subset selection problems. In these cases, the algorithm's performance is a
volatile and piecewise Lipschitz function of its parameters, since tweaking the
parameters can completely change the algorithm's behavior. We give a sufficient
and general condition, dispersion, defining a family of piecewise Lipschitz
functions that can be optimized online and privately, which includes the
functions measuring the performance of the algorithms we study. Intuitively, a
set of piecewise Lipschitz functions is dispersed if no small region contains
many of the functions' discontinuities. We present general techniques for
online and private optimization of the sum of dispersed piecewise Lipschitz
functions. We improve over the best-known regret bounds for a variety of
problems, prove regret bounds for problems not previously studied, and give
matching lower bounds. We also give matching upper and lower bounds on the
utility loss due to privacy. Moreover, we uncover dispersion in auction design
and pricing problems
Validity of particle size analysis techniques for measurement of the attrition that occurs during vacuum agitated powder drying of needle-shaped particles
Analysis of needle-shaped particles of cellobiose octaacetate (COA) obtained from vacuum agitated drying experiments was performed using three particle size analysis techniques: laser diffraction (LD), focused beam reflectance measurements (FBRM) and dynamic image analysis. Comparative measurements were also made for various size fractions of granular particles of microcrystalline cellulose. The study demonstrated that the light scattering particle size methods (LD and FBRM) can be used qualitatively to study the attrition that occurs during drying of needle-shaped particles, however, for full quantitative analysis, image analysis is required. The algorithm used in analysis of LD data assumes the scattering particles are spherical regardless of the actual shape of the particles under evaluation. FBRM measures a chord length distribution (CLD) rather than the particle size distribution (PSD), which in the case of needles is weighted towards the needle width rather than their length. Dynamic image analysis allowed evaluation of the particles based on attributes of the needles such as length (e.g. the maximum Feret diameter) or width (e.g. the minimum Feret diameter) and as such, was the most informative of the techniques for the analysis of attrition that occurred during drying
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