33 research outputs found
Suboptimal solutions to network team optimization problems
Smoothness of the solutions to network team optimization problems with statistical information structure is investigated. Suboptimal solutions expressed as linear combinations of elements from sets of basis functions containing adjustable parameters are considered. Estimates of their accuracy are derived, for basis functions represented by sinusoids with variable frequencies and phases and
Gaussians with variable centers and widthss
Proximal boosting and its acceleration
Gradient boosting is a prediction method that iteratively combines weak
learners to produce a complex and accurate model. From an optimization point of
view, the learning procedure of gradient boosting mimics a gradient descent on
a functional variable. This paper proposes to build upon the proximal point
algorithm when the empirical risk to minimize is not differentiable to
introduce a novel boosting approach, called proximal boosting. Besides being
motivated by non-differentiable optimization, the proposed algorithm benefits
from Nesterov's acceleration in the same way as gradient boosting [Biau et al.,
2018]. This leads to a variant, called accelerated proximal boosting.
Advantages of leveraging proximal methods for boosting are illustrated by
numerical experiments on simulated and real-world data. In particular, we
exhibit a favorable comparison over gradient boosting regarding convergence
rate and prediction accuracy
Schwarz Iterative Methods: Infinite Space Splittings
We prove the convergence of greedy and randomized versions of Schwarz
iterative methods for solving linear elliptic variational problems based on
infinite space splittings of a Hilbert space. For the greedy case, we show a
squared error decay rate of for elements of an approximation
space related to the underlying splitting. For the randomized
case, we show an expected squared error decay rate of on a
class depending on the
probability distribution.Comment: Revised version, accepted in Constr. Appro
A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization
Fixed-basis and variable-basis approximation schemes are compared for the problems of function approximation and functional optimization (also known as infinite programming). Classes of problems are investigated for which variable-basis schemes with sigmoidal computational
units perform better than fixed-basis ones, in terms of the minimum number of computational units needed to achieve a desired error in function approximation or approximate optimization. Previously known bounds on the accuracy are extended, with better rates, to families o