612,978 research outputs found
Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms
We propose a unifying algorithm for non-smooth non-convex optimization. The
algorithm approximates the objective function by a convex model function and
finds an approximate (Bregman) proximal point of the convex model. This
approximate minimizer of the model function yields a descent direction, along
which the next iterate is found. Complemented with an Armijo-like line search
strategy, we obtain a flexible algorithm for which we prove (subsequential)
convergence to a stationary point under weak assumptions on the growth of the
model function error. Special instances of the algorithm with a Euclidean
distance function are, for example, Gradient Descent, Forward--Backward
Splitting, ProxDescent, without the common requirement of a "Lipschitz
continuous gradient". In addition, we consider a broad class of Bregman
distance functions (generated by Legendre functions) replacing the Euclidean
distance. The algorithm has a wide range of applications including many linear
and non-linear inverse problems in signal/image processing and machine
learning
Fixed-point and coordinate descent algorithms for regularized kernel methods
In this paper, we study two general classes of optimization algorithms for
kernel methods with convex loss function and quadratic norm regularization, and
analyze their convergence. The first approach, based on fixed-point iterations,
is simple to implement and analyze, and can be easily parallelized. The second,
based on coordinate descent, exploits the structure of additively separable
loss functions to compute solutions of line searches in closed form. Instances
of these general classes of algorithms are already incorporated into state of
the art machine learning software for large scale problems. We start from a
solution characterization of the regularized problem, obtained using
sub-differential calculus and resolvents of monotone operators, that holds for
general convex loss functions regardless of differentiability. The two
methodologies described in the paper can be regarded as instances of non-linear
Jacobi and Gauss-Seidel algorithms, and are both well-suited to solve large
scale problems
Toward Interpretable Deep Reinforcement Learning with Linear Model U-Trees
Deep Reinforcement Learning (DRL) has achieved impressive success in many
applications. A key component of many DRL models is a neural network
representing a Q function, to estimate the expected cumulative reward following
a state-action pair. The Q function neural network contains a lot of implicit
knowledge about the RL problems, but often remains unexamined and
uninterpreted. To our knowledge, this work develops the first mimic learning
framework for Q functions in DRL. We introduce Linear Model U-trees (LMUTs) to
approximate neural network predictions. An LMUT is learned using a novel
on-line algorithm that is well-suited for an active play setting, where the
mimic learner observes an ongoing interaction between the neural net and the
environment. Empirical evaluation shows that an LMUT mimics a Q function
substantially better than five baseline methods. The transparent tree structure
of an LMUT facilitates understanding the network's learned knowledge by
analyzing feature influence, extracting rules, and highlighting the
super-pixels in image inputs.Comment: This paper is accepted by ECML-PKDD 201
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