29,728 research outputs found
The Sampling-and-Learning Framework: A Statistical View of Evolutionary Algorithms
Evolutionary algorithms (EAs), a large class of general purpose optimization
algorithms inspired from the natural phenomena, are widely used in various
industrial optimizations and often show excellent performance. This paper
presents an attempt towards revealing their general power from a statistical
view of EAs. By summarizing a large range of EAs into the sampling-and-learning
framework, we show that the framework directly admits a general analysis on the
probable-absolute-approximate (PAA) query complexity. We particularly focus on
the framework with the learning subroutine being restricted as a binary
classification, which results in the sampling-and-classification (SAC)
algorithms. With the help of the learning theory, we obtain a general upper
bound on the PAA query complexity of SAC algorithms. We further compare SAC
algorithms with the uniform search in different situations. Under the
error-target independence condition, we show that SAC algorithms can achieve
polynomial speedup to the uniform search, but not super-polynomial speedup.
Under the one-side-error condition, we show that super-polynomial speedup can
be achieved. This work only touches the surface of the framework. Its power
under other conditions is still open
Kinematic Basis of Emergent Energetics of Complex Dynamics
Stochastic kinematic description of a complex dynamics is shown to dictate an
energetic and thermodynamic structure. An energy function emerges
as the limit of the generalized, nonequilibrium free energy of a Markovian
dynamics with vanishing fluctuations. In terms of the and its
orthogonal field , a general vector field
can be decomposed into , where
.
The matrix and scalar , two additional characteristics to the
alone, represent the local geometry and density of states intrinsic to
the statistical motion in the state space at . and
are interpreted as the emergent energy and degeneracy of the motion, with an
energy balance equation ,
reflecting the geometrical . The
partition function employed in statistical mechanics and J. W. Gibbs' method of
ensemble change naturally arise; a fluctuation-dissipation theorem is
established via the two leading-order asymptotics of entropy production as
. The present theory provides a mathematical basis for P. W.
Anderson's emergent behavior in the hierarchical structure of complexity
science.Comment: 7 page
ZOOpt: Toolbox for Derivative-Free Optimization
Recent advances of derivative-free optimization allow efficient approximating
the global optimal solutions of sophisticated functions, such as functions with
many local optima, non-differentiable and non-continuous functions. This
article describes the ZOOpt (https://github.com/eyounx/ZOOpt) toolbox that
provides efficient derivative-free solvers and are designed easy to use. ZOOpt
provides a Python package for single-thread optimization, and a light-weighted
distributed version with the help of the Julia language for Python described
functions. ZOOpt toolbox particularly focuses on optimization problems in
machine learning, addressing high-dimensional, noisy, and large-scale problems.
The toolbox is being maintained toward ready-to-use tool in real-world machine
learning tasks
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