34,415 research outputs found
Statistical and Computational Tradeoff in Genetic Algorithm-Based Estimation
When a Genetic Algorithm (GA), or a stochastic algorithm in general, is
employed in a statistical problem, the obtained result is affected by both
variability due to sampling, that refers to the fact that only a sample is
observed, and variability due to the stochastic elements of the algorithm. This
topic can be easily set in a framework of statistical and computational
tradeoff question, crucial in recent problems, for which statisticians must
carefully set statistical and computational part of the analysis, taking
account of some resource or time constraints. In the present work we analyze
estimation problems tackled by GAs, for which variability of estimates can be
decomposed in the two sources of variability, considering some constraints in
the form of cost functions, related to both data acquisition and runtime of the
algorithm. Simulation studies will be presented to discuss the statistical and
computational tradeoff question.Comment: 17 pages, 5 figure
Meta-Learning by the Baldwin Effect
The scope of the Baldwin effect was recently called into question by two
papers that closely examined the seminal work of Hinton and Nowlan. To this
date there has been no demonstration of its necessity in empirically
challenging tasks. Here we show that the Baldwin effect is capable of evolving
few-shot supervised and reinforcement learning mechanisms, by shaping the
hyperparameters and the initial parameters of deep learning algorithms.
Furthermore it can genetically accommodate strong learning biases on the same
set of problems as a recent machine learning algorithm called MAML "Model
Agnostic Meta-Learning" which uses second-order gradients instead of evolution
to learn a set of reference parameters (initial weights) that can allow rapid
adaptation to tasks sampled from a distribution. Whilst in simple cases MAML is
more data efficient than the Baldwin effect, the Baldwin effect is more general
in that it does not require gradients to be backpropagated to the reference
parameters or hyperparameters, and permits effectively any number of gradient
updates in the inner loop. The Baldwin effect learns strong learning dependent
biases, rather than purely genetically accommodating fixed behaviours in a
learning independent manner
Evolutionary multiobjective optimization of the multi-location transshipment problem
We consider a multi-location inventory system where inventory choices at each
location are centrally coordinated. Lateral transshipments are allowed as
recourse actions within the same echelon in the inventory system to reduce
costs and improve service level. However, this transshipment process usually
causes undesirable lead times. In this paper, we propose a multiobjective model
of the multi-location transshipment problem which addresses optimizing three
conflicting objectives: (1) minimizing the aggregate expected cost, (2)
maximizing the expected fill rate, and (3) minimizing the expected
transshipment lead times. We apply an evolutionary multiobjective optimization
approach using the strength Pareto evolutionary algorithm (SPEA2), to
approximate the optimal Pareto front. Simulation with a wide choice of model
parameters shows the different trades-off between the conflicting objectives
Information-Geometric Optimization Algorithms: A Unifying Picture via Invariance Principles
We present a canonical way to turn any smooth parametric family of
probability distributions on an arbitrary search space into a
continuous-time black-box optimization method on , the
\emph{information-geometric optimization} (IGO) method. Invariance as a design
principle minimizes the number of arbitrary choices. The resulting \emph{IGO
flow} conducts the natural gradient ascent of an adaptive, time-dependent,
quantile-based transformation of the objective function. It makes no
assumptions on the objective function to be optimized.
The IGO method produces explicit IGO algorithms through time discretization.
It naturally recovers versions of known algorithms and offers a systematic way
to derive new ones. The cross-entropy method is recovered in a particular case,
and can be extended into a smoothed, parametrization-independent maximum
likelihood update (IGO-ML). For Gaussian distributions on , IGO
is related to natural evolution strategies (NES) and recovers a version of the
CMA-ES algorithm. For Bernoulli distributions on , we recover the
PBIL algorithm. From restricted Boltzmann machines, we obtain a novel algorithm
for optimization on . All these algorithms are unified under a
single information-geometric optimization framework.
Thanks to its intrinsic formulation, the IGO method achieves invariance under
reparametrization of the search space , under a change of parameters of the
probability distributions, and under increasing transformations of the
objective function.
Theory strongly suggests that IGO algorithms have minimal loss in diversity
during optimization, provided the initial diversity is high. First experiments
using restricted Boltzmann machines confirm this insight. Thus IGO seems to
provide, from information theory, an elegant way to spontaneously explore
several valleys of a fitness landscape in a single run.Comment: Final published versio
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