4,395 research outputs found
Replication or exploration? Sequential design for stochastic simulation experiments
We investigate the merits of replication, and provide methods for optimal
design (including replicates), with the goal of obtaining globally accurate
emulation of noisy computer simulation experiments. We first show that
replication can be beneficial from both design and computational perspectives,
in the context of Gaussian process surrogate modeling. We then develop a
lookahead based sequential design scheme that can determine if a new run should
be at an existing input location (i.e., replicate) or at a new one (explore).
When paired with a newly developed heteroskedastic Gaussian process model, our
dynamic design scheme facilitates learning of signal and noise relationships
which can vary throughout the input space. We show that it does so efficiently,
on both computational and statistical grounds. In addition to illustrative
synthetic examples, we demonstrate performance on two challenging real-data
simulation experiments, from inventory management and epidemiology.Comment: 34 pages, 9 figure
Algorithm Portfolios for Noisy Optimization
Noisy optimization is the optimization of objective functions corrupted by
noise. A portfolio of solvers is a set of solvers equipped with an algorithm
selection tool for distributing the computational power among them. Portfolios
are widely and successfully used in combinatorial optimization. In this work,
we study portfolios of noisy optimization solvers. We obtain mathematically
proved performance (in the sense that the portfolio performs nearly as well as
the best of its solvers) by an ad hoc portfolio algorithm dedicated to noisy
optimization. A somehow surprising result is that it is better to compare
solvers with some lag, i.e., propose the current recommendation of best solver
based on their performance earlier in the run. An additional finding is a
principled method for distributing the computational power among solvers in the
portfolio.Comment: in Annals of Mathematics and Artificial Intelligence, Springer
Verlag, 201
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