19,693 research outputs found
An Exponential Lower Bound for the Runtime of the cGA on Jump Functions
In the first runtime analysis of an estimation-of-distribution algorithm
(EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO
2018) proved that the runtime of the compact genetic algorithm with suitable
parameter choice on jump functions with high probability is at most polynomial
(in the dimension) if the jump size is at most logarithmic (in the dimension),
and is at most exponential in the jump size if the jump size is
super-logarithmic. The exponential runtime guarantee was achieved with a
hypothetical population size that is also exponential in the jump size.
Consequently, this setting cannot lead to a better runtime.
In this work, we show that any choice of the hypothetical population size
leads to a runtime that, with high probability, is at least exponential in the
jump size. This result might be the first non-trivial exponential lower bound
for EDAs that holds for arbitrary parameter settings.Comment: To appear in the Proceedings of FOGA 2019. arXiv admin note: text
overlap with arXiv:1903.1098
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A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs
Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs
Analysis of Different Types of Regret in Continuous Noisy Optimization
The performance measure of an algorithm is a crucial part of its analysis.
The performance can be determined by the study on the convergence rate of the
algorithm in question. It is necessary to study some (hopefully convergent)
sequence that will measure how "good" is the approximated optimum compared to
the real optimum. The concept of Regret is widely used in the bandit literature
for assessing the performance of an algorithm. The same concept is also used in
the framework of optimization algorithms, sometimes under other names or
without a specific name. And the numerical evaluation of convergence rate of
noisy algorithms often involves approximations of regrets. We discuss here two
types of approximations of Simple Regret used in practice for the evaluation of
algorithms for noisy optimization. We use specific algorithms of different
nature and the noisy sphere function to show the following results. The
approximation of Simple Regret, termed here Approximate Simple Regret, used in
some optimization testbeds, fails to estimate the Simple Regret convergence
rate. We also discuss a recent new approximation of Simple Regret, that we term
Robust Simple Regret, and show its advantages and disadvantages.Comment: Genetic and Evolutionary Computation Conference 2016, Jul 2016,
Denver, United States. 201
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