optimize1dMulti: One dimensional optimization of multivariate loss functions

In kernDeepStackNet: Kernel Deep Stacking Networks

Description

Applies a stepwise one dimensional algorithm conditional on the previous best parameter values. The one dimensional algorithm is a combination of golden search and linear interpolation.

Usage

optimize1dMulti(f_input, lower, upper, maxRuns=3, repetitions=5, 
tol_input=.Machine$double.eps^0.25, x_0=NULL, addInfo=TRUE,
nCores=1, envir=parent.frame(), directUse=TRUE, OptTypePar="")

Arguments

f_input

General loss function with multiple inputs and one numeric outcome value. The function must have a x as first argument, e.g. f(x).

lower	Gives the lower bounds of the input parameters (numeric vector). Each variable corresponds to one element of the vector.
upper	Gives the upper bounds of the input parameters (numeric vector). Each variable corresponds to one element of the vector.
maxRuns	Maximal number of iterations in the conditional optimization. Default is three.
repetitions	Maximal number of random starting values to avoid local optima. Default is five.
tol_input	Convergence criteria of each one dimensional sub-optimization. Higher values will be more accurate, but require much more function evaluations. Default is the fourth root of the machine double accuracy.
x_0	Intitial parameter values. If not supplied, a random number is drawn between the given bounds.
addInfo	Should the optimization print additional information? (logical value) Default is TRUE. The information consists of printing, which parameters have been optimized, which iteration and repetition the optimization process just finished.
nCores	Specifies how many cores are used in tuning (integer scalar). Default=1 is serial processing.
envir	Internal variable to store environments. Default is to look up the next higher level environment. Modification is unnecessary.
directUse	Specifies if the optimization is carried out inside a higher level function (see ) or directly (logical scalar). Only relevant in parallel mode initialization.
OptTypePar	Internal variable to store, which higher level function was called previously. Modification has no effect.

Details

First the supplied initional value x_0 is used. If not present a random intitialisation is used. Then each parameter is optimized, conditional on the other starting values. An iteration is finished, if all parameters have been optimized once. The procedure is repeated until convergence or maxRuns is reached. If repetitions is higher than 1, new starting values are generated and the process starts new. In the end the best parameter values according the lowest function value are returned.

Value

• List with following components:

  • minimum: Best parameter values

  • objective: Minimum of function evaluated at the best parameter values

Author(s)

Thomas Welchowski [e-mail]

References

R. Brent, (1973), Algorithms for Minimization without Derivatives, Englewood Cliffs N.J.: Prentice-Hall

See Also

tuneMboLevelCvKDSN, tuneMboLevelGcvKDSN, tuneMboSharedCvKDSN

Examples

library(globalOptTests)
# Two dimensional task
getDefaultBounds("AluffiPentini")
oneDres <- optimize1dMulti (f_input=function (x) 
goTest (x, fnName="AluffiPentini", checkDim=TRUE), 
maxRuns=3, repetitions=5, lower=rep(-12, 2), upper=rep(10, 2),
tol_input=.Machine$double.eps^0.25)
abs(oneDres$objective-getGlobalOpt("AluffiPentini"))

# Four dimensional optimization task
getDefaultBounds("CosMix4")
oneDres <- optimize1dMulti (f_input=function (x) 
goTest (x, fnName="CosMix4", checkDim=TRUE), 
maxRuns=3, repetitions=5, lower=rep(-2, 4), upper=rep(1, 4),
tol_input=.Machine$double.eps^0.25)
abs(oneDres$objective-getGlobalOpt("CosMix4"))

# Ten dimensional optimization task
getDefaultBounds("Rastrigin")
oneDres <- optimize1dMulti (f_input=function (x) 
goTest (x, fnName="Rastrigin", checkDim=TRUE), 
maxRuns=3, repetitions=5, lower=rep(-525, 10), upper=rep(512, 10),
tol_input=.Machine$double.eps^0.25)
abs(oneDres$objective-getGlobalOpt("Rastrigin"))

# Ten dimensional optimization task with higher accuracy
getDefaultBounds("Rastrigin")
oneDres <- optimize1dMulti (f_input=function (x) 
goTest (x, fnName="Rastrigin", checkDim=TRUE), 
maxRuns=3, repetitions=5, lower=rep(-525, 10), upper=rep(512, 10),
tol_input=.Machine$double.eps^0.5)
abs(oneDres$objective-getGlobalOpt("Rastrigin"))

kernDeepStackNet documentation built on May 2, 2019, 8:16 a.m.