OOR {OOR}

Package OOR

Description

This package implements optimistic optimization methods [1,2,3] for global optimization of deterministic or stochastic functions. The algorithms feature guarantees of the convergence to a global optimum. They require minimal assumptions on the (only local) smoothness, where the smoothness parameter does not need to be known. They are expected to be useful for the most difficult functions when we have no information on smoothness and the gradients are unknown or do not exist. Due to the weak assumptions, however, they can be mostly effective only in small dimensions, for example, for hyperparameter tuning [4].

Details

Important functions:
StoSOO
POO

Note

This package is based on the Matlab and Python implementations from the corresponding publications, available from the following webpage: https://team.inria.fr/sequel/software/.

References

[1] R. Munos (2011), Optimistic optimization of deterministic functions without the knowledge of its smoothness, NIPS, 783-791.

[2] M. Valko, A. Carpentier and R. Munos (2013), Stochastic Simultaneous Optimistic Optimization, ICML, 19-27 https://inria.hal.science/hal-00789606.

[3] J.-B. Grill, M. Valko and R. Munos (2015), Black-box optimization of noisy functions with unknown smoothness, NIPS, 667-675 https://inria.hal.science/hal-01222915.

[4] S. Samothrakis, D. Perz, S. Lucas (2013), Training gradient boosting machines using curve-fitting and information-theoretic features for causal direction detection, NIPS Workshop on Causality.

Examples

#------------------------------------------------------------
# Example 1 : Deterministic optimization with SOO
#------------------------------------------------------------
## Define objective
fun1 <- function(x) return(-guirland(x))

## Optimization
Sol1 <- StoSOO(par = NA, fn = fun1, nb_iter = 1000, control = list(type = "det", verbose = 1))

## Display objective function and solution fund
curve(fun1, n = 1001)
abline(v = Sol1$par, col = 'red')

#------------------------------------------------------------
# Example 2 : Stochastic optimization with StoSOO
#------------------------------------------------------------
set.seed(42)

## 2-dimensional noisy objective function, defined on [0, pi/4]^2
fun2 <- function(x){return(-sin1(x[1]) * sin1(1 - x[2]) + runif(1, min = -0.05, max = 0.05))}

## Optimizing
Sol2 <- StoSOO(par = rep(NA, 2), fn = fun2, upper = rep(pi/4, 2), nb_iter = 1000)

## Display solution
xgrid <- seq(0, pi/4, length.out = 101)
Xgrid <- expand.grid(xgrid, xgrid)
ref <- apply(Xgrid, 1, function(x){(-sin1(x[1]) * sin1(1 - x[2]))})
filled.contour(xgrid, xgrid, matrix(ref, 101), color.palette  = terrain.colors,
plot.axes = {axis(1); axis(2); points(Xgrid[which.min(ref),, drop = FALSE], pch = 21);
             points(Sol2$par[1], Sol2$par[2], pch = 13)})

## Not run: 
#------------------------------------------------------------
# Example 3 : Stochastic optimization with POO
#------------------------------------------------------------
set.seed(10)
noise.level <- 0.05

## Define and display objective
fun3 <- function(x){return(double_sine(x) + runif(1, min = -noise.level, max = noise.level))}
xgrid <- seq(0, 1, length.out = 1000)
plot(xgrid, sapply(xgrid, double_sine), type = 'l', ylab = "double_sine(x)", xlab = 'x')

## Maximization
Sol3 <- POO(fun3, horizon = 1000, noise.level = noise.level)

## Display result
abline(v = Sol3$par)

## End(Not run)