In bmgaldo/graDiEnt: Stochastic Quasi-Gradient Differential Evolution Optimization

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devtools::load_all(quiet=TRUE)

graDiEnt

This package makes accessible the the Stochastic Quasi-Gradient Differential Evolution Optimization algorithm first published by Sala, Baldanzini, and Pierini (2018). This optimization algorithm fuses the robustness of the population-based global optimization algorithm "Differential Evolution" with the efficiency of gradient-based optimization. The derivative-free algorithm uses population members to build stochastic gradient estimates, without any additional objective function evaluations. Sala, Baldanzini, and Pierini argue this algorithm is useful for 'difficult optimization problems under a tight function evaluation budget.' This package can run SQG-DE in parallel and sequentially.

Installation

# install.packages("devtools")
devtools::install_github("bmgaldo/graDiEnt")

Example (serial)

This is a basic application of the package to a toy optimization problem.

library(graDiEnt)
set.seed(123)
##############
# Maximum Likelihood Example
##############

# simulate from model
dataExample=matrix(rnorm(100,c(-1,1,0,1),c(1,1,1,1)),ncol=4,byrow = TRUE)

# list parameter names
param_names_example=c("mu_1","mu_2","mu_3","mu_4")

# negative log likelihood
ExampleObjFun=function(x,data,param_names){
  out=0

  names(x) <- param_names

  # log likelihoods
  out=out+sum(dnorm(data[,1],x["mu_1"],sd=1,log=TRUE))
  out=out+sum(dnorm(data[,2],x["mu_2"],sd=1,log=TRUE))
  out=out+sum(dnorm(data[,3],x["mu_3"],sd=1,log=TRUE))
  out=out+sum(dnorm(data[,4],x["mu_4"],sd=1,log=TRUE))

  return(out*-1)
}

########################
# run optimization
out <- optim_SQGDE(ObjFun = ExampleObjFun,
                   control_params = GetAlgoParams(n_params=length(param_names_example),
                                                  n_iter = 200,
                                                  n_particles = 12,
                                                  n_diff = 2,
                                                  return_trace = TRUE),
                   data = dataExample,
                   param_names = param_names_example)

#SQG DE solution
out$solution

#analytic solution
apply(dataExample, 2, mean)

Example (parallel)

library(graDiEnt)
set.seed(123)
##############
# Maximum Likelihood Example
##############

# simulate from model
dataExample=matrix(rnorm(100,c(-1,1,0,1),c(1,1,1,1)),ncol=4,byrow = TRUE)

# list parameter names
param_names_example=c("mu_1","mu_2","mu_3","mu_4")

# negative log likelihood
ExampleObjFun=function(x,data,param_names){
  out=0

  names(x) <- param_names

  # log likelihoods
  out=out+sum(dnorm(data[,1],x["mu_1"],sd=1,log=TRUE))
  out=out+sum(dnorm(data[,2],x["mu_2"],sd=1,log=TRUE))
  out=out+sum(dnorm(data[,3],x["mu_3"],sd=1,log=TRUE))
  out=out+sum(dnorm(data[,4],x["mu_4"],sd=1,log=TRUE))

  return(out*-1)
}

########################
# run optimization
out <- optim_SQGDE(ObjFun = ExampleObjFun,
                   control_params = GetAlgoParams(n_params=length(param_names_example),
                                                  n_iter = 200,
                                                  n_particles = 12,
                                                  n_diff = 2,
                                                  return_trace = TRUE,
                                                  n_cores_use = 4,
                                                  parallel_type = 'FORK'),
                   data = dataExample,
                   param_names = param_names_example)


#SQG DE solution
out$solution

#analytic solution
apply(dataExample, 2, mean)