Stochastic Quasi-Gradient Differential Evolution Optimization.

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)
#> [1] "initalizing population..."
#> [1] "1 / 12"
#> [1] "2 / 12"
#> [1] "3 / 12"
#> [1] "4 / 12"
#> [1] "5 / 12"
#> [1] "6 / 12"
#> [1] "7 / 12"
#> [1] "8 / 12"
#> [1] "9 / 12"
#> [1] "10 / 12"
#> [1] "11 / 12"
#> [1] "12 / 12"
#> [1] "population initialization complete  :)"
#> [1] "running SQG-DE..."
#> [1] "iter 100/200"
#> [1] "Convergence criterion met. Stopping optimization early"
#> [1] "run complete!"

#SQG DE solution
out$solution
#> [1] -0.9623938  1.1032798  0.1835086  1.0376028

#analytic solution
apply(dataExample, 2, mean)
#> [1] -0.9625315  1.1031771  0.1835243  1.0374537

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)
#> [1] "initalizing population..."
#> [1] "1 / 12"
#> [1] "2 / 12"
#> [1] "3 / 12"
#> [1] "4 / 12"
#> [1] "5 / 12"
#> [1] "6 / 12"
#> [1] "7 / 12"
#> [1] "8 / 12"
#> [1] "9 / 12"
#> [1] "10 / 12"
#> [1] "11 / 12"
#> [1] "12 / 12"
#> [1] "population initialization complete  :)"
#> [1] "initalizing FORK cluser with 4 cores"
#> [1] "running SQG-DE..."
#> [1] "iter 100/200"
#> [1] "Convergence criterion met. Stopping optimization early"
#> [1] "run complete!"


#SQG DE solution
out$solution
#> [1] -0.9623173  1.1034912  0.1838107  1.0369257

#analytic solution
apply(dataExample, 2, mean)
#> [1] -0.9625315  1.1031771  0.1835243  1.0374537