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optimize.jl
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optimize.jl
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"""
```
mutable struct optimization_result{T}
minimizer::Vector{T}
minimum::T
converged::Bool
iterations::Int
```
Container type for various optimization outputs
"""
mutable struct optimization_result{T}
minimizer::Vector{T}
minimum::T
converged::Bool
iterations::Int
end
"""
```
optimize!(m::Union{AbstractDSGEModel,AbstractVARModel}, data::Matrix;
method::Symbol = :csminwel,
xtol::Real = 1e-32, # default from Optim.jl
ftol::Float64 = 1e-14, # Default from csminwel
grtol::Real = 1e-8, # default from Optim.jl
iterations::Int = 1000,
store_trace::Bool = false,
show_trace::Bool = false,
extended_trace::Bool = false,
mle::Bool = false, # default from estimate.jl
step_size::Float64 = .01,
toggle::Bool = true, # default from estimate.jl
verbose::Symbol = :none)
```
Wrapper function to send a model to csminwel (or another optimization routine).
"""
function optimize!(m::Union{AbstractDSGEModel,AbstractVARModel},
data::AbstractArray;
method::Symbol = :csminwel,
xtol::Real = 1e-32, # default from Optim.jl
ftol::Float64 = 1e-14, # Default from csminwel
grtol::Real = 1e-8, # default from Optim.jl
iterations::Int = 1000,
store_trace::Bool = false,
show_trace::Bool = false,
extended_trace::Bool = false,
mle::Bool = false, # default from estimate.jl
step_size::Float64 = .01,
toggle::Bool = true, # default from estimate.jl
verbose::Symbol = :none)
########################################################################################
### Step 1: Setup
########################################################################################
# For now, only csminwel should be used
optimizer = if method == :csminwel
csminwel
elseif method == :simulated_annealing
simulated_annealing
elseif method == :nelder_mead
nelder_mead
elseif method == :combined_optimizer
combined_optimizer
elseif method == :lbfgs
lbfgs
else
error("Method ", method, " is not supported.")
end
regime_switching = haskey(get_settings(m), :regime_switching) && get_setting(m, :regime_switching)
# Inputs to optimization
para_free_inds = ModelConstructors.get_free_para_inds(get_parameters(m);
regime_switching = regime_switching, toggle = toggle)
H0 = 1e-4 * eye(length(para_free_inds))
x_model = transform_to_real_line(get_parameters(m); regime_switching = regime_switching)
x_opt = x_model[para_free_inds]
########################################################################################
### Step 2: Initialize f_opt
########################################################################################
function f_opt(x_opt)
try
x_model[para_free_inds] = x_opt
transform_to_model_space!(m, x_model; regime_switching = regime_switching)
catch
return Inf
end
if mle
out = -likelihood(m, data; catch_errors = true)
else
out = -posterior(m, data; catch_errors = true)
end
out = !isnan(out) ? out : Inf
return out
end
########################################################################################
### Step 3: Optimizer-specific setup, call optimizer
########################################################################################
# variables used across several optimizers
rng = get_rng(m)
temperature = get_setting(m, :simulated_annealing_temperature)
max_cycles = get_setting(m, :combined_optimizer_max_cycles)
block_frac = get_setting(m, :simulated_annealing_block_proportion)
H_ = nothing
neighbor! = if isa(m, AbstractDSGEModel)
function _neighbor_dsge!(x, x_proposal)
# This function computes a proposal "next step" during simulated annealing.
# Inputs:
# - `x`: current position (of non-fixed states)
# - `x_proposal`: proposed next position (of non-fixed states).
# (passed in for pre-allocation purposes)
# Outputs:
# - `x_proposal`
T = eltype(x)
npara = length(x)
subset_inds = []
while length(subset_inds) == 0
subset_inds = randsubseq(para_free_inds,block_frac)
end
# Convert x_proposal to model space and expand to full parameter vector
x_all = T[ModelConstructors.get_values(get_parameters(m); regime_switching = regime_switching)] # to get fixed values
x_all[para_free_inds] = x # this is from real line
x_all_model = transform_to_model_space(get_parameters(m), x_all; regime_switching = regime_switching)
x_proposal_all = copy(x_all_model)
success = false
while !success
# take a step in model space
for i in subset_inds
# TODO: generalize to regime-switching. Key problem is that we need to construct a dictionary which maps
# the indices of `x_all` or at least `para_free_inds` to the location in get_parameters(m)
if regime_switching
p_i, reg_i = x_ind_2_pvec_ind[i] # returns index within get_parameters(m) and the regime
else
p_i = i
end
prior_var = moments(get_parameters(m)[i])[2] # moments(get(get_parameters(m)[i].prior))[2]
proposal_in_bounds = false
proposal = x_all_model[i]
if haskey(get_parameters(m)[i].regimes, :valuebounds)
lower = regime_valuebounds(get_parameters(m)[i], 1)[1]
upper = regime_valuebounds(get_parameters(m)[i], 1)[2]
else
lower = get_parameters(m)[i].valuebounds[1]
upper = get_parameters(m)[i].valuebounds[2]
end
# draw a new parameter value, and redraw if out of bounds
while !proposal_in_bounds # TODO: generalize to regime-switching
r = rand([-1 1]) * rand()
proposal = x_all_model[i] + (r * step_size * prior_var)
if lower < proposal < upper
proposal_in_bounds = true
end
end
@inbounds x_proposal_all[i] = proposal
end
# check that model can be solved
try
DSGE.update!(m, x_proposal_all)
compute_system(m; tvis = haskey(get_settings(m), :tvis_information_set))
x_proposal_all = transform_to_real_line(get_parameters(m), x_proposal_all;
regime_switching = regime_switching)
success = true
catch ex
if !(typeof(ex) in [DomainError, ParamBoundsError, GensysError])
rethrow(ex)
end
end
end
x_proposal[1:end] = x_proposal_all[para_free_inds]
return
end
elseif isa(m, AbstractDSGEVARModel)
function _neighbor_dsgevar!(x, x_proposal)
T = eltype(x)
npara = length(x)
subset_inds = []
while length(subset_inds) == 0
subset_inds = randsubseq(para_free_inds,block_frac)
end
# Convert x_proposal to model space and expand to full parameter vector
x_all = T[ModelConstructors.get_values(get_parameters(m); regime_switching = regime_switching)] # to get fixed values
x_all[para_free_inds] = x # this is from real line
x_all_m = transform_to_model_space(get_parameters(m), x_all;
regime_switching = regime_switching)
x_proposal_all = copy(x_all_m)
success = false
while !success
# take a step in model space
for i in subset_inds
prior_var = moments(get_parameters(m)[i])[2]#moments(get(m.parameters[i].prior))[2] # TODO: generalize to regime-switching
proposal_in_bounds = false
proposal = x_all_m[i]
lower = get_parameters(m)[i].valuebounds[1] # TODO: generalize to regime-switching
upper = get_parameters(m)[i].valuebounds[2]
# draw a new parameter value, and redraw if out of bounds
while !proposal_in_bounds # TODO: generalize to regime-switching
r = rand([-1 1]) * rand()
proposal = x_all_m[i] + (r * step_size * prior_var)
if lower < proposal < upper
proposal_in_bounds = true
end
end
@inbounds x_proposal_all[i] = proposal
end
# check that model can be solved
try
DSGE.update!(m, x_proposal_all)
compute_system(m; tvis = haskey(get_settings(m), :tvis_information_set))
x_proposal_all = transform_to_real_line(get_parameters(m), x_proposal_all;
regime_switching = regime_switching)
success = true
catch ex
if !(typeof(ex) in [DomainError, ParamBoundsError, GensysError])
rethrow(ex)
end
end
end
x_proposal[1:end] = x_proposal_all[para_free_inds]
return
end
else
error("The simulated annealing function for a model of type $(typeof(m)) has not been implemented yet")
end
temperature = get_setting(m, :simulated_annealing_temperature)
rng = get_rng(m)
if method == :simulated_annealing
if regime_switching
error("Simulated annealing with regime switching currently does not work.")
end
opt_result = optimizer(f_opt, x_opt;
iterations = iterations, step_size = step_size,
store_trace = store_trace, show_trace = show_trace,
extended_trace = extended_trace,
neighbor! = neighbor!, verbose = verbose, rng = rng,
temperature = temperature)
converged = opt_result.iteration_converged
out = optimization_result(opt_result.minimizer, opt_result.minimum, converged,
opt_result.iterations)
elseif method == :nelder_mead
opt_result = optimizer(f_opt, x_opt;
iterations = iterations,
store_trace = store_trace, show_trace = show_trace,
extended_trace = extended_trace, verbose = verbose, rng = rng)
converged = opt_result.iteration_converged
out = optimization_result(opt_result.minimizer, opt_result.minimum, converged,
opt_result.iterations)
elseif method == :csminwel
opt_result, H_ = optimizer(f_opt, x_opt, H0;
xtol = xtol, ftol = ftol, grtol = grtol,
iterations = iterations,
store_trace = store_trace, show_trace = show_trace,
extended_trace = extended_trace,
verbose = verbose, rng = rng)
converged = opt_result.g_converged || opt_result.f_converged #|| opt_result.x_converged
out = optimization_result(opt_result.minimizer, opt_result.minimum, converged,
opt_result.iterations)
elseif method == :lbfgs
opt_result = optimizer(f_opt, x_opt;
xtol = xtol, ftol = ftol, grtol = grtol, iterations = iterations,
store_trace = store_trace, show_trace = show_trace,
extended_trace = extended_trace,
verbose = verbose, rng = rng)
converged = opt_result.g_converged || opt_result.f_converged #|| opt_result.x_converged
out = optimization_result(opt_result.minimizer, opt_result.minimum, converged,
opt_result.iterations)
elseif method == :combined_optimizer
opt_result = optimizer(f_opt, x_opt;
xtol = xtol, ftol = ftol, grtol = grtol, iterations = iterations,
step_size = step_size, store_trace = store_trace,
show_trace = show_trace, extended_trace = extended_trace,
neighbor! = neighbor!, verbose = verbose, rng = rng,
temperature = temperature, max_cycles = max_cycles)
converged = opt_result.g_converged || opt_result.f_converged || opt_result.x_converged
converged = opt_result.method == "Simulated Annealing" ? opt_result.iteration_converged : converged
out = optimization_result(opt_result.minimizer, opt_result.minimum, converged,
opt_result.iterations)
end
########################################################################################
### Step 4: transform output, populate Hessian
########################################################################################
x_model[para_free_inds] = out.minimizer
transform_to_model_space!(m, x_model; regime_switching = regime_switching)
# Match original dimensions
out.minimizer = ModelConstructors.get_values(get_parameters(m); regime_switching = regime_switching)
npara = regime_switching ? n_parameters_regime_switching(m) : n_parameters(m)
H = zeros(npara, npara)
if H_ != nothing
# Fill in rows/cols of zeros corresponding to location of fixed parameters
# For each row corresponding to a free parameter, fill in columns corresponding to
# free parameters. Everything else is 0.
for (row_free, row_full) in enumerate(para_free_inds)
H[row_full, para_free_inds] = H_[row_free,:]
end
end
return out, H
end