Pass information between optimization iteration

Specific Domains Optimization (Mathematical)
1

Hi everyone,

I am trying to optimize a likelihood function. However, for each guess of the parameter value, I need to solve a value function iteration (VFI) problem to compute the likelihood. To speed up the process, I would like to use the value function of the previous iteration of the optimizer as an initial value for the value function of the current iteration of the optimizer. This would significantly improve the efficiency of my code when parameter guesses are close to each others.

I am not aware of any way to do this. Here is a simple version of the current implementation of my code where the initial guess of the value function is always the same:

# Value function iteration 
function VFI(param, W_old = nothing)
    if W_old = nothing
        W_old = XYZ ;
    end
    for i = 1:itermax
        # Call bellman operator to get a new value function
        W_new = T(W_old,param)
        if abs(W_new-W_old) <= gtol
            return W_new
        end
        W_old = W_new
    end
end
# Likelihood function 
function loglik(param)
    W_new = VFI(param)
    return -log(F(W_new,param)) # F is some function
end
# Optimizer 
outmax = optimize(loglik(x), x0) ;

Thank you!

2

You can create a custom type to store the old solution

# Likelihood function 
mutable struct LogLik
    W
end

function (l::LogLik)(param)
    W_new = VFI(param, l.W)
    l.W = W_new
    return -log(F(W_new,param)) # F is some function
end

# Optimizer 
loglik = LogLik(nothing)
outmax = optimize(loglik(x), x0) ;
1 Like
3

Ah yes, that works ! Thanks a lot.