Black-box Optimizers vs Taste Shocks

TL;DR

This paper compares different optimization methods for solving dynamic programming models with discrete and continuous choices, highlighting the effectiveness of Powell's routine with B-splines.

Contribution

It evaluates and extends solution methods for complex dynamic models, demonstrating the limitations of taste shocks and identifying the most effective algorithms.

Findings

Powell's routine with B-splines is the most viable method.

BOBYQA performs well among derivative-free algorithms.

Taste shocks fail to converge in multidimensional problems.

Abstract

We evaluate and extend the solution methods for models with binary and multiple continuous choice variables in dynamic programming, particularly in cases where a discrete state space solution method is not viable. Therefore, we approximate the solution using taste shocks or black-box optimizers that applied mathematicians use to benchmark their algorithms. We apply these methods to a default framework in which agents have to solve a portfolio problem with long-term debt. We show that the choice of solution method matters, as taste shocks fail to attain convergence in multidimensional problems. We compare the relative advantages of using four optimization algorithms: the Nelder-Mead downhill simplex algorithm, Powell's direction-set algorithm with LINMIN, the conjugate gradient method BOBYQA, and the quasi-Newton Davidon-Fletcher-Powell (DFPMIN) algorithm. All of these methods, except for the last one, are preferred when derivatives cannot be easily computed. Ultimately, we find that Powell's routine evaluated with B-splines, while slow, is the most viable option. BOBYQA came in second place, while the other two methods performed poorly.