An Evolutionary Approach to Passive Learning in Optimal Control Problems.

Area of Science:

• Econometrics
• Control Theory
• Computational Economics

Background:

• Traditional optimal control methods for nonlinear econometric models with parameter uncertainty often rely on linearization and linear-quadratic optimization.
• These traditional methods are sensitive to initial conditions and can produce outlier results, potentially distorting the optimization outcome.
• Linearization risks altering the original nonlinear problem, leading to solutions for a modified, potentially inaccurate, model.

Purpose of the Study:

• To extend the approach of addressing parameter uncertainty using Monte Carlo simulations and heuristic optimization to include passive learning (open-loop feedback) in nonlinear econometric models.
• To develop a more robust method for optimal control that avoids the pitfalls of traditional linear-quadratic approaches.
• To demonstrate the benefits of heuristic optimization, specifically Differential Evolution, in handling parameter uncertainty and learning within complex economic models.

Main Methods:

• Utilized a large Monte Carlo experiment to simulate various parameter realizations, explicitly addressing parameter uncertainty.
• Applied the Differential Evolution algorithm for optimization, a heuristic method capable of handling nonlinear problems directly.
• Extended the established methodology for parameter uncertainty to incorporate passive learning strategies within the optimal control framework.

Main Results:

• The proposed approach yields more robust results compared to traditional methods when dealing with parameter uncertainty and passive learning.
• The heuristic optimization method demonstrates greater benefit derived from the learning process.
• The method successfully optimizes the nonlinear problem without requiring prior linearization, preserving the integrity of the original model.

Conclusions:

• Heuristic optimization methods, such as Differential Evolution, offer a powerful and robust alternative for solving optimal control problems in nonlinear econometric models with parameter uncertainty and passive learning.
• This approach provides significant benefits from learning and avoids the need to modify the original nonlinear problem structure.
• The findings open new research directions for applying heuristic optimization to learning strategies in optimal control within economics and related fields.