Locally Weighted Regression with Approximate Derivatives for Data-based optimization

Interpolation and approximation of data provided in terms of a Look-Up Table (LUT) is a common and well-known task, and is especially relevant for industrial applications. When using the function for point-wise evaluation, the method choice only affects the accuracy of the function value itself. However, when the LUT is used as part of an optimization problem formulation, a bad method choice can prevent convergence or alter significantly the outcome of the solver. Moreover, computational efficiency becomes critical due to the much higher number of evaluations required. This work focuses on a variation of Locally Weighted Regression, with approximate derivatives computation. The result is a method that allows one to obtain the function value together with the first n derivatives, at a reduced computational cost. Theoretical properties of the approach are analyzed, and the results of a minimization problem using the proposed method are compared with more traditional ones. The new approach shows promising performance and results, both for computational efficiency and effectiveness when used in optimization.