The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case

TL;DR

This paper analyzes how intrinsic noise affects the evaluation complexity of deterministic trust-region optimization methods, providing bounds, optimality estimates, and insights into the impact of inexact computations.

Contribution

It introduces evaluation complexity bounds for trust-region methods considering intrinsic noise, a novel analysis contrasting with fully controllable inexactness.

Findings

Intrinsic noise can dominate evaluation complexity bounds.

The analysis estimates the optimality level achievable under noise.

Inexact computer arithmetic impacts evaluation complexity.

Abstract

Intrinsic noise in objective function and derivatives evaluations may cause premature termination of optimization algorithms. Evaluation complexity bounds taking this situation into account are presented in the framework of a deterministic trust-region method. The results show that the presence of intrinsic noise may dominate these bounds, in contrast with what is known for methods in which the inexactness in function and derivatives' evaluations is fully controllable. Moreover, the new analysis provides estimates of the optimality level achievable, should noise cause early termination. It finally sheds some light on the impact of inexact computer arithmetic on evaluation complexity.