Approximate IPA: Trading Unbiasedness for Simplicity

TL;DR

This paper introduces Approximate IPA, a method that trades unbiasedness for simplicity in sensitivity estimation, enabling scalable optimization in discrete event systems with controlled bias.

Contribution

It proposes a new approximate sensitivity analysis approach that balances estimator complexity and accuracy, expanding the applicability of Perturbation Analysis in large systems.

Findings

Provides guidelines for developing biased approximate estimators

Demonstrates the approach on a queue buffer-cost example

Establishes bounds on the relative error of the approximation

Abstract

When Perturbation Analysis (PA) yields unbiased sensitivity estimators for expected-value performance functions in discrete event dynamic systems, it can be used for performance optimization of those functions. However, when PA is known to be unbiased, the complexity of its estimators often does not scale with the system's size. The purpose of this paper is to suggest an alternative approach to optimization which balances precision with computing efforts by trading off complicated, unbiased PA estimators for simple, biased approximate estimators. Furthermore, we provide guidelines for developing such estimators, that are largely based on the Stochastic Flow Modeling framework. We suggest that if the relative error (or bias) is not too large, then optimization algorithms such as stochastic approximation converge to a (local) minimum just like in the case where no approximation is used. We apply this approach to an example of balancing loss with buffer-cost in a finite-buffer queue, and prove a crucial upper bound on the relative error. This paper presents the initial study of the proposed approach, and we believe that if the idea gains traction then it may lead to a significant expansion of the scope of PA in optimization of discrete event systems.