Differentiable Calibration of Inexact Stochastic Simulation Models via Kernel Score Minimization

TL;DR

This paper introduces a differentiable calibration method for inexact stochastic simulation models using kernel score minimization, enabling uncertainty quantification solely from output data despite model intractability.

Contribution

It presents a novel approach combining kernel score minimization and stochastic gradient descent for calibrating inexact models with output data, including uncertainty quantification.

Findings

Effective calibration on G/G/1 queueing models

Quantifies uncertainty despite model inexactness

Works with only output-level data

Abstract

Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios, only output-level data are available to learn the input model parameters, which is challenging due to the often intractable likelihood of the stochastic simulation model. Moreover, stochastic simulation models are frequently inexact, with discrepancies between the model and the target system. No existing methods can effectively learn and quantify the uncertainties of input parameters using only output-level data. In this paper, we propose to learn differentiable input parameters of stochastic simulation models using output-level data via kernel score minimization with stochastic gradient descent. We quantify the uncertainties of the learned input parameters using a frequentist confidence set procedure based on a new asymptotic normality result that accounts for model inexactness. The proposed method is evaluated on exact and inexact G/G/1 queueing models.