Learning to Simulate: Generative Metamodeling via Quantile Regression
L. Jeff Hong Yanxi Hou Qingkai Zhang Xiaowei Zhang
Stochastic simulation models, while effective in capturing the dynamics of
complex systems, are often too slow to run for real-time decision-making.
Metamodeling techniques are widely used to learn the relationship between a
summary statistic of the outputs (e.g., the mean or quantile) and the inputs of
the simulator, so that it can be used in real time. However, this methodology
requires the knowledge of an appropriate summary statistic in advance, making
it inflexible for many practical situations. In this paper, we propose a new
metamodeling concept, called generative metamodeling, which aims to construct a
"fast simulator of the simulator". This technique can generate random outputs
substantially faster than the original simulation model, while retaining an
approximately equal conditional distribution given the same inputs. Once
constructed, a generative metamodel can instantaneously generate a large amount
of random outputs as soon as the inputs are specified, thereby facilitating the
immediate computation of any summary statistic for real-time decision-making.
Furthermore, we propose a new algorithm -- quantile-regression-based generative
metamodeling (QRGMM) -- and study its convergence and rate of convergence.
Extensive numerical experiments are conducted to investigate the empirical
performance of QRGMM, compare it with other state-of-the-art generative
algorithms, and demonstrate its usefulness in practical real-time
decision-making.