Optimization Through Digital Twins: Algorithms Under Model Uncertainty

Modern decision systems increasingly rely on digital twins and simulation models to guide optimization and control. In such settings algorithms do not interact directly with the real environment but compute decisions using a model that approximates reality. While digital twins are widely adopted in practice, the algorithmic consequences of model- mediated decision-making remain largely unexplored from a theoretical perspective. This paper introduces a framework for analyzing algorithms that operate under model uncertainty. Decisions are computed using a model environment, while performance is evaluated in the real environ- ment. To quantify the impact of model mismatch, the Model Uncertainty Ratio is defined as a worst-case measure comparing the performance of a model-mediated algorithm with the optimal decision obtainable when the real environment is known. The framework is instantiated on a scheduling problem. Upper and lower bounds are derived that relate distortions between the model and the real environment to the resulting degradation in decision quality. The analysis shows that even small discrepancies between the two environments may lead to multiplicative performance loss, revealing structural sensitivities that are not captured by classical optimization analyses. Overall, the framework provides an algorithmic perspective on optimization through digital representations of complex systems and suggests new directions for studying algorithms that operate under model uncertainty.