This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming problem or various SDE models. More precisely, we develop a systematic construction of highly accurate confidence intervals by using a moderate deviation principle-based approach. It is shown that the proposed confidence intervals are statistically optimal in the sense that they satisfy criteria regarding exponential accuracy, minimality, consistency, mischaracterization probability, and eventual uniformly most accurate (UMA) property. The confidence intervals suggested by this approach are expressed as solutions to robust optimization problems, where the uncertainty is expressed via the underlying moderate deviation rate function induced by the data-generating process. We demonstrate that for many models these optimization problems admit tractable reformulations as finite convex programs even when they are infinite-dimensional.

Recently, it has been widely accepted by the research community that interactions between humans and cyber-physical infrastructures have played a significant role in determining the performance of the latter. The existing paradigm for designing cyber-physical systems for optimal performance focuses on developing models based on historical data. The impacts of context factors driving human system interaction are challenging and are difficult to capture and replicate in existing design models. As a result, many existing models do not or only partially address those context factors of a new design owing to the lack of capabilities to capture the context factors. This limitation in many existing models often causes performance gaps between predicted and measured results. We envision a new design environment, a cyber-physical human system (CPHS) where decision-making processes for physical infrastructures under design are intelligently connected to distributed resources over cyberinfrastructure such as experiments on design features and empirical evidence from operations of existing instances. The framework combines existing design models with context-aware design-specific data involving human-infrastructure interactions in new designs, using a machine learning approach to create augmented design models with improved predictive powers.