This paper considers contextual stochastic optimization with endogenous uncertainty, where random outcomes depend on both contextual information and decisions. We analyze the statistical properties of solutions from two prominent approaches: predict-then-optimize (PTO), which first predicts a model between outcomes, contexts, and decisions, and then optimizes the downstream objective; and estimate- then-optimize (ETO), which directly estimates the conditional expectation of the objective and optimizes it. Unlike many existing studies that assume independent and identically distributed observations and/or decision/context-independent noise, we consider a setting where historical observations form a general time series, allowing for arbitrary dependencies between current outcomes and past realizations, contexts, and decisions. For both approaches, we establish non-asymptotic performance guarantees using two criteria, approximation error and regret, deriving slow and fast convergence rates.
Article
View Statistical Inference of Contextual Stochastic Optimization with Endogenous Uncertainty