Statistical Inference of Contextual Stochastic Optimization with Endogenous Uncertainty

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.

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