Overview
Distributionally robust optimization (DRO) frameworks aim to safeguard decisions against uncertainties stemming from unknown data distributions. A core component of DRO is the ambiguity set, which characterizes the range of possible distributions. However, a misalignment between the geometry of this ambiguity set and observed predictive errors can necessitate larger radii for the set, potentially leading to overly conservative decision-making. This research introduces a novel method, diagnostic-transport DRO (DT-DRO), designed to dynamically adjust the ambiguity-set geometry based on observed predictive errors, utilizing held-out calibration data.
DT-DRO addresses systematic probability misallocation by employing the conditional probability integral transform cumulative distribution function (CDF). This diagnostic information is then translated into an outcome-level transport mechanism. This mechanism serves to jointly refine both the center of the ambiguity set and the ground cost function within the optimization problem. The resulting DT-DRO formulation is amenable to a computationally tractable dual reformulation.
Approach
The DT-DRO methodology integrates a diagnostic step with a transport mechanism to recalibrate the ambiguity set. The diagnostic component leverages the conditional probability integral transform CDF. This transform is utilized to identify instances of systematic misallocation of probabilities within predictive models. The information derived from this diagnosis then informs an outcome-level transport operation.
This outcome-level transport mechanism plays a dual role: it adjusts the central point of the ambiguity set and simultaneously modifies the ground cost. This joint adjustment is crucial for adapting the ambiguity set's geometry to better reflect the observed predictive errors from calibration data. The formulation developed allows for a dual reformulation, which enhances its computational tractability.
Findings
- DT-DRO can eliminate the nonvanishing robustness floor that can arise due to model misspecification.
- The approach yields valid ambiguity radii and provides decision-risk guarantees. These guarantees are observed to tighten as estimation and approximation errors are reduced.
- Empirical evaluations, conducted through synthetic experiments and applied to a power-outage scenario, indicated an improvement in decision quality. This improvement was particularly noted under conditions of structural and tail misspecification within the models.