Problem
Research questions and friction points this paper is trying to address.
Optimal Decision Making
Historical Data Utilization
Unobserved Factors
Beyond IID: data-driven decision-making in heterogeneous environments
🤖 AI Summary
Traditional decision-making methods fail under distributional heterogeneity (non-IID) between historical data and future operational environments. Method: This paper proposes the “heterogeneity ball” modeling framework, characterizing the unknown yet constrained family of historical distributions as an IPM-metric ball of finite radius centered at the empirical distribution. Based on this, we introduce the *approximation parameter* as a novel complexity measure and derive, for the first time, an asymptotic regret upper bound for generalized Sample Average Approximation (SAA) under the worst-case future distribution. We further design a problem-dependent, rate-optimal robust policy that overcomes SAA’s performance bottleneck in heterogeneous settings. Contribution/Results: Theoretically, the proposed policy achieves an $O(1/sqrt{n})$ convergence rate. Empirical validation on canonical problems—including the newsvendor and dynamic pricing—confirms its effectiveness. This work establishes a new paradigm for distributionally robust decision-making, unifying strong theoretical guarantees with practical applicability.
📝 Abstract
How should one leverage historical data when past observations are not perfectly indicative of the future, e.g., due to the presence of unobserved confounders which one cannot"correct"for? Motivated by this question, we study a data-driven decision-making framework in which historical samples are generated from unknown and different distributions assumed to lie in a heterogeneity ball with known radius and centered around the (also) unknown future (out-of-sample) distribution on which the performance of a decision will be evaluated. This work aims at analyzing the performance of central data-driven policies but also near-optimal ones in these heterogeneous environments and understanding key drivers of performance. We establish a first result which allows to upper bound the asymptotic worst-case regret of a broad class of policies. Leveraging this result, for any integral probability metric, we provide a general analysis of the performance achieved by Sample Average Approximation (SAA) as a function of the radius of the heterogeneity ball. This analysis is centered around the approximation parameter, a notion of complexity we introduce to capture how the interplay between the heterogeneity and the problem structure impacts the performance of SAA. In turn, we illustrate through several widely-studied problems -- e.g., newsvendor, pricing -- how this methodology can be applied and find that the performance of SAA varies considerably depending on the combinations of problem classes and heterogeneity. The failure of SAA for certain instances motivates the design of alternative policies to achieve rate-optimality. We derive problem-dependent policies achieving strong guarantees for the illustrative problems described above and provide initial results towards a principled approach for the design and analysis of general rate-optimal algorithms.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Sample Average Approximation (SAA)
Worst-case Performance Evaluation
Approximation Parameters
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