Abstract:We study decision problems under uncertainty, where the decision-maker has access to $K$ data sources that carry {\em biased} information about the underlying risk factors. The biases are measured by the mismatch between the risk factor distribution and the $K$ data-generating distributions with respect to an optimal transport (OT) distance. In this situation the decision-maker can exploit the information contained in the biased samples by solving a distributionally robust optimization (DRO) problem, where the ambiguity set is defined as the intersection of $K$ OT neighborhoods, each of which is centered at the empirical distribution on the samples generated by a biased data source. We show that if the decision-maker has a prior belief about the biases, then the out-of-sample performance of the DRO solution can improve with $K$ -- irrespective of the magnitude of the biases. We also show that, under standard convexity assumptions, the proposed DRO problem is computationally tractable if either $K$ or the dimension of the risk factors is kept constant.
From: Adrián Esteban-Perez [view email]
[v1]
Thu, 18 Jul 2024 15:24:54 UTC (827 KB)
[v2]
Tue, 17 Sep 2024 12:42:35 UTC (828 KB)
[v3]
Wed, 9 Sep 2026 19:32:53 UTC (561 KB)
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