Wasserstein Distributionally Robust Optimization with Heterogeneous Data Sources
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914950429016064 |
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| author | Rychener, Yves Esteban-Perez, Adrian Morales, Juan M. Kuhn, Daniel |
| author_facet | Rychener, Yves Esteban-Perez, Adrian Morales, Juan M. Kuhn, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wasserstein Distributionally Robust Optimization with Heterogeneous Data Sources Rychener, Yves Esteban-Perez, Adrian Morales, Juan M. Kuhn, Daniel Optimization and Control Probability Statistics Theory 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. |
| title | Wasserstein Distributionally Robust Optimization with Heterogeneous Data Sources |
| topic | Optimization and Control Probability Statistics Theory |
| url | https://arxiv.org/abs/2407.13582 |