Differentiable Distributionally Robust Optimization Layers
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910499772301312 |
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| author | Ma, Xutao Ning, Chao Du, Wenli |
| author_facet | Ma, Xutao Ning, Chao Du, Wenli |
| contents | In recent years, there has been a growing research interest in decision-focused learning, which embeds optimization problems as a layer in learning pipelines and demonstrates a superior performance than the prediction-focused approach. However, for distributionally robust optimization (DRO), a popular paradigm for decision-making under uncertainty, it is still unknown how to embed it as a layer, i.e., how to differentiate decisions with respect to an ambiguity set. In this paper, we develop such differentiable DRO layers for generic mixed-integer DRO problems with parameterized second-order conic ambiguity sets and discuss its extension to Wasserstein ambiguity sets. To differentiate the mixed-integer decisions, we propose a novel dual-view methodology by handling continuous and discrete parts of decisions via different principles. Specifically, we construct a differentiable energy-based surrogate to implement the dual-view methodology and use importance sampling to estimate its gradient. We further prove that such a surrogate enjoys the asymptotic convergency under regularization. As an application of the proposed differentiable DRO layers, we develop a novel decision-focused learning pipeline for contextual distributionally robust decision-making tasks and compare it with the prediction-focused approach in experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differentiable Distributionally Robust Optimization Layers Ma, Xutao Ning, Chao Du, Wenli Optimization and Control Artificial Intelligence Machine Learning Systems and Control In recent years, there has been a growing research interest in decision-focused learning, which embeds optimization problems as a layer in learning pipelines and demonstrates a superior performance than the prediction-focused approach. However, for distributionally robust optimization (DRO), a popular paradigm for decision-making under uncertainty, it is still unknown how to embed it as a layer, i.e., how to differentiate decisions with respect to an ambiguity set. In this paper, we develop such differentiable DRO layers for generic mixed-integer DRO problems with parameterized second-order conic ambiguity sets and discuss its extension to Wasserstein ambiguity sets. To differentiate the mixed-integer decisions, we propose a novel dual-view methodology by handling continuous and discrete parts of decisions via different principles. Specifically, we construct a differentiable energy-based surrogate to implement the dual-view methodology and use importance sampling to estimate its gradient. We further prove that such a surrogate enjoys the asymptotic convergency under regularization. As an application of the proposed differentiable DRO layers, we develop a novel decision-focused learning pipeline for contextual distributionally robust decision-making tasks and compare it with the prediction-focused approach in experiments. |
| title | Differentiable Distributionally Robust Optimization Layers |
| topic | Optimization and Control Artificial Intelligence Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2406.16571 |