Differentiable Distributionally Robust Optimization Layers

• URL: http://arxiv.org/abs/2406.16571v1
• Date: Mon, 24 Jun 2024 12:09:19 GMT
• Title: Differentiable Distributionally Robust Optimization Layers
• Authors: Xutao Ma, Chao Ning, Wenli Du,
• Abstract summary: We develop differentiable DRO layers for generic mixed-integer DRO problems with parameterized second-order conic ambiguity sets. 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.
• Score: 10.667165962654996
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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