Differentiable Distributionally Robust Optimization Layers
<|reference_start|>Differentiable Distributionally Robust Optimization Layers: 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.<|reference_end|>
@article{ma2024differentiable,
    title={Differentiable Distributionally Robust Optimization Layers},
    author={Xutao Ma, Chao Ning, Wenli Du},
    journal={arXiv preprint arXiv:2406.16571},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.16571},
    primaryClass={math.OC cs.AI cs.LG cs.SY eess.SY}
}