让神经网络自动学习有用且可靠的不确定性估计，提升决策稳定性。
End-to-End Conformal Calibration for Optimization Under Uncertainty
- 用输入凸神经网络构建可优化的不确定性集，端到端训练。
- 在储能套利和投资组合优化中，性能优于传统两阶段方法。
- 结合置信预测保证校准性，适合对可靠性要求高的决策场景。
机器学习可显著提升不确定性环境下决策的性能，但确保鲁棒性需精确的不确定性估计，而神经网络难以实现。高维情况下存在多种有效不确定性估计，其对下游决策的价值不同。本文提出一种端到端框架，通过下游决策损失指导学习条件鲁棒优化所需的不确定性集，利用置信预测提供鲁棒性和校准保证。同时，采用部分输入凸神经网络表示通用凸不确定性集，并作为框架的一部分进行学习。在储能套利与投资组合优化的实际应用中，该方法持续优于两阶段估计-再优化基线。
原文摘要 · Abstract (English)
Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to achieve with neural networks. Moreover, in high-dimensional settings, there may be many valid uncertainty estimates, each with its own performance profile - i.e., not all uncertainty is equally valuable for downstream decision-making. To address this problem, this paper develops an end-to-end framework to learn uncertainty sets for conditional robust optimization in a way that is informed by the downstream decision-making loss, with robustness and calibration guarantees provided by conformal prediction. In addition, we propose to represent general convex uncertainty sets with partially input-convex neural networks, which are learned as part of our framework. Our approach consistently improves upon two-stage estimate-then-optimize baselines on concrete applications in energy storage arbitrage and portfolio optimization.
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