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arXiv · 2605.26796

Incentive-Based Load Curtailment with Limited Information: A Bilevel Zeroth-Order Learning Approach

Zhisen Jiang·Florian Dörfler·Saverio Bolognani
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Abstract

Incentive-based load curtailment unlocks critical demand-side flexibility but is hindered by the limited knowledge of private user parameters and the inherent nonsmoothness of responses due to physical device constraints. We address this via a constrained bilevel optimization framework and propose the Bi-ZOL (Bilevel Zeroth-Order Learning) algorithm. Unlike conventional black-box methods, Bi-ZOL exploits the bilevel structure to decompose the hypergradient, integrating the exact analytical information of the SO's objective with a zeroth-order estimate of the unknown response sensitivity. This structural decomposition-based learning method mathematically smoothes the nonsmooth response landscape and reduces hypergradient estimation error. We provide theoretical convergence guarantees to an approximate stationary point and demonstrate through simulations that Bi-ZOL achieves near-optimal performance.

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Zhisen Jiang, Florian Dörfler, Saverio Bolognani. 2026-05-26. Incentive-Based Load Curtailment with Limited Information: A Bilevel Zeroth-Order Learning Approach. https://arxiv.org/abs/2605.26796

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