(60e) Self-Supervised Learning to Tune Low-Fidelity Optimization Models

Optimization models have long been a fundamental tool for decision-making in the planning, operation, and control of physical systems. In practice, such optimization models are solved repeatedly with minor changes to their parameters, with each instance determined by evolving external conditions such as market prices, forecasts, or disturbances. Due to their computational tractability, such optimization models are often approximated by low-fidelity surrogate models, which are derived using model-based domain knowledge. However, the accuracy of such surrogates tends to degrade under atypical operating conditions, potentially leading to economically inefficient and unsafe decisions.

Over recent years, machine learning has provided a way to provide proxies to such optimization models using historical or synthetically generated data [1], [2]. Such proxies map the changing parameters into approximate decisions. Although often expensive to train, these models offer unparalleled speed to provide near-optimal solutions, making them highly appealing in time-sensitive applications. One key limitation of data-driven proxies is the lack of explicit representation of the underlying models and constraints, which generally results in solutions that fail to satisfy feasibility requirements [3]. This limitation hinders the potential use of such proxies for decision-making in safe-critical systems.

Tuned low-fidelity optimization models have arisen as a promising alternative [4], [5]. Unlike purely data-driven models, which rely solely on historical observations, tuned low-fidelity optimization models blend historical information with known system dynamics and constraints to dictate decision-making. Such models are interpretable while providing more reliable solutions, especially in safety-critical or low-data regimes. Tuning such models is computationally expensive as it requires solving bilevel optimization models to determine the optimal tunable parameters for each representative operating condition [6].

This work proposes a novel self-supervised learning approach for tuning low-fidelity optimization models using differentiable optimization layers [7], [8], thereby bypassing the high computational cost associated with generating optimal tunable parameters in the supervised setting. The proposed framework integrates into a deep learning architecture: (i) a machine learning model to predict the optimal tunable parameters, (ii) the low-fidelity model represented as a differentiable optimization layer that maps each predicted tunable parameter and operating condition to an approximate solution, and (iii) the high-fidelity model, which serves an implicit loss function to evaluate the quality of the low-fidelity solution. The proposed approach is evaluated using the AC Optimal Power Flow (AC-OPF) problem as the high-fidelity model and the DC-OPF problem as its low-fidelity counterpart. Numerical experiments on several test systems of the Power Grid Library [9] demonstrate that the proposed approach significantly outperforms its supervised counterpart in terms of data efficiency, training time, and solution quality.

[1] J. Mandi et al., “Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities,” J. Artif. Intell. Res., vol. 80, pp. 1623–1701, Aug. 2024, doi: 10.1613/jair.1.15320.

[2] B. Wilder, B. Dilkina, and M. Tambe, “Melding the data-decisions pipeline: decision-focused learning for combinatorial optimization,” in Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence and Thirty-First Innovative Applications of Artificial Intelligence Conference and Ninth AAAI Symposium on Educational Advances in Artificial Intelligence, in AAAI’19/IAAI’19/EAAI’19, vol. 33. Honolulu, Hawaii, USA: AAAI Press, Jan. 2019, pp. 1658–1665. doi: 10.1609/aaai.v33i01.33011658.

[3] F. Fioretto, P. Van Hentenryck, T. W. K. Mak, C. Tran, F. Baldo, and M. Lombardi, “Lagrangian Duality for Constrained Deep Learning,” in Machine Learning and Knowledge Discovery in Databases. Applied Data Science and Demo Track, Springer, Cham, 2021, pp. 118–135. doi: 10.1007/978-3-030-67670-4_8.

[4] R. Gupta and Q. Zhang, “Data-driven decision-focused surrogate modeling,” AIChE J., vol. 70, no. 4, p. e18338, 2024, doi: 10.1002/aic.18338.

[5] S. Dixit, R. Gupta, and Q. Zhang, “Decision-Focused Surrogate Modeling for Mixed-Integer Linear Optimization,” Trans. Mach. Learn. Res., 2025.

[6] G. Constante Flores, A. Quisaguano, A. Conejo, and C. Li, “AC-Network-Informed DC Optimal Power Flow for Electricity Markets,” in 58th Hawaii International Conference on System Sciences (HICSS), Hawaii, USA, Jan. 2025.

[7] B. Amos and J. Z. Kolter, “OptNet: Differentiable Optimization as a Layer in Neural Networks,” in Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research, vol. 70. PMLR, 2017, pp. 136–145.

[8] A. Agrawal, B. Amos, S. Barratt, S. Boyd, S. Diamond, and Z. Kolter, “Differentiable Convex Optimization Layers,” in Advances in Neural Information Processing Systems, 2019.

[9] S. Babaeinejadsarookolaee et al., “The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms.” 2021. [Online]. Available: https://arxiv.org/abs/1908.02788