(430f) Decision-Focused Learning of Constraint Parameters with Feasibility Guarantee

In traditional data-driven optimization, we often follow a two-step predict-then-optimize approach, i.e. we first predict the unknown model parameters from data with external features and then solve the optimization problem with those predicted inputs. Here, the learning step focuses on minimizing the parameter estimation error; however, this does not necessarily lead to the best decisions (evaluated with the true parameter values) in the optimization step. In contrast, decision-focused learning (Wilder et al., 2019), also known as smart predict-then-optimize (Elmachtoub and Grigas, 2022), integrates the two steps to explicitly account for the quality of the optimization solution in the learning of the model parameters (i.e. minimize the decision error).

Existing works on decision-focused learning, many of which are based on deep learning with differentiable optimization layers (Amos and Kolter, 2017), have shown that significantly improved solutions can be achieved compared to the traditional predict-then-optimize approach. However, virtually all of them consider the case where the unknown model parameters only affect the objective function, which simplifies the problem considerably since feasibility is not a concern. Yet in many applications, we also need to use data to predict parameters in the constraints; the treatment of this case is in theory possible but difficult using existing methods.

In this work, we address this problem by formulating the learning problem as a bilevel optimization problem with constraints that ensure the feasibility of the optimal solutions obtained with the estimated parameter model. To solve this problem, we leverage our recently proposed efficient penalty-based block coordinate descent algorithm (Gupta and Zhang, 2022). In a computational case study, we demonstrate the effectiveness of the proposed approach and highlight its benefits compared with the conventional predict-then-optimize approach.

References:

Amos, B. and Kolter, J.Z., 2017. Optnet: Differentiable optimization as a layer in neural networks. Proceedings of the International Conference on Machine Learning, pp. 136-145.

Elmachtoub, A.N. and Grigas, P., 2022. Smart “predict, then optimize”. Management Science, 68(1), pp. 9-26.

Gupta, R. and Zhang, Q., 2023. Efficient learning of decision-making models: A penalty block coordinate descent algorithm for data-driven inverse optimization. Computers and Chemical Engineering, 170, p.108123.

Wilder, B., Dilkina, B., and Tambe, M., 2019. Melding the data-decisions pipeline: Decision-focused learning for combinatorial optimization. Proceedings of the AAAI Conference on Artificial Intelligence, pp. 1658-1665.