Learning-Assisted Algorithm Unrolling for Online Optimization with Budget Constraints
This work addresses online optimization problems with strict inventory constraints, which is incremental as it builds on existing unrolling methods by incorporating ML assistance.
The paper tackles the challenge of online optimization with multiple budget constraints by proposing LAAU, a machine learning-assisted unrolling approach that updates Lagrangian multipliers online, resulting in improved performance over existing baselines as shown in numerical results.
Online optimization with multiple budget constraints is challenging since the online decisions over a short time horizon are coupled together by strict inventory constraints. The existing manually-designed algorithms cannot achieve satisfactory average performance for this setting because they often need a large number of time steps for convergence and/or may violate the inventory constraints. In this paper, we propose a new machine learning (ML) assisted unrolling approach, called LAAU (Learning-Assisted Algorithm Unrolling), which unrolls the online decision pipeline and leverages an ML model for updating the Lagrangian multiplier online. For efficient training via backpropagation, we derive gradients of the decision pipeline over time. We also provide the average cost bounds for two cases when training data is available offline and collected online, respectively. Finally, we present numerical results to highlight that LAAU can outperform the existing baselines.