Learning-Assisted Algorithm Unrolling for Online Optimization with Inventory Constraints

Jianyi Yang

Abstract: Online optimization with multiple budget constraints is chal- lenging since the online decisions over a short time hori- zon are coupled together by strict inventory constraints. The existing manually-designed algorithms cannot achieve sat- isfactory 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 Un- rolling), which unrolls the agent’s online decision pipeline and leverages an ML model for updating the Lagrangian mul- tiplier 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. Fi- nally, we present numerical results to highlight that LAAU can outperform the existing baselines.