Learning-Assisted Algorithm Unrolling for Online Optimization with Budget Constraints

TL;DR

This paper introduces LAAU, a machine learning-assisted unrolling method for online optimization with budget constraints, improving decision-making efficiency and constraint satisfaction over traditional algorithms.

Contribution

The paper proposes a novel ML-assisted unrolling approach that updates Lagrangian multipliers online, with theoretical cost bounds and demonstrated superior performance.

Findings

LAAU outperforms existing baseline algorithms in numerical tests.

The method effectively updates Lagrangian multipliers online.

Provides theoretical bounds for average costs in different training data scenarios.

Abstract

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.