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.
翻译:现有人工设计的算法无法为这一环境实现令人满意的平均业绩,因为它们往往需要大量的时间步骤才能趋同和/或可能违反库存限制。 在本文件中,我们提议采用新的机器学习(ML)辅助拆滚方法,称为LAAU(学习-协助高压自动滚动),该方法将在线决定管道解开,并利用ML模型更新Lagrangian的在线乘数。为了通过反向调整进行高效培训,我们从决定管道的梯度中逐渐得出。我们还提供两个案例的平均成本界限,即培训数据可以离线并在线收集。最后,我们提出数字结果,以强调LAAU能够超越现有基线。