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Multivariate time series forecasting with hierarchical structure is widelyused in real-world applications, e.g., sales predictions for the geographicalhierarchy formed by cities, states, and countries. The hierarchical time series(HTS) forecasting includes two sub-tasks, i.e., forecasting and reconciliation.In the previous works, hierarchical information is only integrated in thereconciliation step to maintain coherency, but not in forecasting step foraccuracy improvement. In this paper, we propose two novel tree-based featureintegration mechanisms, i.e., top-down convolution and bottom-up attention toleverage the information of the hierarchical structure to improve theforecasting performance. Moreover, unlike most previous reconciliation methodswhich either rely on strong assumptions or focus on coherent constraintsonly,we utilize deep neural optimization networks, which not only achievecoherency without any assumptions, but also allow more flexible and realisticconstraints to achieve task-based targets, e.g., lower under-estimation penaltyand meaningful decision-making loss to facilitate the subsequent downstreamtasks. Experiments on real-world datasets demonstrate that our tree-basedfeature integration mechanism achieves superior performances on hierarchicalforecasting tasks compared to the state-of-the-art methods, and our neuraloptimization networks can be applied to real-world tasks effectively withoutany additional effort under coherence and task-based constraints

SLOTH: Structured Learning and Task-based Optimization for Time Series Forecasting on Hierarchies