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Multi-task Online Learning for Probabilistic Load Forecasting

Onintze Zaballa, Verónica Álvarez, Santiago Mazuelas

TL;DR

This work tackles probabilistic load forecasting for multiple entities under nonstationary consumption by introducing an online learning multi-task framework built on vector-valued hidden Markov models (HMMs). It learns dynamic inter-entity relationships via calendar-conditioned mean/covariance parameters and produces probabilistic forecasts with mean $\widehat{\mathbf{s}}_{t+i}$ and uncertainty $\widehat{\mathbf{E}}_{t+i}$, updated recursively with forgetting factors. The approach extends single-task online probabilistic forecasting to the multi-task setting through matrices $\mathbf{M}_{s,c}$, $\boldsymbol{\Sigma}_{s,c}$, $\mathbf{M}_{r,c}$, and $\boldsymbol{\Sigma}_{r,c}$, allowing coordinated predictions across $K$ entities. Experiments on ISO New England, GEFCom2017, and SMART datasets show that the proposed method generally achieves lower RMSE and MAPE than offline multi-task methods (MTGP, KMT) and can adapt to evolving consumption patterns while providing calibrated probabilistic forecasts.

Abstract

Load forecasting is essential for the efficient, reliable, and cost-effective management of power systems. Load forecasting performance can be improved by learning the similarities among multiple entities (e.g., regions, buildings). Techniques based on multi-task learning obtain predictions by leveraging consumption patterns from the historical load demand of multiple entities and their relationships. However, existing techniques cannot effectively assess inherent uncertainties in load demand or account for dynamic changes in consumption patterns. This paper proposes a multi-task learning technique for online and probabilistic load forecasting. This technique provides accurate probabilistic predictions for the loads of multiple entities by leveraging their dynamic similarities. The method's performance is evaluated using datasets that register the load demand of multiple entities and contain diverse and dynamic consumption patterns. The experimental results show that the proposed method can significantly enhance the effectiveness of current multi-task learning approaches across a wide variety of load consumption scenarios.

Multi-task Online Learning for Probabilistic Load Forecasting

TL;DR

This work tackles probabilistic load forecasting for multiple entities under nonstationary consumption by introducing an online learning multi-task framework built on vector-valued hidden Markov models (HMMs). It learns dynamic inter-entity relationships via calendar-conditioned mean/covariance parameters and produces probabilistic forecasts with mean and uncertainty , updated recursively with forgetting factors. The approach extends single-task online probabilistic forecasting to the multi-task setting through matrices , , , and , allowing coordinated predictions across entities. Experiments on ISO New England, GEFCom2017, and SMART datasets show that the proposed method generally achieves lower RMSE and MAPE than offline multi-task methods (MTGP, KMT) and can adapt to evolving consumption patterns while providing calibrated probabilistic forecasts.

Abstract

Load forecasting is essential for the efficient, reliable, and cost-effective management of power systems. Load forecasting performance can be improved by learning the similarities among multiple entities (e.g., regions, buildings). Techniques based on multi-task learning obtain predictions by leveraging consumption patterns from the historical load demand of multiple entities and their relationships. However, existing techniques cannot effectively assess inherent uncertainties in load demand or account for dynamic changes in consumption patterns. This paper proposes a multi-task learning technique for online and probabilistic load forecasting. This technique provides accurate probabilistic predictions for the loads of multiple entities by leveraging their dynamic similarities. The method's performance is evaluated using datasets that register the load demand of multiple entities and contain diverse and dynamic consumption patterns. The experimental results show that the proposed method can significantly enhance the effectiveness of current multi-task learning approaches across a wide variety of load consumption scenarios.

Paper Structure

This paper contains 11 sections, 1 theorem, 10 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Load forecasting
  3. Problem formulation
  4. Preliminaries
  5. Multi-task probabilistic load forecasting based on online learning
  6. Learning
  7. Prediction
  8. Experiments
  9. Datasets and experimental setup
  10. Numerical results
  11. Conclusion

Key Result

Theorem 1

Let $\left\{\mathbf{s}_t, \mathbf{r}_t \right\}_{t\geq 1}$ be an HMM characterized by parameters $\Theta$ defined in eq:theta_parameters. Then, for $i=1,2,...,L$ where mean $\widehat{\mathbf{s}}_{t+i}$ and covariance matrix $\widehat{\mathbf{E}}_{t+i}$ can be recursively obtained by $\text{with }\mathbf{W}_1 = \mathbf{\Sigma}_{s,c} + \mathbf{M}_{s,c}\mathbf{N} \widehat{\mathbf{E}}_{t+i-1}(\mathbf

Figures (2)

  • Figure 1: Consumption patterns of different entities can be similar (entity 1 and entity 2). Single-task learning techniques can only leverage information from the corresponding entity, while multi-task learning techniques use information from multiple entities.
  • Figure 2: Load demand prediction and CDF in GEFCom2017 dataset.

Theorems & Definitions (1)

  • Theorem 1