Adaptive Multi-task Learning for Probabilistic Load Forecasting

TL;DR

The paper tackles adaptive probabilistic load forecasting for multiple entities by proposing Multi-APLF, an online learning approach based on vector-valued Hidden Markov Models that captures inter-entity dependencies and nonstationary consumption patterns. It introduces calendar-conditioned parameter updates with forgetting factors, enabling recursive learning and probabilistic forecasts with quantified uncertainty. Experimental results across diverse datasets show that Multi-APLF improves forecasting accuracy and uncertainty calibration compared to single-task and multi-task baselines, while maintaining favorable computational complexity for real-time deployment. The work advances practical large-scale, online multi-entity load forecasting with strong theoretical and empirical support.

Abstract

Simultaneous load forecasting across multiple entities (e.g., regions, buildings) is crucial for the efficient, reliable, and cost-effective operation of power systems. Accurate load forecasting is a challenging problem due to the inherent uncertainties in load demand, dynamic changes in consumption patterns, and correlations among entities. Multi-task learning has emerged as a powerful machine learning approach that enables the simultaneous learning across multiple related problems. However, its application to load forecasting remains underexplored and is limited to offline learning-based methods, which cannot capture changes in consumption patterns. This paper presents an adaptive multi-task learning method for probabilistic load forecasting. The proposed method can dynamically adapt to changes in consumption patterns and correlations among entities. In addition, the techniques presented provide reliable probabilistic predictions for loads of multiples entities and assess load uncertainties. Specifically, the method is based on vectorvalued hidden Markov models and uses a recursive process to update the model parameters and provide predictions with the most recent parameters. The performance of the proposed method is evaluated using datasets that contain the load demand of multiple entities and exhibit diverse and dynamic consumption patterns. The experimental results show that the presented techniques outperform existing methods both in terms of forecasting performance and uncertainty assessment.

Figures (8)

• Figure 1: The proposed multi-task method leverages information from multiple entities to learn the consumption patterns over time. In particular, a vector-valued HMM enables to capture the relationship between multiple consecutive loads, $p(\mathbf{s}_t|\mathbf{s}_{t-1})$, and between multiple loads and observations, $p(\mathbf{r}_t|\mathbf{s}_t)$.
• Figure 2: Heat maps corresponding to hourly and daily loads of four entities in Australia. The consumptions in New South Wales and Tasmania exhibit similar patterns, the consumptions in Queensland show moderate differences from New South Wales, and the consumptions in South Australia are substantially different. The figure also shows how such similarities can change often over time.
• Figure 3: Multi-APLF method obtains load forecasts together with reliable uncertainty assessments of load demand.
• Figure 4: Diagram of the proposed Multi-APLF methods.
• Figure 5: Multi-APLF method outperforms existing techniques and achieves more accurate predictions.

Theorems & Definitions (7)

• Theorem 1
• proof
• Theorem 2
• proof
• Lemma 3
• proof
• proof : Proof of Theorem \ref{['theorem']}