Temperature Forecasting with Markov Expert Aggregations

A multitude of Numerical Weather Prediction (NWP) models, along with their associated Model Output Statistics (MOS), are readily available. Expert Aggregation (EA) algorithms combine them in an online and adaptive manner. While EA competes optimally against the best-fixed combination of experts (Wintenberger 2017), it falls short in handling rapid changes. We introduce the class of Markov-EA algorithms, extending the seminal work of Mourtada and Maillard (2017) on Exponentiated Weights to other EA algorithms such as BOA and ML-Poly. Understanding how and when to adjust the weights is crucial for obtaining optimal second-order regret bounds. Assuming a (non-homogeneous) Markovian dynamic, we enhance the EA predictions of short and poorly predicted events, such as the cold event in the Chamonix valley, using weight sharing and strategies involving sleeping experts. This work is done in collaboration with Leo Pfitzner and Olivier Mestre (Météo France).