Sequential Regularized Ensemble Forecasting by Online Policy Learning

Aggregating point forecasts from multiple experts often improves accuracy relative to relying on a single expert, but sequential ensemble forecasting becomes difficult for time series data when expert performances change over time. In this paper, we formulate sequential ensemble forecasting as an online policy learning problem and incorporate the recently proposed offline Regularized Ensemble Forecasting (REF) framework. At each forecasting period, the policy objective selects the optimal ensemble weight by balancing the variation of current forecasts, shrinkage toward historical performances, and stabilization toward preceding optimal weights. In the case of a large expert pool, we impose a sparse parameterization that permits exact zero weights and facilitates expert selection over time. Under suitable conditions, we develop an online regret bound that vanishes as the total number of periods goes to infinity. Numerical studies, including applications to the M5 competition and the Survey of Professional Forecasters (SPF), show that the proposed online REF policy performs favorably against standard ensemble benchmarks and offline REF.