An Evidence-Theoretic Framework for Online Learning from Expert Advice

The use of belief function theory (BFT) in machine learning has gained attention as researchers seek more principled foundations for decision-making in uncertain environments. However, research has mostly focused on the setting of batch learning. In this article, in contrast and to our knowledge for the first time in the literature, we study the application of BFT to the setting of online (machine) learning. Within this context, online learning from expert advice (LEA) offers a framework where learners iteratively update their predictions based on experts' input and (adversarially labeled) observed outcomes. Despite extensive study and strong theoretical results, the epistemological underpinnings of LEA remain largely heuristic. This work addresses this gap by proposing belief function theory (BFT) as a formal foundation for LEA. Here we report a theoretical and algorithmic integration of BFT into LEA, showing that classical LEA algorithms such as Halving and Weighted Majority can be derived as special cases of evidential reasoning. We further introduce two novel LEA algorithms - Evidential Halving and Evidential Weighted Majority - which fully exploit BFT and support cautious prediction through abstention. These new algorithms demonstrate improved regret bounds over traditional methods, under mild assumptions. These findings open a new direction in online learning by leveraging the full expressive power of BFT to design theoretically grounded algorithms.