arxivcs.LGcs.AI2026-07-20
Generalised Bellman recurrence and three dualities in sequential decision-making
Fernando E. Rosas, David Hyland, Daniel Polani
What gives the Bellman equation its form? We show that the recursive properties of optimal value functions follow from three conditions: that the dynamics decomposes through sufficient statistics, that the return decomposes recursively, and that the aggregation of uncertainty is…