Roy Fox proposes utility-probability duality via Legendre transform

The article presents a theoretical proposal by Roy Fox, not an experimental result. It builds on reinforcement learning, where behavior is seen as expected utility maximization. Fox's idea is to define capability by the set of environment dynamics an agent can bring about, which is a shift from focusing on reward functions. This leads to a mathematical duality via the Legendre-Fenchel transform, linking probabilities and utilities. For AI alignment, this could offer a clearer way to specify and compare what agents are capable of achieving, potentially helping to ensure their behavior aligns with human values. However, the article is a TLDR, so details are limited, and it is a framework proposal, not a validated method. Its significance lies in providing a new perspective on agent capability, which is a central concern in alignment research.