Utilities as Legendre duals of probabilities

TLDR: In recent work, Roy Fox proposes to understand an agent's capabilities in terms of the set of environment dynamics it can bring about.[1] This leads to an intriguing duality between probabilities and utilities via the Legendre-Fenchel transform.IntroductionSome agents are more powerful than others. Indeed, some can yield a wider range of outcomes, maybe because they are capable long-term planners or because they have built rich world models. Being able to clearly delineate the capabilities...