Utilities as Legendre duals of probabilities

A new theoretical perspective on AI alignment suggests that an agent's capabilities can be understood through a mathematical duality between probabilities and utilities. As LessWrong reports, this approach uses the Legendre-Fenchel transform to derive utility functions from the set of environmental dynamics an agent is actually capable of producing. By focusing on achievable outcomes rather than predefined rewards, the framework aims to provide a more natural way to describe and delineate the power of different AI agents.

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