beliefstate

Belief state, in artificial intelligence and decision-making under uncertainty, refers to an agent's internal representation of the possible states of the world. It is a probability distribution over the true world states conditioned on all past actions and observations. The belief state serves as the agent's best available estimate when the environment is only partially observable.

In planning and control under partial observability, such as partially observable Markov decision processes (POMDPs), the belief state is the central object. Starting from a prior belief, actions update it via the action model, and observations refine it via the observation model. The resulting posterior belief summarizes what the agent considers possible after each interaction with the environment.

The belief state is a sufficient statistic for the history under the standard Markovian assumption: given the current belief, the future is conditionally independent of earlier history when actions and observations are known. This property enables online planning and learning without storing the entire sequence of past events.

Computationally, belief states can be represented explicitly as a discrete probability distribution, implicitly through particle filtering, or parametrically (for example, as a Gaussian in linear-Gaussian models). Exact updates are tractable for small problems; larger or continuous state spaces typically employ approximate methods.

Belief states are foundational in robotics, autonomous systems, and AI planning where full state information is unavailable. They provide a principled framework for making decisions under uncertainty and for fusing information from actions and observations.