What is belief state and how is it updated?

Belief state — this is a representation of the current knowledge or assumptions of a system about the state of the surrounding world, especially in tasks with uncertainty, such as in dialogue systems or robotics.

The belief state is updated based on new observations and actions of the system, using probabilistic inference methods. The Bayesian formula is typically used to adjust the probabilities of various hypotheses about the state.

Example: in a dialogue agent, the belief state may contain probabilities of the user's intentions. When a new user input is received, the system updates these probabilities, refining its understanding of the query.

Thus, the belief state helps the system make decisions, taking into account uncertainty and changing information.