What does this equation mean?

with $\eta$ a normalizing constant. Kaelbling, Littman and Cassandra’s original treatment of this update is also where the difficulty is made explicit: they show that the amount of memory an optimal policy needs is not bounded in advance by the size of the problem, and that reducing the reliability of a single observation channel in their own worked example forces a much larger plan graph, and a correspondingly larger memory requirement, just to stay confident [ 4 ] . Applied to a long-running LLM agent, s is everything true about the task — every file changed, every external call made, every fact established — and b is whatever the agent’s context window currently represents. The update above is exact only if the full state and its full history are kept; an agent cannot keep them, because the context window is finite and every token inside it costs money and attention.