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Equation 9 · Part 3 · The Hardest Unsolved Problems in AI Agent Architecture

Symbol eta

b′(s′)=η O(o∣s′,a)∑sT(s′∣s,a) b(s),b'(s') = \eta \, O(o \mid s', a) \sum_{s} T(s' \mid s, a)\, b(s),
η\eta

What this part means

the normalizing constant.

Its job in the formula

eta is an input to the expression that computes the quantity on the left.

Where the article explains it

with η\eta a normalizing constant.

The passage around this formula

…possible states before an observation, a is the action just taken, o is the observation that followed, T is the environment’s transition model and O its observation model, the updated belief is b′(s′)=η O(o∣s′,a)∑sT(s′∣s,a) b(s)b'(s') = \eta \, O(o \mid s', a) \sum_{s} T(s' \mid s, a)\, b(s). with η\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…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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