Equation 9 · Part 4 · The Hardest Unsolved Problems in AI Agent Architecture

Symbol O

b'(s') = \eta \, O(o \mid s', a) \sum_{s} T(s' \mid s, a)\, b(s),

O

What this part means

the observation model.

Its job in the formula

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

Full expressionSymbol OArticle meaning

Where the article explains it

In the classical formalism, if b(s) is the agent’s probability distribution over 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 $b'(s') = \eta \, O(o \mid s', a) \sum_{s} T(s' \mid s, a)\, b(s)$ .

The passage around this formula

…over the true state of its task, updated as new observations arrive. In the classical formalism, if b(s) is the agent’s probability distribution over 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 $b'(s') = \eta \, O(o \mid s', a) \sum_{s} T(s' \mid s, a)\, b(s)$ . with $\eta$ a normalizing constant. Kaelbling, Littman and Cassandra’s original treatment of this update is also where the difficulty is made explicit:…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

[4] Planning and Acting in Partially Observable Stochastic Domains ↗

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