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Equation 6 · Part 8 · From Autocomplete to Delegation: The Technical History Behind OpenAI Codex

Symbol E

at∼πθ(a∣o≤t,ht,g),ot+1=E(st,at),a_t\sim\pi_\theta(a\mid o_{\le t},h_t,g), \qquad o_{t+1}=E(s_t,a_t),
EE

What this part means

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

Its job in the formula

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

The passage around this formula

An agent trajectory can be represented as at∼πθ(a∣o≤t,ht,g),ot+1=E(st,at)a_t\sim\pi_\theta(a\mid o_{\le t},h_t,g), \qquad o_{t+1}=E(s_t,a_t). where the model policy chooses an action, environment E executes it against state sts_t , and the result becomes the next observation. This closes a feedback loop absent from one-shot completion.

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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 article section

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