← All parts of this equation

Equation 6 · Part 10 · From Autocomplete to Delegation: The Technical History Behind OpenAI Codex

=

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),
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.