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Equation 6 · Part 11 · 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

Less than or equal to.

Its job in the formula

Less than or equal to.

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 inequality compares values without claiming they are equal. It describes a range, threshold, or bound that a quantity may satisfy.

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Sources cited in the article section

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