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

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sts_t

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the environment e executes it against state. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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sts_t

Symbol s_t

the environment e executes it against state.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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What the article says around this equation

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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