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Published equation contexts

ak∼πθ(a∣o≤k,g,hk)a_k \sim \pi_{\theta}(a\mid o_{\le k},g,h_k)

Why this formula appears here

At an agent step k , a model receives an observation history o≤ko_{\le k} , task goal g , and harness state hkh_k , then proposes an action: ak∼πθ(a∣o≤k,g,hk)a_k \sim \pi_{\theta}(a\mid o_{\le k},g,h_k). The action might request a file read, search, patch, shell command, test, browser interaction, or delegation. It is not yet an environmental transition. The harness parses the proposal, checks that it matches an available tool schema, applies policy, executes permitted operations, and converts results into the next observation.

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aka_k

Symbol a_k

aka_k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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πθ\pi_{\theta}

Symbol pi_θ

pi_θ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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aa

Symbol a

a is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

ak∼πθ(a∣o≤k,g,hk).a_k \sim \pi_{\theta}(a\mid o_{\le k},g,h_k).

Equation 14 · AI Agents & Systems

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

At an agent step k , a model receives an observation history o≤ko_{\le k} , task goal g , and harness state hkh_k , then proposes an action: ak∼πθ(a∣o≤k,g,hk)a_k \sim \pi_{\theta}(a\mid o_{\le k},g,h_k). The action might request a file read, search, patch, shell command, test, browser interaction, or delegation. It is not yet an environmental transition. The harness parses the proposal, checks that it matches an available tool schema, applies policy, executes permitted operations, and converts results into the next observation.

Meanings in this article

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