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Published equation contexts

R=Eg∼DEτ∼P(τ∣g)[V(sT,g)]R=\mathbb{E}_{g\sim D}\mathbb{E}_{\tau\sim P(\tau\mid g)} \left[V(s_T,g)\right]

Why this formula appears here

where sts_t is environmental state, oto_t the agent’s observation, and ata_t its action. Task success is not a property of the final message. It is an externally evaluated predicate V(sTs_T,g) over final state and goal g . System reliability under task distribution D is R=Eg∼DEτ∼P(τ∣g)[V(sT,g)]R=\mathbb{E}_{g\sim D}\mathbb{E}_{\tau\sim P(\tau\mid g)} \left[V(s_T,g)\right]. Every term matters. Change the task distribution, model, harness, tools, retry budget, permissions, environment, or evaluator and the reliability estimate changes.

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gg

Symbol g

g appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

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τ\tau

Symbol τ

τ appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

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PP

Symbol P

P appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

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VV

Symbol V

V appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

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sTs_T

Symbol s_T

sTs_T appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

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Published contexts (1)

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R=Eg∼DEτ∼P(τ∣g)[V(sT,g)].R=\mathbb{E}_{g\sim D}\mathbb{E}_{\tau\sim P(\tau\mid g)} \left[V(s_T,g)\right].

Equation 8 · AI Agents & Systems

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

where sts_t is environmental state, oto_t the agent’s observation, and ata_t its action. Task success is not a property of the final message. It is an externally evaluated predicate V(sTs_T,g) over final state and goal g . System reliability under task distribution D is R=Eg∼DEτ∼P(τ∣g)[V(sT,g)]R=\mathbb{E}_{g\sim D}\mathbb{E}_{\tau\sim P(\tau\mid g)} \left[V(s_T,g)\right]. Every term matters. Change the task distribution, model, harness, tools, retry budget, permissions, environment, or evaluator and the reliability estimate changes.

Meanings in this article

  • RR: System reliability under task distribution D.
  • DD: the system reliability under task distribution.
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