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Published equation contexts

U=∑i[pivi−Ci−Hi−(1−pi) qiLi]U=\sum_i\left[p_i v_i-C_i-H_i-(1-p_i)\,q_i L_i\right]

Why this formula appears here

Let viv_i be the value of correctly completing task i , CiC_i direct inference and infrastructure cost, HiH_i human specification and review cost, and LiL_i loss from an accepted failure. Expected net value is U=∑i[pivi−Ci−Hi−(1−pi) qiLi]U=\sum_i\left[p_i v_i-C_i-H_i-(1-p_i)\,q_i L_i\right]. where qiq_i is the probability a failure escapes detection and is accepted. A high resolve rate can have negative utility if it requires extreme review or creates rare, expensive escapes. A lower autonomous rate can be valuable if the system reliably identifies useful partial progress and makes review cheap.

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ii

Symbol i

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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viv_i

Symbol v_i

the value of correctly completing task i , CiC_i direct inference and infrastructure cost, HiH_i human specification and review cost, and LiL_i loss from an accepted failure.

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ii

Starting index or lower bound: i

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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Published contexts (1)

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U=∑i[pivi−Ci−Hi−(1−pi) qiLi],U=\sum_i\left[p_i v_i-C_i-H_i-(1-p_i)\,q_i L_i\right],

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

Let viv_i be the value of correctly completing task i , CiC_i direct inference and infrastructure cost, HiH_i human specification and review cost, and LiL_i loss from an accepted failure. Expected net value is U=∑i[pivi−Ci−Hi−(1−pi) qiLi]U=\sum_i\left[p_i v_i-C_i-H_i-(1-p_i)\,q_i L_i\right]. where qiq_i is the probability a failure escapes detection and is accepted. A high resolve rate can have negative utility if it requires extreme review or creates rare, expensive escapes. A lower autonomous rate can be valuable if the system reliably identifies useful partial progress and makes review cheap.

Meanings in this article

  • UU: Expected net value.
  • viv_i: the value of correctly completing task i , CiC_i direct inference and infrastructure cost, HiH_i human specification and review cost, and LiL_i loss from an accepted failure.
  • qiq_i: the probability a failure escapes detection and is accepted.
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