Example. Whole-chain maximum and per-task oracle [ftip-00F8]
Example. Whole-chain maximum and per-task oracle [ftip-00F8]
Consider two equally weighted tasks and an archive containing two chains \(a,b\), with score vectors \((s_1(a),s_2(a))=(1,0)\) and \((s_1(b),s_2(b))=(0,1)\) under the same evaluation law. The archive envelope is
\[J(a)=J(b)=J_D^{\max }=\frac 12.\]Either chain attains this maximum. In contrast, a per-task oracle has value
\[\frac 12\sum _{i=1}^2\max _{c\in \{a,b\}}s_i(c)=1.\]The oracle selects \(a\) on the first task and \(b\) on the second. A configuration constrained to select one archived chain before observing task identity obtains mean \(1/2\) in this example. If task-dependent routing is permitted, the resulting combined policy must itself be declared and evaluated, including its routing and execution costs. The oracle value is not automatically the score of either archived chain.
Incompatible execution configurations create a separate obstacle: an archived maximizing chain may be ineligible for a named target configuration. That feasibility restriction does not alter the distinction between the two score functionals above.