Tuning Social Performance Index On Training-Data
摘要
To help a (perhaps artificial) decision-maker in comparing performance of its (perhaps artificial) social agents, a type of abstract evaluation-machine (structured on a Yaari-Quiggin functional-index) is presented. Designed on a certain sequence of increasingly severe goals \(O_{0},O_{1},...,O_{l}\ldots .,O_{L}\) , whenever applied to any agent A in a certain class \(\mathcal {D}\) , it would evaluate its performance, taking into account conditions \(x:=X\) , provided that value-gains parameters \(\omega _{l|x}:=Val_{|x}(O_{l})-Val_{|x}(O_{l-1})\) have been assigned, standardized on the behavior of a certain reference-agent \(A^{*}\) (chosen to represent a fair, wishable behavior, by the designer point of view). The specific question of interest herein (frameable into machine learning) concerns a structured, possibly automatizable, approach for extracting meaningful (normalized on assumed design-specifications) values \(\omega _{|x}^{*}\) , to be assigned to parameters \(\omega _{l|x}\) within a probabilistic setting, so that such values result properly tuned/calibrated on the training-data set \(\chi [A^{*}]\) associated to the reference-agent \(A^{*}\) . In a Dirichlet-multinomial setup, a “principle of orthogonality” (applied to a certain updating variation operator \(\boldsymbol{\Delta }_{\mathcal {X}[A^{*}]}T\) with respect to the sub-manifold associated to specifications of constraints on hyper-parameter space) is adopted to extract standardized values \(\omega _{|x}^{*}\) which result tuned on training-data set \(\chi [A^{*}]\) , structured on a 3-way table which relates conditions to performance responses.