une ▁situation ▁that ▁great ▁reward ▁is ▁possible ▁even ▁in ▁the ▁presence ▁of ▁little ▁ambient ▁uncertainty . ▁O pport un eness ▁is ▁defined ▁as ▁a ▁best - case ▁scenario ▁up ▁to ▁the ▁horizon ▁of ▁uncertainty : ▁how ▁small ▁can ▁the ▁horizon ▁of ▁uncertainty ▁be ▁and ▁still , ▁in ▁the ▁best ▁case , ▁achieve ▁the ▁wind fall ▁reward ? ▁ ▁The ▁imm unity ▁functions ▁ ▁and ▁ ▁are ▁complement ary ▁and ▁are ▁defined ▁in ▁an ▁anti - sym metric ▁sense . ▁Thus ▁" b igger ▁is ▁better " ▁for ▁ ▁while ▁" big ▁is ▁bad " ▁for ▁. ▁The ▁imm unity ▁functions ▁— ▁robust ness ▁and ▁opportun eness ▁— ▁are ▁the ▁basic ▁decision ▁functions ▁in ▁info - g ap ▁decision ▁theory . ▁ ▁Opt im ization ▁ ▁The ▁robust ness ▁function ▁involves ▁a ▁maxim ization , ▁but ▁not ▁of ▁the ▁performance ▁or ▁outcome ▁of ▁the ▁decision : ▁in ▁general ▁the ▁outcome ▁could ▁be ▁arbitr arily ▁bad . ▁R ather , ▁it ▁maxim izes ▁the ▁level ▁of ▁uncertainty ▁that ▁would ▁be ▁required ▁for ▁the ▁outcome ▁to ▁fail . ▁ ▁The ▁greatest ▁toler able ▁uncertainty ▁is ▁found ▁at ▁which ▁decision ▁ ▁satisf ices ▁the ▁performance ▁at ▁a ▁critical ▁surv ival - level . ▁One ▁may ▁establish ▁one ' s ▁prefer ences ▁among ▁the ▁available ▁actions ▁ ▁according ▁to ▁their ▁robust ness es ▁, ▁where by ▁larger ▁robust ness ▁eng enders ▁higher ▁preference . ▁In ▁this ▁way ▁the ▁robust ness ▁function ▁under lies ▁a ▁satisf icing ▁decision ▁algorithm ▁which ▁maxim izes ▁the ▁imm unity ▁to ▁per n icious