CMP.4:4.5 - Preserve the meaning of bounds during computation

A mathematical bound must retain its direction in the arithmetic that computes it. For a maximizing search, an upper bound rounded downward without justification may exclude a better answer. Conservative rounding, interval bounds or a justified rational calculation can preserve the exclusion. A score predicted by a model is an estimate unless a suitable bound property has been established.

Use stronger arithmetic or independent checking where an erroneous exclusion could alter a consequential result. Ordinary exploratory search can instead keep a borderline branch or report a qualified result. C.11.DUA selects that extra work by its possible effect on the receiving decision.

Keep a bound for the unprocessed work, including a state whose expansion is interrupted. For maximization with an incumbent L, the whole optimum is at most max(L, max U(s)) over the states still pending. The incumbent supplies a lower bound. If a pending state lacks an upper bound, a finite global upper bound is not yet supplied by this account.