This is paper is available on arxiv under CC 4.0 DEED license. Authors: (1) Leah Chrestien, Czech Technical University in Prague; (2) Tomá˘s Pevný, Czech Technical University in Prague, and Gen Digital, Inc.; (3) Stefan Edelkamp, Czech Technical University in Prague; (4) Antonín Komenda, Czech Technical University in Prague. Table of Links Abstract & Introduction Preliminaries Conditions on strictly optimally efficient heuristic Loss functions Related Work Experiments Conclusion and References Appendix 7 Conclusion The motivation of this paper stemmed from the observation that even the cost-to-goal, considered to be an optimal heuristic, fails to guarantee a strictly optimally efficient search. Since a large body of existing research optimizes this quantity, we are effectively lost with respect to what should be optimized. To fill this gap, we have stated the necessary and sufficient conditions guaranteeing the forward search to be strictly optimally efficient. These conditions show that the absolute value of the heuristic is not important, but that the ranking of states in the Open list is what controls the efficiency. Ranking can be optimized by minimizing the ranking loss functions, but its concrete implementation needs to correspond to a variant of the forward search. In case of mismatch, the resulting heuristic can perform poorly, which has been demonstrated when the heuristic optimized for BGFS search was used with A* search. The other benefit of ranking losses is that from the point of view of statistical learning theory, they solve a simpler problem than ubiquitous regression in estimating the cost-to-goal. We do not question the existence of a strictly optimally efficient heuristic. 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