  Machine-learning assisted jet substructure tagging techniques have the
potential to significantly improve searches for new particles and Standard
Model measurements in hadronic final states. Techniques with simple analytic
forms are particularly useful for establishing robustness and gaining physical
insight. We introduce a procedure to automate the construction of a large class
of observables that are chosen to completely specify $M$-body phase space. The
procedure is validated on the task of distinguishing $H\rightarrow b\bar{b}$
from $g\rightarrow b\bar{b}$, where $M=3$ and previous brute-force approaches
to construct an optimal product observable for the $M$-body phase space have
established the baseline performance. We then use the new method to design
tailored observables for the boosted $Z'$ search, where $M=4$ and brute-force
methods are intractable. The new classifiers outperform standard $2$-prong
tagging observables, illustrating the power of the new optimization method for
improving searches and measurement at the LHC and beyond.
