Preference-Shaped Expected Hypervolume and R2 Improvement: Exact Computation and Monotonicity

ArXi:2605.28746v1 Announce Type: cross This paper studies preference-shaped expected improvement criteria for Bayesian multiobjective optimization. We consider two indicator families which are often used for similar algorithmic purposes, but which are geometrically different. The hypervolume indicator is based on a dystopian reference point and measures dominated volume in objective space. The R2 indicator is based on a utopian point and evaluates approximation sets through weighted Tchebycheff scalarization envelopes.