No Sigmoid Required: Exact Feasibility for Constrained $q$EHVI

Constrained multi-objective optimization is essential for engineering design, requiring sample-efficient batch evaluation strategies due to costly simulations. Although Bayesian optimization using $q$CEHVI is highly effective, estimating its probability of feasibility (PoF) relies on a sigmoid relaxation, which introduces bias and a tunable parameter. Na\"ive marginalization can eliminate the sigmoid, but we find that it can lead to overestimation of the acquisition function for $Q>1$ when running points are spatially concentrated. This paper theoretically analyzes this error's source and derives an unbiased, low-variance Rao-Blackwellized (RB) estimator that replaces the candidate feasibility indicator with its exact conditional expectation. Using a synthetic problem that reproduces a concentrated scenario, we first verify that the RB approach suppresses the overestimation in the infeasible region. Furthermore, our approach resolves the sigmoid-induced PoF overestimation, improving sample efficiency near the feasibility boundary. Experiments on real-world benchmark problems demonstrate that our method yields stable performance, eliminating the parameter sensitivity of the sigmoid relaxation.