Predictive entropy search for multi-objective Bayesian optimization with constraints

⚠️ Curated Limitations & Negative Results

• Existence and measurability of the feasible Pareto target require assumptions beyond boundedness of the input domain. Distinguish no observed feasible incumbent, no feasible grid point in an approximate search, and a posterior function draw whose feasible region is empty. The paper’s recommendation relaxation on PDFp.33 is not a specified posterior-empty-draw acquisition policy. Per-constraint probability thresholds also do not imply the same simultaneous feasibility probability.
• The 2019 institutional author manuscript is dated May3,2019 and has a visible gap from printedp.8 to printedp.10; the separate official supplement is dated May13,2019. The six-page September2016 arXivv2 is an earlier version. No claim of reading the inaccessible final publisher layout or the missing page is made; relevant accessible methods and the earlier independent-prior assumptions are cited explicitly.
• Main Eq8 on PDFp.15 includes self comparisons with Theta(0)=1, making the literal product zero for any nonempty feasible supplied set; removing self comparisons still requires tie handling and does not make nondominated-membership factors enforce equality to the complete Pareto set. Eq10 has the minimization comparison orientation stated in the main text. The prose saying that every supplied Pareto point dominates each other point is too strong: being better in one objective does not imply dominance.
• Main PDFp.17 Eq13 and supplement PDFp.9 Eq15 place constraint factors at the sampled Pareto location although their exact comparison factors depend on competitor feasibility. Main Eq7 lacks a half coefficient on the constraint log-variance terms; Eq15 lacks a common half coefficient; Eqs17–18 bind task indices instead of the Pareto-sample index in the expectation. These displays are not certified literal executable formulas.
• The supplement contains further algebraic and notation defects, including the feasibility log-normalizer curvature in PDFp.12 Eq22, the observation-first difference orientation in PDFp.15 Eq30, exponential grouping in PDFpp.16–17 Eqs40/43, singular difference-Hessian inverses in PDFp.18 Eqs45–48, and covariance/precision mixing in PDFp.22 Eq61. The same section first describes a precision diagonal as a variance and then gives an inverse diagonal on p.23. Its damping prose on p.24 ends with non-positive definiteness as the stopping state. The record preserves the supported EP mechanism without claiming a complete repaired implementation or guaranteed convergence.
• Selective inspection of a separately pinned May2020 author implementation provides context, not an official erratum: it uses competitor constraint values, a minimization sign, zeroed self sites, half-log entropy differences and inverse precision construction. It also caps retained observations, changes candidate covariance, damps one candidate pass, and clips sampled task scores before averaging. The empty-sample and numerical safeguards are version-specific. No author code was executed, and no equivalence to every paper equation is asserted.
• Finite features, approximate search, finite Pareto representatives, EP factorization, limited candidate updates and hyperparameter averaging introduce approximation. The original bounded checks in research/discovery/pesmoc-boundaries.py establish selected finite and Gaussian counterexamples only; they are not a PESMOC implementation, empirical validation, efficiency claim or universal convergence proof.