In this paper, we formulate the new multi-objective coverage (MOC) problem where our goal is to identify a small set of representative samples whose predicted outcomes broadly cover the feasible multi-objective space. This problem is of great importance in many critical real-world applications, e.g., drug discovery and materials design, as this representative set can be evaluated much faster than the whole feasible set, thus significantly accelerating the scientific discovery process. Existing works cannot be directly applied as they either focus on sample space coverage or multi-objective optimization that targets the Pareto front. However, chemically diverse samples often yield identical objective profiles, and safety constraints are usually defined on the objectives. To solve this MOC problem, we propose a novel search algorithm, MOC-CAS, which employs an upper confidence bound-based acquisition function to select optimistic samples guided by Gaussian process posterior predictions. For enabling efficient optimization, we develop a smoothed relaxation of the hard feasibility test and derive an approximate optimizer. Compared to the competitive baselines, we show that our MOC-CAS empirically achieves superior performances across large-scale protein-target datasets for SARS-CoV-2 and cancer, each assessed on five objectives derived from SMILES-based features.
Figures & tables
Figure 1. An example of the MOC problem where f1,f2 are two objective functions and τ1,τ2 are two thresholds defining the feasible region shown in light green. 15 samples are selected as representative feasible samples, each with a coverage ball whose radius is r . Illustration of a multi-objective coverage problem in two-dimensional objective space. Two threshold lines define a feasible region. Fifteen feasible samples are plotted inside the feasible region, and each sample is surrounded by a circular coverage neighborhood with radius r to show how the selected samples collectively cover the feasible region.
Figure 2. Quantitative comparison on the SARS-CoV-2 3CLPro target dataset. Quantitative comparison on the SARS-CoV-2 3CLPro target dataset using three metrics over iterations. The figure contains multiple line plots with a legend for different methods. Panels report fill distance, cumulative number of feasible discoveries, and the area under the positives curve. Lower fill distance and higher discovery and area-under-curve indicate better performance.
Figure 3. Quantitative comparison on the Cancer RTCB (top row) and Cancer 6T2W (bottom row) target datasets. Two-row grid of quantitative comparisons on cancer target datasets. The top row corresponds to the RTCB target and the bottom row corresponds to the 6T2W target. For each target, multiple methods are compared with line plots over iterations using fill distance, cumulative number of feasible discoveries, and the area under the positives curve.
Figure 4. Ablation of coverage resolution r on the SARS-CoV-2 3CLpro dataset. Ablation study of the coverage resolution parameter r on the SARS-CoV-2 3CLpro dataset. The figure compares several r settings using line plots over iterations for three metrics: fill distance, cumulative number of feasible discoveries, and the area under the positives curve.
Figure 5. Ablation of optimism schedule βt on the SARS-CoV-2 3CLpro dataset. Ablation study of the optimism schedule on the SARS-CoV-2 3CLpro dataset. Multiple optimism schedules are compared with line plots over iterations for fill distance, cumulative number of feasible discoveries, and the area under the positives curve.
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6. Quantitative comparison on the Cancer WRN target dataset. Quantitative comparison on the cancer WRN target dataset. The figure contains multiple line plots over iterations comparing methods with three metrics: fill distance, cumulative number of feasible discoveries, and the area under the positives curve.
Method
T@50 (mean ± std over 4 trials)
RANDOM
171.2±14.6
ONE-STEP
100.0±26.7
STRADDLE
>220 (not converge)
MOO+CLUSTER
152.5±42.4
MOC-CAS (ours)
75.0±5.4
Appendix
Table 1. T@50 on Cancer 6T2W dataset (smaller is better).
Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose STAGE-BO, Sequential Targeting Adaptive Gap-Filling ε-Constraint Bayesian Optimization: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in ε-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.
Yaohong Yang, Sammie Katt, Samuel Kaski
Department of Computer Science, Aalto University, Espoo, Finland · ELLIS Institute Finland · Department of Computer Science, University of Manchester, Manchester, United Kingdom
Multiobjective Bayesian optimization (MOBO) with Gaussian process (GP) surrogates is a sample efficient approach to solving multiobjective optimization problems. In MOBO, a Bayesian decision theoretic acquisition function guides the adaptive selection of new candidate inputs, on which objectives and constraints are evaluated to update the surrogate model sequentially. Existing approaches maintain independent GP models for the objectives and constraints, with new observations evaluating all objectives and constraints in a coupled fashion. However, the objectives and constraints often contain inherent correlations which, if exploited, can enable decoupled evaluations where only a subset of them are evaluated at each round. We present a new approach that leverages a multitask GP model to jointly learn all objectives and constraints, and propose a total correlation metric that enables identifying an optimal subset of objectives and constraints to be evaluated at every round, even under uniform evaluation costs. Theoretically, we show that our acquisition policy is asymptotically consistent despite decoupling and that our proposed decoupled subset selection rule maximizes the expected posterior entropy reduction about unevaluated tasks under mild conditions. Empirically, we show that our approach outperforms coupled and decoupled baselines in the state of the art.
Ashwin Renganathan, Peter Bachman
Aerospace Engineering Pennsylvania State University University Park, PA 16802 · Institute of Computational and Data Sciences (ICDS) Pennsylvania State University University Park, PA 16802
Molecular optimization in drug discovery, materials design, and catalysis requires searching vast chemical spaces under tight evaluation budgets, since high-fidelity oracles and experimental measurements are costly. The practical impact of an optimization method therefore hinges on its sample efficiency: how few evaluations it needs to find strong candidates. We introduce Sample Efficient Generative Optimization (SEGO), a framework for Bayesian optimization on adaptively generated molecules. In SEGO, a probabilistic surrogate model forms a hypothesis about where hits lie in chemical space, a generative model is steered to propose candidates in that region, the most promising candidate is selected via an acquisition function, and the resulting oracle call is used both to sharpen the surrogate and to anchor the generator in real reward. SEGO attains state-of-the-art performance on the practical molecular optimization (PMO) benchmark using only one tenth of the oracle calls consumed by other methods, and on a multiparameter docking task it reaches ten hits in roughly half the oracle calls of existing approaches. These gains move molecular optimization closer to campaigns driven by direct experimental feedback.
Sarina Kopf, Cristina Nevado, Philippe Schwaller
LIAC, ISIC, EPFL, Lausanne, Switzerland · Department of Chemistry, University of Zurich, Zurich, Switzerland · Centre of Competence in Research (NCCR) Catalysis, Zurich, Switzerland