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).
Department of Computer Science, Aalto University, Espoo, Finland · ELLIS Institute Finland · Department of Computer Science, University of Manchester, Manchester, United Kingdom
Aerospace Engineering Pennsylvania State University University Park, PA 16802 · Institute of Computational and Data Sciences (ICDS) Pennsylvania State University University Park, PA 16802
LIAC, ISIC, EPFL, Lausanne, Switzerland · Department of Chemistry, University of Zurich, Zurich, Switzerland · Centre of Competence in Research (NCCR) Catalysis, Zurich, Switzerland