Research map / Probabilistic and scientific modeling / Bayesian optimization
BOtied: Multi-objective Bayesian optimization with tied multivariate ranks
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes BOtied, a multi-objective Bayesian optimization acquisition function based on the joint multivariate CDF (estimated with vine copulas) plus a Pareto-compliant CDF indicator, invariant to monotonic objective transformations and scalable to many objectives.
Problem
Multi-objective Bayesian optimization needs acquisition functions that identify Pareto-optimal solutions while scaling to many objectives and being robust to rescaling or monotonic transformations of objectives; hypervolume-based methods scale poorly and are sensitive to transformations.
Approach
Connects non-dominated solutions to extreme levels of the joint CDF of objectives, defines a Pareto-compliant CDF indicator, and uses a vine-copula estimate of the CDF as the acquisition function (1 - CDF), giving scale and monotonic-transformation invariance and efficient high-dimensional computation.
Key results
- On DTLZ2 (d=7, M=6, q=1), BOtied v2 reaches HV 0.42 (0.02) versus 0.38 for NParEGO and 0.27 for NEHVI.
- On Penicillin (M=3, q=1), BOtied v2 achieves the lowest I_CDF of 0.20 (0.02) and BOtied v1 the highest HV of 325741 among methods in the main table, with BOtied v2 at 342762 the best HV.
- BOtied is reported to be as fast as NParEGO in wall-clock time, while NEHVI and JES become very slow for M>=3.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BOtied v2 instead of MES | MOBO on Penicillin (d=7, M=3, q=1) · Penicillin (d=7, M=3, q=1) | I_CDF: 0.24 (0.02) -> 0.20 (0.02) | Helped |
| Use BOtied v2 instead of JES | MOBO on Penicillin (d=7, M=3, q=1) · Penicillin (d=7, M=3, q=1) | HV: 316302 (21193) -> 342762 (13599) | Helped |
| Use BOtied v2 instead of NParEGO | MOBO on DTLZ2 (d=6, M=4, q=1) · DTLZ2 (d=6, M=4, q=1) | I_CDF: 0.10 (0.02) -> 0.11 (0.02) | Hurt |
| Use BOtied v2 instead of NParEGO | MOBO on DTLZ2 (d=6, M=4, q=1) · DTLZ2 (d=6, M=4, q=1) | HV: 2.20 (0.11) -> 2.32 (0.06) | Helped |
| Use BOtied v2 instead of MES | MOBO on DTLZ2 (d=7, M=6, q=1) · DTLZ2 (d=7, M=6, q=1) | I_CDF: 0.059 (0.004) -> 0.064 (0.004) | Hurt |
| Use BOtied v2 instead of NParEGO | MOBO on DTLZ2 (d=7, M=6, q=1) · DTLZ2 (d=7, M=6, q=1) | HV: 0.38 (0.02) -> 0.42 (0.02) | Helped |
| Fit the CDF on pooled posterior samples rather than posterior means (ablation) | BOtied on Penicillin (d=7, M=3, q=1) · Penicillin (d=7, M=3, q=1) | I_CDF: 0.20 (0.02) -> 0.26 (0.01) | Hurt |
| Fit the CDF on pooled posterior samples rather than posterior means (ablation) | BOtied on Penicillin (d=7, M=3, q=1) · Penicillin (d=7, M=3, q=1) | HV: 342762 (13599) -> 325741 (29515) | Hurt |
| Fit the CDF on pooled posterior samples rather than posterior means (ablation) | BOtied on DTLZ2 (d=6, M=4, q=1) · DTLZ2 (d=6, M=4, q=1) | I_CDF: 0.11 (0.02) -> 0.25 (0.01) | Hurt |
| Fit the CDF on pooled posterior samples rather than posterior means (ablation) | BOtied on DTLZ2 (d=6, M=4, q=1) · DTLZ2 (d=6, M=4, q=1) | HV: 2.32 (0.06) -> 2.26 (0.09) | Hurt |
| Fit the CDF on pooled posterior samples rather than posterior means (ablation) | BOtied on DTLZ2 (d=7, M=6, q=1) · DTLZ2 (d=7, M=6, q=1) | I_CDF: 0.064 (0.004) -> 0.071 (0.005) | Hurt |
| Fit the CDF on pooled posterior samples rather than posterior means (ablation) | BOtied on DTLZ2 (d=7, M=6, q=1) · DTLZ2 (d=7, M=6, q=1) | HV: 0.42 (0.02) -> 0.36 (0.03) | Hurt |
Surprising findings
- No single acquisition function wins on all datasets; NParEGO is a close competitor on several tasks, e.g. DTLZ2 (d=6, M=4) where NParEGO and MES tie for best I_CDF.
Limitations
- Increasing M requires more flexible copula models, adding modeling choices (selected via AIC).
- The current BOtied implementation is not differentiable, requiring gradient-free CMA-ES for acquisition optimization.
Experimental setup
Datasets: DTLZ2 Penicillin Caco2 DDMOP
Benchmarks: DTLZ2 Penicillin Caco2+ DDMOP Branin-Currin
Metrics: hypervolume CDF indicator wall-clock time
Baselines: NEHVI NParEGO predictive entropy search max-value entropy search joint entropy search random (Sobol) selection
Builds on: expected hypervolume improvement noisy expected hypervolume improvement ParEGO vine copulas
Closest papers by meaning
- Simple Extensions of Single-Objective Acquisition Functions and Hedge Strategies for Multi-Objective Bayesian Optimization (NeurIPS 2026 · similarity 0.90)
- MOBO-OSD: Batch Multi-Objective Bayesian Optimization via Orthogonal Search Directions (NeurIPS 2025 · similarity 0.90)
- Trading Off Quality and Uncertainty Through Multi-Objective Optimisation in Batch Bayesian Optimisation (AAAI 2025 · similarity 0.90)
- Pareto Front-Diverse Batch Multi-Objective Bayesian Optimization (AAAI 2024 · similarity 0.90)
- User Preference Meets Pareto-Optimality in Multi-Objective Bayesian Optimization (AAAI 2025 · similarity 0.89)
- Are You Concerned about Limited Function Evaluations: Data-Augmented Pareto Set Learning for Expensive Multi-Objective Optimization (AAAI 2024 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.