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User Preference Meets Pareto-Optimality in Multi-Objective Bayesian Optimization
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Proposes PUB-MOBO, a preference-based multi-objective Bayesian optimization method that adds a GP-gradient-based local multi-gradient descent stage (with gradient-information acquisition) to utility-driven search, plus a preference-dominated utility function (PDUF).
Problem
Preference-based multi-objective Bayesian optimization yields solutions that may be dominated and are not near the Pareto-front; estimating the full Pareto-front is expensive and ignores user preferences.
Approach
Combine utility-driven global search (EUBO and qEIUU) with a local multi-gradient descent stage using GP-estimated gradients, where gradient uncertainty is reduced via the gradient information acquisition, and introduce PDUF, a sum of logistic-product functions that enforces dominance while encoding preferences.
Key results
- PUB-MOBO consistently outperforms EUBO+qEIUU and the PG ablations in utility regret and distance to the Pareto-front across all six benchmarks (median over 20 seeds, 100 evaluation budget).
- EUBO+qEIUU is the poorest-performing method on all synthetic benchmarks, and PG+OE beats PG in most experiments.
- PUB-MOBO-PG+OE performs poorly on the harder real-world problems, similar to EUBO and PUB-MOBO-PG.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add local gradient descent to EUBO+qEIUU | PUB-MOBO · DTLZ1, DTLZ2, DH1 | utility regret | Helped |
| add local gradient descent to EUBO+qEIUU | PUB-MOBO · DTLZ1, DTLZ2, DH1 | distance to Pareto-front | Helped |
| add local gradient descent with gradient-uncertainty reduction to EUBO+qEIUU | PUB-MOBO · Vehicle Safety, Conceptual Marine Design, Car Side Impact | utility regret | Helped |
| add local gradient descent with gradient-uncertainty reduction to EUBO+qEIUU | PUB-MOBO · Vehicle Safety, Conceptual Marine Design, Car Side Impact | distance to Pareto-front | Helped |
| use predicted gradients without outcome evaluations or gradient-information optimizations (ablation) | PUB-MOBO-PG · DTLZ1, DTLZ2, DH1 | utility regret | Hurt |
| use predicted gradients without outcome evaluations or gradient-information optimizations (ablation) | PUB-MOBO-PG · DTLZ1, DTLZ2, DH1 | distance to Pareto-front | Hurt |
| use predicted gradients without outcome evaluations or gradient-information optimizations (ablation) | PUB-MOBO-PG · Vehicle Safety, Conceptual Marine Design, Car Side Impact | utility regret | Hurt |
| use predicted gradients without outcome evaluations or gradient-information optimizations (ablation) | PUB-MOBO-PG · Vehicle Safety, Conceptual Marine Design, Car Side Impact | distance to Pareto-front | Hurt |
| add an outcome evaluation at every gradient-descent step (ablation) | PUB-MOBO-PG+OE · DTLZ1, DTLZ2, DH1 | utility regret | Helped |
| add an outcome evaluation at every gradient-descent step (ablation) | PUB-MOBO-PG+OE · DTLZ1, DTLZ2, DH1 | distance to Pareto-front | Helped |
| add an outcome evaluation at every gradient-descent step (ablation) | PUB-MOBO-PG+OE · Vehicle Safety, Conceptual Marine Design, Car Side Impact | utility regret | No clear effect |
| add an outcome evaluation at every gradient-descent step (ablation) | PUB-MOBO-PG+OE · Vehicle Safety, Conceptual Marine Design, Car Side Impact | distance to Pareto-front | No clear effect |
Surprising findings
- Predicted-gradient-only local search (PUB-MOBO-PG) performs poorly, largely due to inaccurate surrogate gradient estimates, and often terminates prematurely.
Limitations
- Gradients are estimated from GP surrogates, which can be inaccurate on complex real-world landscapes.
- Local search can terminate prematurely when updates leave the feasible set or gradient norm falls below threshold.
Experimental setup
Datasets: DTLZ1 DTLZ2 DH1 Vehicle Safety Conceptual Marine Design Car Side Impact
Benchmarks: DTLZ1 DTLZ2 DH1 Vehicle Safety Conceptual Marine Design Car Side Impact
Metrics: utility regret distance to Pareto-front
Baselines: EUBO+qEIUU PUB-MOBO-PG PUB-MOBO-PG+OE
Builds on: EUBO qEIUU MGDA Gradient Information acquisition
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