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Amortized Active Generation of Pareto Sets
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Proposes A-GPS, an amortized active generative framework that learns a preference-conditioned generative model of the Pareto set using a non-dominance class probability estimator and preference direction vectors for online discrete multi-objective black-box optimization.
Problem
Online discrete black-box multi-objective optimization where the goal is to approximate the Pareto set and allow a-posteriori user preference conditioning without retraining.
Approach
Extends variational search (active generation) to Pareto sets: a Pareto non-dominance CPE (shown to estimate probability of hypervolume improvement) guides a generative model, which is amortized over unit-norm preference direction vectors and an alignment CPE, trained with off-policy importance-weighted gradients.
Key results
- On Branin-Currin, A-GPS rapidly outpaces qNParEGO but is dominated by qNEHVI/qEHVI; on DTLZ7 it still outperforms qNParEGO where EHVI methods do not scale.
- On bi-grams, A-GPS-TFM and VSD perform best, followed by LaMBO-2, while CbAS overfits early.
- On Ehrlich vs naturalness, A-GPS performs similarly to VSD, CbAS is overly exploitative, and LaMBO-2 underperforms.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use off-policy importance-weighted gradients instead of on-policy gradients (ablation) | A-GPS · Ehrlich vs. Naturalness (M=32) | hypervolume performance | No clear effect |
| Use off-policy importance-weighted gradients instead of on-policy gradients (ablation) | A-GPS · Ehrlich vs. Naturalness (M=32) | runtime: almost an order of magnitude less | Helped |
| Use causal transformer backbone instead of masked-transformer backbone (ablation) | A-GPS · Bi-grams | relative hypervolume improvement | Helped |
| Use causal transformer backbone instead of masked-transformer backbone (ablation) | A-GPS · Bi-grams | runtime: 30.99 vs 40.32 | Helped |
| Use the causal transformer backbone (ablation) | A-GPS · Bi-grams | sequence diversity | Mixed |
| Use LaMBO-2 instead of A-GPS | Discrete sequence optimization · Ehrlich vs. Naturalness | relative hypervolume improvement | Hurt |
| Use A-GPS instead of LaMBO-2 | Discrete sequence optimization · Stability vs. SASA | relative hypervolume improvement | Helped |
| Use A-GPS instead of qNParEGO | Synthetic continuous optimization · Branin-Currin | relative hypervolume | Helped |
| Use A-GPS instead of EHVI-based methods | Synthetic continuous optimization · Branin-Currin | relative hypervolume | Hurt |
Surprising findings
- Pareto-set CPE trained on non-dominance labels is shown to implicitly estimate probability of hypervolume improvement.
- On continuous synthetic functions, A-GPS is outperformed by GP-based direct acquisition methods on Branin-Currin and ZDT3.
Limitations
- Sensitive to choice of prior model, which requires careful dropout and early-stopping procedure.
- MLP generative backbone for continuous functions does not scale well to higher dimensions.
- Theory assumes noise-free observations; noisy extension is left for future work.
Experimental setup
Datasets: Branin-Currin DTLZ7 ZDT3 DTLZ2 GMM Ehrlich function (poli) ProtBert naturalness bi-grams task (poli) FoldX stability/SASA (poli)
Benchmarks: Branin-Currin DTLZ7 ZDT3 DTLZ2 GMM Ehrlich vs naturalness bi-grams stability vs SASA
Metrics: relative hypervolume indicator sequence diversity (edit distance) runtime
Baselines: qNEHVI qEHVI qParEGO CbAS VSD LaMBO-2 Random (greedy)
Builds on: Variational Search Distributions (VSD) CbAS LaMBO-2 Pareto set learning FiLM
Closest papers by meaning
- Preference-Guided Diffusion for Multi-Objective Offline Optimization (NeurIPS 2025 · similarity 0.87)
- User Preference Meets Pareto-Optimality in Multi-Objective Bayesian Optimization (AAAI 2025 · similarity 0.87)
- Multi-Objective Bayesian Optimization with Active Preference Learning (AAAI 2024 · similarity 0.87)
- Preference-Aware Constrained Multi-Objective Bayesian Optimization (Student Abstract) (AAAI 2024 · similarity 0.86)
- ParetoFlow: Guided Flows in Multi-Objective Optimization (ICLR 2025 · similarity 0.86)
- Preference Optimization on Pareto Sets: On a Theory of Multi-Objective Optimization (NeurIPS 2025 · similarity 0.85)
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