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Constrained Offline Black-Box Optimization via Risk Evaluation and Management
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Proposes COOREM, which uses a dual-energy model to separately estimate OOD risk and constraint risk and adaptively scales gradient-ascent step sizes with these risks to find stable, feasible, high-scoring designs in constrained offline optimization.
Problem
Constrained offline black-box optimization: finding high-scoring, feasible designs that surpass the offline dataset while avoiding out-of-distribution (OOD) overestimation and constraint violations, using only a pre-collected dataset.
Approach
A three-head DNN gives a surrogate (trained with a constraint-suppression term on infeasible designs) plus two energy-based risk heads (OOD and constraint) trained by contrastive divergence; during gradient ascent, a composite risk suppression factor adaptively sets step size and direction so the optimizer can retreat from OOD-risky regions and escape infeasible ones.
Key results
- On the welded beam task COOREM reaches a best score of -2.93 with OI 0.82 and SI 1.05, versus -8.83 for DE-PF(S) and PRIME failing with 1406.50 OI.
- COOREM achieves best-design quality of -264.72 on Three-bar and -2.09 on Process synthesis, close to the offline best (-265.89 and -2.22 offline reference values in Table 2 context).
- Previous COO methods (DE-PF, PRIME) fail to find feasible designs on Cassini 1, where COOREM finds a feasible design with best value -12.92 and OI 1.01.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use COOREM instead of prior constrained offline optimization methods | constrained offline optimization · Cassini 1 and Cassini 1-MINLP | feasible high-quality design performance | Helped |
| remove adaptive risk management and use normal gradient ascent (ablation) | COOREM · Welded beam design | performance | Hurt |
| remove constraint suppression from the surrogate model (ablation) | COOREM · Welded beam design | performance | Hurt |
| replace adaptive constraint control with static constraint control (ablation) | COOREM · Welded beam design | performance | Hurt |
| use a learning rate based on the product of OOD and constrained risk factors (ablation) | COOREM · Welded beam design | performance | Mixed |
| manage only OOD risk instead of both OOD and constrained risk (ablation) | COOREM · Welded beam design | optimization progress | Hurt |
| manage only constrained risk instead of both OOD and constrained risk (ablation) | COOREM · Welded beam design | optimization progress | Hurt |
| use PRIME instead of COOREM | constrained offline optimization · CEC tasks | optimality and stability | Hurt |
Surprising findings
- Prior COO methods such as DE-PF and PRIME could not find any feasible design on the Cassini 1 task in the reported runs.
- The authors report COOREM can outperform some constrained online methods (SCBO, CEO, Lagrange) that actively query the objective on certain space mission tasks.
Limitations
- Performance on Welded beam and some tasks is mixed; COOREM does not uniformly beat every baseline in OI/SI.
- Relies on a surrogate with generalization that the authors identify as a remaining challenge; the method has many hyperparameters (K, sigma, tau, lambda, momentum).
Experimental setup
Datasets: gtopx Cassini 1 gtopx Cassini1-MINLP CEC three-bar truss design CEC process synthesis CEC welded beam design
Benchmarks: Cassini 1 Cassini 1-MINLP Three-bar truss design Process synthesis Welded beam design
Metrics: Optimality Indicator (OI) Stability Indicator (SI) best feasible objective value
Baselines: DE-PF(S) DE-PF(A) DE-SFP(A) PRIME SCBO CEO Lagrange multiplier method
Builds on: PRIME ARCOO COMs Energy-based models
Closest papers by meaning
- Offline Multi-Objective Optimization (ICML 2024 · similarity 0.85)
- Learning Surrogates for Offline Black-Box Optimization via Gradient Matching (ICML 2024 · similarity 0.85)
- Boosting Offline Optimizers with Surrogate Sensitivity (ICML 2024 · similarity 0.84)
- ROOT: Rethinking Offline Optimization as Distributional Translation via Probabilistic Bridge (NeurIPS 2025 · similarity 0.84)
- Offline Model-Based Optimization by Learning to Rank (ICLR 2025 · similarity 0.83)
- Guided Trajectory Generation with Diffusion Models for Offline Model-based Optimization (NeurIPS 2024 · similarity 0.82)
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