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Pareto Front-Diverse Batch Multi-Objective Bayesian Optimization
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Proposes PDBO, a batch multi-objective Bayesian optimization method that uses a discounted-reward multi-armed bandit to pick acquisition functions and a DPP over cheap Pareto sets to select Pareto-front-diverse batches.
Problem
Batch multi-objective optimization of expensive black-box functions where the goal is high-quality and output-space-diverse Pareto fronts, with parallel evaluations.
Approach
Combines a full-information Hedge-style bandit over an acquisition-function portfolio (with discounted, normalized hypervolume-improvement rewards) with a multi-objective DPP that selects batches from the cheap Pareto set, using a convex combination of GP kernels fitted by maximizing likelihood of individual hypervolume contributions.
Key results
- PDBO outperforms baselines in Pareto-front diversity (DPF) across benchmarks and batch sizes B in {2,4,8,16}.
- PDBO matches or exceeds baselines on hypervolume in most experiments, outperforming all baselines in most settings.
- DGEMO fails beyond 3 objectives and qEHVI runs out of memory beyond batch size 8, while PDBO scales to any dimension and batch size.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PDBO instead of prior batch MOO methods | PDBO · MOO benchmarks | Diversity of Pareto Front (DPF) | Helped |
| Use PDBO instead of prior batch MOO methods | PDBO · MOO benchmarks | hypervolume | Mixed |
| Use adaptive acquisition-function selection instead of a static acquisition function (ablation) | USEMO · MOO benchmarks, batch size 1 | performance | Helped |
| Use DPP-based batch selection instead of USEMO's uncertainty-based selection (ablation) | USEMO-EI · MOO benchmarks, batch sizes 2, 4, 8, and 16 | DPF | Helped |
| Use DPP-based batch selection instead of USEMO's uncertainty-based selection (ablation) | USEMO-EI · MOO benchmarks, batch sizes 2, 4, 8, and 16 | hypervolume | Helped |
| Use the proposed relative-hypervolume, discounted, normalized reward instead of the sum-of-posterior-means reward (ablation) | PDBO · MOO benchmarks | performance | Helped |
| Select batches using DPP instead of greedy highest individual hypervolume contribution (ablation) | PDBO · Synthetic and real-world problems | hypervolume | Mixed |
Surprising findings
- Hypervolume alone does not capture Pareto front diversity, motivating a new DPF metric.
- Prior batch MOO methods such as DGEMO and qEHVI were not evaluated on diversity before this work.
Limitations
- Hyperparameters of the bandit (decay rate and selection temperature) are set manually.
- Cannot handle high-dimensional search spaces.
- Regret bound proven only for sequential selection; batch extension left unproven.
Experimental setup
Datasets: ZDT-1 ZDT-2 ZDT-3 DTLZ-1 DTLZ-3 DTLZ-5 Gear train design SW-LLVM UAV power system design
Benchmarks: ZDT-1 ZDT-2 ZDT-3 DTLZ-1 DTLZ-3 DTLZ-5 Gear train design SW-LLVM UAV power system design
Metrics: hypervolume diversity of Pareto front (DPF) IGD runtime
Baselines: DGEMO qEHVI qParEGO USEMO-EI NSGA-II random selection
Builds on: GP-Hedge USEMO DGEMO k-DPP batch BO
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