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Voronoi-grid-based Pareto Front Learning and Its Application to Collaborative Federated Learning
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Proposes PHN-HVVS, a Pareto-front-learning method that partitions the preference simplex into GA-optimized Voronoi grids for ray sampling and adds a hypervolume-plus-distance loss, then applies it to multi-task learning and federated learning benefit-graph tasks.
Problem
Pareto-front learning with hypernetworks struggles to sample preference rays in high-dimensional objective spaces and often fails to cover the full (especially convex or boundary) Pareto front.
Approach
Decompose the preference hyperplane into Voronoi grids whose sites are optimized by a genetic algorithm for uniform point counts, and train a hypernetwork with a hypervolume-gradient loss plus a distance-to-preference-line penalty to cover the whole front.
Key results
- On multi-task benchmarks, PHN-HVVS reports the highest hypervolume on all six datasets, e.g., SARCOS 0.939±0.026 vs PHN-HVI 0.929±0.031 and MultiMNIST 3.008 vs 2.993.
- On toy problems, PHN-HVVS achieves the top HV on all eight problems, e.g., ZDT1 3.735 vs 3.654 for the next best (PHN-LS).
- Adding HVVS to CE on CIFAR-10 Pathological raises MTA from 74.38 to 86.88; on eICU the FedEgoists average AUC rises from 74.79 to 79.80.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PHN-HVVS instead of the strongest reported baseline | Pareto-front learning · Problem 1 | HV: 3.832±0.000526 -> 3.833±0.000026 | Helped |
| Use PHN-HVVS instead of the strongest reported baseline | Pareto-front learning · Problem 2 | HV: 3.374±0.011347 -> 3.387±0.007168 | Helped |
| Use PHN-HVVS instead of the strongest reported baseline | Pareto-front learning · DTLZ2 | HV: 7.385±0.006708 -> 7.388±0.001225 | Helped |
| Use PHN-HVVS instead of the strongest reported baseline | Pareto-front learning · DTLZ4 | HV: 7.383±0.005471 -> 7.386±0.003612 | Helped |
| Use PHN-HVVS instead of the strongest reported baseline | Pareto-front learning · ZDT1 | HV: 3.654±0.085641 -> 3.735±0.001754 | Helped |
| Use PHN-HVVS instead of the strongest reported baseline | Pareto-front learning · ZDT2 | HV: 3.321±0.022386 -> 3.323±0.004026 | No clear effect |
| Use PHN-HVVS instead of the strongest reported baseline | Pareto-front learning · VLMOP1 | HV: 3.825±0.010152 -> 3.829±0.000629 | No clear effect |
| Use PHN-HVVS instead of the strongest reported baseline | Pareto-front learning · VLMOP2 | HV: 3.329±0.012204 -> 3.339±0.000001 | Helped |
| Add HVVS | CE · CIFAR-10, pathological distribution | MTA: 74.38±4.00 -> 86.88±2.57 | Helped |
| Add HVVS | CE · CIFAR-10, Dir(β=0.5) | MTA: 47.13±2.03 -> 58.35±2.37 | Helped |
| Add HVVS | FedCompetitors · CIFAR-10, Dir(β=0.5) | MTA: 47.96 ± 0.75 -> 51.72 ± 1.39 | Helped |
| Add HVVS | FedEgoists · eICU | AUC: 74.79 -> 79.80 | Helped |
Surprising findings
- On CIFAR-10 Pathological with FedEgoists at competition ratio 0.05, the HVVS variant is slightly lower (80.41 vs 80.60).
Limitations
- HV is estimated by Monte Carlo sampling in more than 3 objectives with stated 1–5% error, and HV is computed only once for final evaluation.
- Several table entries show high variance (e.g., eICU per-client results, COSMOS failing to converge on Drug Review), and some FL comparisons are mixed (e.g., v3 and v5 lower with HVVS).
Experimental setup
Datasets: MultiMNIST Multi-Fashion Multi-(Fashion+MNIST) Drug Review Jura SARCOS CIFAR-10 eICU ZDT1 ZDT2 DTLZ2 DTLZ4
Benchmarks: MultiMNIST Multi-Fashion Multi-(Fashion+MNIST) Drug Review Jura SARCOS CIFAR-10 eICU ZDT1 ZDT2 DTLZ2 DTLZ4
Metrics: hypervolume mean test accuracy AUC
Baselines: PHN-EPO PHN-LS PHN-TCHE COSMOS PHN-HVI FedCompetitors FedEgoists
Builds on: Pareto HyperNetworks (PHN) PHN-LS PHN-EPO HVmax COSMOS
Closest papers by meaning
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- Interactive Hyperparameter Optimization in Multi-Objective Problems via Preference Learning (AAAI 2024 · similarity 0.85)
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