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Hephaestus: Mixture Generative Modeling with Energy Guidance for Large-scale QoS Degradation
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Proposes Hephaestus, a Forge-Morph-Refine generative framework (PPS approximation with SPAGAN estimator, energy-guided mixture of conditional VAEs, and latent-space RL) for the nonlinear Quality of Service Degradation problem on networks.
Problem
Quality of Service Degradation (QoSD): an adversary increases edge weights under budget constraints to push shortest paths of critical source-target pairs above a threshold; existing ML methods only handle linear, small-scale variants and classical methods rely on combinatorial optimization.
Approach
Combines a shortest-path-attention-guided approximation (PPS) to generate a feasible solution dataset, an energy-based model that guides a mixture of conditional VAEs with dynamically added experts, and an RL agent that refines latent codes using a differentiable feasibility-and-cost reward, handling nonlinear edge-cost functions.
Key results
- On Skitter at T=260%, Hephaestus reduces total cost by 28.1% versus the second-best method DIFFILO (2199372 vs about 3.01M).
- On RoadCA, Hephaestus reduces total cost by 16.8% versus DIFFILO at the highest threshold.
- On linear-cost Email and Gnutella at T=260%, Hephaestus is slightly better than DIFFILO (9601 vs 9695; 10495 vs 10987), but slightly worse at 140% in some cases.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Hephaestus instead of DIFFILO | QoSD solutions on Skitter at threshold 260% · Skitter 260% | total cost: 28.1% | Helped |
| Use Hephaestus instead of DIFFILO | QoSD solutions on RoadCA at threshold 260% · RoadCA 260% | total cost: 16.8% | Helped |
| Use Hephaestus instead of DIFFILO | QoSD solutions on Gnutella at threshold 260% · Gnutella 260% | total cost: 4.5% | Helped |
| Use Hephaestus instead of DIFFILO | QoSD solutions on Gnutella at threshold 140% · Gnutella 140% | total cost: 7 units | Hurt |
| Add more experts to the Mix-CVAE (ablation) | Mix-CVAE guided by EBM on the synthetic dataset · Synthetic maximum-density graph | distribution alignment: from 3 to 9 | Helped |
Surprising findings
- On Email and Gnutella at lowest thresholds, the exact solver and DiffILO outperform Hephaestus, so the advantage is mainly at high thresholds and large graphs.
Limitations
- Quality depends on the initial solutions from the approximation algorithm used in Forge.
- Generalization to unseen graphs depends on the GNN estimator (SPAGAN) and graph representation quality.
- No error bars or statistical significance reported.
Experimental setup
Datasets: Email Gnutella RoadCA Skitter synthetic Erdős–Rényi graphs
Benchmarks: Email Gnutella RoadCA Skitter synthetic Erdős–Rényi (n=1024)
Metrics: total perturbation budget (lower is better)
Baselines: Adaptive Trading Iterative Greedy Sampling Algorithm DiffILO Predict-and-Search L-MILPOPT Exact Solver (Gurobi)
Builds on: CVAE energy-based models Predict-and-Search DiffILO Gurobi
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