Hephaestus: Mixture Generative Modeling with Energy Guidance for Large-scale QoS Degradation

TL;DR

QoSD seeks minimal budget perturbations to raise all critical shortest-path costs above $T$, even with nonlinear edge-cost functions. Hephaestus combines a scalable Forge phase (PPS guided by SPAGAN) for feasible solution generation, a Morph phase (Energy-Based Model guided Mix-CVAE with dynamic expert augmentation) to model the multimodal solution space, and a Refine phase (latent-space RL with a differentiable reward) to iteratively improve solutions; PPS-I provides a 100% feasibility guarantee when needed. The framework demonstrates strong performance and scalability on synthetic and real networks across linear, quadratic-convex, and log-concave cost regimes, often outperforming classical and learning-based baselines, with ablations confirming the value of each phase. Theoretical guarantees (PPS ratio, expert augmentation efficiency, normalization-free minimax, and safe latent-ball properties) underpin robust performance, while extensive experiments show resilience to SPAGAN errors and data quality variations. Overall, Hephaestus offers a scalable, principled approach to large-scale QoSD and represents a generalizable blueprint for combining predictive modeling, energy-guided generation, and latent-space optimization in graph-based constrained optimization.

Abstract

We study the Quality of Service Degradation (QoSD) problem, in which an adversary perturbs edge weights to degrade network performance. This setting arises in both network infrastructures and distributed ML systems, where communication quality, not just connectivity, determines functionality. While classical methods rely on combinatorial optimization, and recent ML approaches address only restricted linear variants with small-size networks, no prior model directly tackles the QoSD problem under nonlinear edge-weight functions. This work proposes \PIMMA, a self-reinforcing generative framework that synthesizes feasible solutions in latent space, to fill this gap. Our method includes three phases: (1) Forge: a Predictive Path-Stressing (PPS) algorithm that uses graph learning and approximation to produce feasible solutions with performance guarantee, (2) Morph: a new theoretically grounded training paradigm for Mixture of Conditional VAEs guided by an energy-based model to capture solution feature distributions, and (3) Refine: a reinforcement learning agent that explores this space to generate progressively near-optimal solutions using our designed differentiable reward function. Experiments on both synthetic and real-world networks show that our approach consistently outperforms classical and ML baselines, particularly in scenarios with nonlinear cost functions where traditional methods fail to generalize.

Figures (19)

• Figure 1: Given a graph dataset, we train SPAGAN to predict shortest path costs and guide PPS in generating feasible solutions across varying thresholds, forming a Pretrained Solution Dataset. Then, EBM approximates the underlying solution distribution, while a Mix-CVAE learns to closely match this distribution. Once the Mix-CVAE converges, an RL agent modifies latent samples, which are decoded into lower-cost solutions. The top-$k$ high-reward samples are added back to the Solution Dataset to retrain both the EBM and Mix-CVAE in future episodes, enabling continual improvement.
• Figure 2: At each iteration, the generative model $\Omega(x)$ adds an expert in regions where the log-ratio $\chi(x) = \log \left(q(x) / \Omega(x) \right)$ exceeds $\delta$, thereby covering more of $q(x)$. Meanwhile, $q(x)$ adapts to align with $p(x)$. As the steps progress, $q(x)$ increasingly approximates $p(x)$, and $\Omega(x)$, augmented by new experts, converges to $q(x)$, ultimately yielding $p(x) \approx q(x) \approx \Omega(x)$.
• Figure 3: Our solution quality on the testing synthetic graph with varying density is evaluated under Linear, Quadratic Convex, and Log-Concave functions. ML-based ILPs are compared with the best-performing approximation baseline AT for Linear weights but excluded for the other two due to incompatibility; exact solver also does not support Log-Concave.
• Figure 4: Comparison between the distribution from the EBM and the distribution from the Mix-CVAE with varying numbers of experts on a synthetic dataset with maximum density. Increasing the number of experts improves mode coverage and alignment with the target EBM distribution.
• Figure 5: An example of conditional latent space visualization via UMAP mcinnes2018umap for the trained Mix-CVAE on the same synthetic graph and pairs but different thresholds. Points represent latent vectors $\mathbf{z}$, colored by threshold $T$. Clear clustering shows the latent space captures meaningful patterns.

Theorems & Definitions (9)

• Theorem 1
• Theorem 2
• Theorem 3
• Lemma 1
• Theorem 4
• Remark 1
• Remark 2
• Remark 3: Trade-off between Lipschitz control and expressiveness
• Remark 4: Local Lipschitz behavior on latent support