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 Hephaestus, 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.

This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size n subject to a knapsack constraint, DLA and RLA. DLA is a deterministic algorithm that provides an approximation factor of nearly 6 while RLA is a randomized algorithm with an approximation factor of nearly 4. Both run in linear query complexity. The key idea to obtain a constant approximation ratio with linear query lies in: (1) dividing the ground set into two appropriate subsets to find the near-optimal solution over these subsets with linear queries, and (2) combining a threshold greedy with properties of two disjoint sets or a random selection process to improve solution quality. In addition to the theoretical analysis, we have evaluated our proposed solutions with three applications: Revenue Maximization, Image Summarization, and Maximum Weighted Cut, showing that our algorithms not only return comparative results to state-of-the-art algorithms but also require significantly fewer queries.

This paper proposes two fast streaming algorithms for the problem of k-submodular maximization over the ground set of n elements under the knapsack constraint which is important and popular in combinatorial optimization and machine learning. Our algorithms are the first ones that provide constant-approximation ratios within O(nk) query complexity. The first algorithm is a single-pass streaming algorithm that returns a 1/10-approximation solution, the second one is a multi-pass streaming algorithm and improves the approximation ratio to nearly 1/4. Although these ratios are simply near to the state-of-the-art algorithms yet the number of queries can diminish by a large factor. We further investigate the performance of our algorithms by directing several experiments on instances of the issue: Influence Maximization and Sensor Placement. The outcomes confirm that our algorithms not only methodology in the quality arrangement of the cutting edge techniques including streaming and non-streaming algorithms yet in addition significantly reduce the number of queries.