Tree-Based Stochastic Optimization for Solving Large-Scale Urban Network Security Games

• URL: http://arxiv.org/abs/2511.10072v1
• Date: Fri, 14 Nov 2025 01:30:26 GMT
• Title: Tree-Based Stochastic Optimization for Solving Large-Scale Urban Network Security Games
• Authors: Shuxin Zhuang, Linjian Meng, Shuxin Li, Minming Li, Youzhi Zhang,
• Abstract summary: Urban Network Security Games (UNSGs) model the strategic allocation of limited security resources on city road networks.<n>Finding a Nash Equilibrium (NE) in large-scale UNSGs is challenging due to their massive and action spaces.<n>We introduce Tree-based Optimization (TSO), a framework that bridges the gap between NE-finding and the demands of UNSGs.
• Score: 19.12896663564658
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Urban Network Security Games (UNSGs), which model the strategic allocation of limited security resources on city road networks, are critical for urban safety. However, finding a Nash Equilibrium (NE) in large-scale UNSGs is challenging due to their massive and combinatorial action spaces. One common approach to addressing these games is the Policy-Space Response Oracle (PSRO) framework, which requires computing best responses (BR) at each iteration. However, precisely computing exact BRs is impractical in large-scale games, and employing reinforcement learning to approximate BRs inevitably introduces errors, which limits the overall effectiveness of the PSRO methods. Recent advancements in leveraging non-convex stochastic optimization to approximate an NE offer a promising alternative to the burdensome BR computation. However, utilizing existing stochastic optimization techniques with an unbiased loss function for UNSGs remains challenging because the action spaces are too vast to be effectively represented by neural networks. To address these issues, we introduce Tree-based Stochastic Optimization (TSO), a framework that bridges the gap between the stochastic optimization paradigm for NE-finding and the demands of UNSGs. Specifically, we employ the tree-based action representation that maps the whole action space onto a tree structure, addressing the challenge faced by neural networks in representing actions when the action space cannot be enumerated. We then incorporate this representation into the loss function and theoretically demonstrate its equivalence to the unbiased loss function. To further enhance the quality of the converged solution, we introduce a sample-and-prune mechanism that reduces the risk of being trapped in suboptimal local optima. Extensive experimental results indicate the superiority of TSO over other baseline algorithms in addressing the UNSGs.

Related papers

• Joint Optimization of Model Partitioning and Resource Allocation for Anti-Jamming Collaborative Inference Systems [52.842088497389746]
  This letter focuses on an anti-jamming collaborative inference system in the presence of a malicious jammer.<n>We first analyze the effects of jamming and DNN partitioning on inference accuracy via data regression.<n>We propose an efficient alternating optimization-based algorithm, which decomposes the problem into three subproblems.
  arXiv  Detail & Related papers  (2026-03-03T03:52:52Z)
• Deep Hierarchical Learning with Nested Subspace Networks [53.71337604556311]
  We propose Nested Subspace Networks (NSNs) for large neural networks.<n>NSNs enable a single model to be dynamically and granularly adjusted across a continuous spectrum of compute budgets.<n>We show that NSNs can be surgically applied to pre-trained LLMs and unlock a smooth and predictable compute-performance frontier.
  arXiv  Detail & Related papers  (2025-09-22T15:13:14Z)
• NDCG-Consistent Softmax Approximation with Accelerated Convergence [67.10365329542365]
  We propose novel loss formulations that align directly with ranking metrics.<n>We integrate the proposed RG losses with the highly efficient Alternating Least Squares (ALS) optimization method.<n> Empirical evaluations on real-world datasets demonstrate that our approach achieves comparable or superior ranking performance.
  arXiv  Detail & Related papers  (2025-06-11T06:59:17Z)
• Reconfigurable Intelligent Surface (RIS)-Assisted Entanglement Distribution in FSO Quantum Networks [62.87033427172205]
  Quantum networks (QNs) relying on free-space optical (FSO) quantum channels can support quantum applications in environments where establishing an optical fiber infrastructure is challenging and costly. A reconfigurable intelligent surface (RIS)-assisted FSO-based QN is proposed as a cost-efficient framework providing a virtual line-of-sight between users for entanglement distribution.
  arXiv  Detail & Related papers  (2024-01-19T17:16:40Z)
• Nonconvex Stochastic Bregman Proximal Gradient Method with Application to Deep Learning [9.202586157819693]
  quadratic methods for minimizing robustness for non composite objective functions typically rely on the Lipschitz smoothness of the differentiable part.<n>We propose a family of Bregman (SBPG) methods that only adaptivity.<n>MSBPG, a momentum-based variant, enhances convergence sensitivity by relaxing the minibatch size requirement.
  arXiv  Detail & Related papers  (2023-06-26T08:54:46Z)
• Learning k-Level Structured Sparse Neural Networks Using Group Envelope Regularization [4.0554893636822]
  We introduce a novel approach to deploy large-scale Deep Neural Networks on constrained resources. The method speeds up inference time and aims to reduce memory demand and power consumption.
  arXiv  Detail & Related papers  (2022-12-25T15:40:05Z)
• Simulation-guided Beam Search for Neural Combinatorial Optimization [13.072343634530883]
  We propose simulation-guided beam search (SGBS) for neural optimization problems. We hybridize SGBS with efficient active search (EAS), where SGBS enhances the quality of solutions backpropagated in EAS. We evaluate our methods on well-known CO benchmarks and show that SGBS significantly improves the quality of the solutions found under reasonable assumptions.
  arXiv  Detail & Related papers  (2022-07-13T13:34:35Z)
• Learning Representation for Bayesian Optimization with Collision-free Regularization [13.476552258272402]
  Large-scale, high-dimensional, and non-stationary datasets are common in real-world scenarios. Recent works attempt to handle such input by applying neural networks ahead of the classical Gaussian process to learn a latent representation. We show that even with proper network design, such learned representation often leads to collision in the latent space. We propose LOCo, an efficient deep Bayesian optimization framework which employs a novel regularizer to reduce the collision in the learned latent space.
  arXiv  Detail & Related papers  (2022-03-16T14:44:16Z)
• Edge Rewiring Goes Neural: Boosting Network Resilience via Policy Gradient [62.660451283548724]
  ResiNet is a reinforcement learning framework to discover resilient network topologies against various disasters and attacks. We show that ResiNet achieves a near-optimal resilience gain on multiple graphs while balancing the utility, with a large margin compared to existing approaches.
  arXiv  Detail & Related papers  (2021-10-18T06:14:28Z)
• Improved Branch and Bound for Neural Network Verification via Lagrangian Decomposition [161.09660864941603]
  We improve the scalability of Branch and Bound (BaB) algorithms for formally proving input-output properties of neural networks. We present a novel activation-based branching strategy and a BaB framework, named Branch and Dual Network Bound (BaDNB) BaDNB outperforms previous complete verification systems by a large margin, cutting average verification times by factors up to 50 on adversarial properties.
  arXiv  Detail & Related papers  (2021-04-14T09:22:42Z)
• Resource Allocation via Model-Free Deep Learning in Free Space Optical Communications [119.81868223344173]
  The paper investigates the general problem of resource allocation for mitigating channel fading effects in Free Space Optical (FSO) communications. Under this framework, we propose two algorithms that solve FSO resource allocation problems.
  arXiv  Detail & Related papers  (2020-07-27T17:38:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.