BRAID: Learning Equilibrium Maps in Interdependent Security Games via Weight-Tied Iterative Graph Neural Networks

• URL: http://arxiv.org/abs/2608.14856v1
• Date: Fri, 14 Aug 2026 19:53:34 GMT
• Title: BRAID: Learning Equilibrium Maps in Interdependent Security Games via Weight-Tied Iterative Graph Neural Networks
• Abstract summary: Best-Response Amortized Iterative Dynamics model (BRAID) learns a direct map from game parameters to Nash equilibrium effort profiles.<n>BRAID effectively predicts Nash equilibria and recovers equilibrium sensitivities across utility specifications and network sizes.
• Score: 14.370967816962837
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Computing Nash equilibria in interdependent security (IDS) games on networks is computationally expensive: best-response dynamics may need hundreds of iterations per instance, and downstream tasks such as auditing, stress-testing, and incentive design often require repeatedly re-solving the game under parameter perturbations. We propose BRAID, a Best-Response Amortized Iterative Dynamics model that uses a weight-tied iterative graph neural network to learn a direct map from game parameters to Nash equilibrium effort profiles, replacing iterative best response computation with a single forward pass that is up to 43X faster per instance. BRAID is derived from the best-response fixed-point structure of IDS games: its SUM aggregation reflects additive neighbor coupling, and a weight-tied gated recurrent unit (GRU) mirrors a damped best-response update. The same architecture applies across IDS specifications that vary investment-cost curvature and neighborhood aggregation, including log-linear, quadratic-cost, and log constant-elasticity-of-substitution (CES) utilities. Beyond equilibrium prediction, BRAID also recovers how equilibrium efforts change under perturbations to game parameters, including costs and network edge weights. We make this sensitivity recovery an explicit evaluation target and introduce two training strategies, interior-equilibrium training and input-noise regularization, that improve the local behavior of the learned equilibrium map without using sensitivity labels. Experiments show that BRAID effectively predicts Nash equilibria and recovers equilibrium sensitivities across utility specifications and network sizes.

Related papers

• Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification [47.720075875232226]
  We introduce PCA--RaNN, a neural operator that combines a PCA-based dimensionality reduction with fixed random features.<n>It recasts operator learning as fixed regression, reducing latent regression to three orders of magnitude.
  arXiv  Detail & Related papers  (2026-06-28T15:02:26Z)
• FedSQ: Optimized Weight Averaging via Fixed Gating [1.2058208023553034]
  Federated learning enables collaborative training across organizations without sharing raw data.<n>We propose FedSQ (Federated Structural-Quantitative learning), a transfer-d neural federated procedure based on a DualCopy.<n>Fixing the gating reduces learning to within-regime affine refinements, which stabilizes aggregation under heterogeneous partitions.
  arXiv  Detail & Related papers  (2026-04-03T11:54:23Z)
• A Replicate-and-Quantize Strategy for Plug-and-Play Load Balancing of Sparse Mixture-of-Experts LLMs [64.8510381475827]
  Sparse Mixture-of-Experts (SMoE) architectures are increasingly used to scale large language models efficiently.<n>SMoE models often suffer from severe load imbalance across experts, where a small subset of experts receives most tokens while others are underutilized.<n>We present a systematic analysis of expert routing during inference and identify three findings: (i) load imbalance persists and worsens with larger batch sizes, (ii) selection frequency does not reliably reflect expert importance, and (iii) overall expert workload and importance can be estimated using a small calibration set.
  arXiv  Detail & Related papers  (2026-02-23T15:11:16Z)
• Generalizing GNNs with Tokenized Mixture of Experts [75.8310720413187]
  We show that improving stability requires reducing reliance on shift-sensitive features, leaving an irreducible worst-case generalization floor.<n>We propose STEM-GNN, a pretrain-then-finetune framework with a mixture-of-experts encoder for diverse computation paths.<n>Across nine node, link, and graph benchmarks, STEM-GNN achieves a stronger three-way balance, improving robustness to degree/homophily shifts and to feature/edge corruptions while remaining competitive on clean graphs.
  arXiv  Detail & Related papers  (2026-02-09T22:48:30Z)
• Pruning as a Game: Equilibrium-Driven Sparsification of Neural Networks [1.1458853556386799]
  We show that sparsity emerges naturally when continued participation becomes a dominated strategy at equilibrium.<n>We derive a simple equilibrium-driven pruning algorithm that jointly updates network parameters and participation variables without relying on explicit importance scores.
  arXiv  Detail & Related papers  (2025-12-26T18:25:38Z)
• APRIL: Auxiliary Physically-Redundant Information in Loss - A physics-informed framework for parameter estimation with a gravitational-wave case study [0.0]
  Physics-Informed Neural Networks (PINNs) embed the partial differential equations governing the system under study directly into the training of Neural Networks.<n>We present a complementary approach by including auxiliary physically-redundant information in loss.<n>We mathematically demonstrate that these terms preserve the true physical minimum while reshaping the loss landscape.
  arXiv  Detail & Related papers  (2025-10-15T15:34:19Z)
• Weight transport through spike timing for robust local gradients [0.5236468296934584]
  plasticity in functional neural networks is frequently expressed as gradient descent on a cost.<n>This imposes symmetry constraints that are difficult to reconcile with local computation.<n>We introduce spike-based alignment learning, which uses spike timing statistics to extract and correct the asymmetry between effective reciprocal connections.
  arXiv  Detail & Related papers  (2025-03-04T14:05:39Z)
• Machine learning in and out of equilibrium [58.88325379746631]
  Our study uses a Fokker-Planck approach, adapted from statistical physics, to explore these parallels. We focus in particular on the stationary state of the system in the long-time limit, which in conventional SGD is out of equilibrium. We propose a new variation of Langevin dynamics (SGLD) that harnesses without replacement minibatching.
  arXiv  Detail & Related papers  (2023-06-06T09:12:49Z)
• Rotational Equilibrium: How Weight Decay Balances Learning Across Neural Networks [33.88586668321127]
  This study investigates how weight decay affects the update behavior of individual neurons in deep neural networks. We show that explicitly controlling the rotation provides the benefits of weight decay while substantially reducing the need for learning rate warmup.
  arXiv  Detail & Related papers  (2023-05-26T19:14:01Z)
• Can pruning improve certified robustness of neural networks? [106.03070538582222]
  We show that neural network pruning can improve empirical robustness of deep neural networks (NNs) Our experiments show that by appropriately pruning an NN, its certified accuracy can be boosted up to 8.2% under standard training. We additionally observe the existence of certified lottery tickets that can match both standard and certified robust accuracies of the original dense models.
  arXiv  Detail & Related papers  (2022-06-15T05:48:51Z)
• Efficient Model-based Multi-agent Reinforcement Learning via Optimistic Equilibrium Computation [93.52573037053449]
  H-MARL (Hallucinated Multi-Agent Reinforcement Learning) learns successful equilibrium policies after a few interactions with the environment. We demonstrate our approach experimentally on an autonomous driving simulation benchmark.
  arXiv  Detail & Related papers  (2022-03-14T17:24:03Z)
• Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks [2.580765958706854]
  We describe and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks. PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. For inverse modeling using sequential training, we find that inverse-Dirichlet weighting protects a PINN against catastrophic forgetting.
  arXiv  Detail & Related papers  (2021-07-02T10:01:37Z)

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.