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Memory-Guided Trust-Region Bayesian Optimization (MG-TuRBO) for High Dimensions EngageTriBoost: Predictive Modeling of User Engagement in Digital Mental Health Intervention Using Explainable Machine Learning Reservoir observer enhanced with residual calibration and attention mechanism Efficient RL Training for LLMs with Experience Replay Wireless Communication Enhanced Value Decomposition for Multi-Agent Reinforcement Learning Adversarial Sensor Errors for Safe and Robust Wind Turbine Fleet Control IKKA: Inversion Classification via Critical Anomalies for Robust Visual Servoing Adaptive Simulation Experiment for LLM Policy Optimization EvoLen: Evolution-Guided Tokenization for DNA Language Model Smartwatch-Based Sitting Time Estimation in Real-World Office Settings Structural Evaluation Metrics for SVG Generation via Leave-One-Out Analysis Loom: A Scalable Analytical Neural Computer Architecture Spectral Geometry of LoRA Adapters Encodes Training Objective and Predicts Harmful Compliance Finite-Sample Analysis of Nonlinear Independent Component Analysis:Sample Complexity and Identifiability Bounds How does Chain of Thought decompose complex tasks? 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Iterative Methods via Locally Evolving Set Process
Baojian Zhou, Yifan Sun, Reza Babanezhad Harikandeh, Xingzhi Guo · 2024-10-19 · via cs.LG updates on arXiv.org

Given the damping factor $α$ and precision tolerance $ε$, \citet{andersen2006local} introduced Approximate Personalized PageRank (APPR), the \textit{de facto local method} for approximating the PPR vector, with runtime bounded by $Θ(1/(αε))$ independent of the graph size. Recently, \citet{fountoulakis2022open} asked whether faster local algorithms could be developed using $\tilde{O}(1/(\sqrtαε))$ operations. By noticing that APPR is a local variant of Gauss-Seidel, this paper explores the question of \textit{whether standard iterative solvers can be effectively localized}. We propose to use the \textit{locally evolving set process}, a novel framework to characterize the algorithm locality, and demonstrate that many standard solvers can be effectively localized. Let $\overline{\operatorname{vol}}{ (S_t)}$ and $\overlineγ_{t}$ be the running average of volume and the residual ratio of active nodes $\textstyle S_{t}$ during the process. We show $\overline{\operatorname{vol}}{ (S_t)}/\overlineγ_{t} \leq 1/ε$ and prove APPR admits a new runtime bound $\tilde{O}(\overline{\operatorname{vol}}(S_t)/(α\overlineγ_{t}))$ mirroring the actual performance. Furthermore, when the geometric mean of residual reduction is $Θ(\sqrtα)$, then there exists $c \in (0,2)$ such that the local Chebyshev method has runtime $\tilde{O}(\overline{\operatorname{vol}}(S_{t})/(\sqrtα(2-c)))$ without the monotonicity assumption. Numerical results confirm the efficiency of this novel framework and show up to a hundredfold speedup over corresponding standard solvers on real-world graphs.

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