Problem
Research questions and friction points this paper is trying to address.
Graph Structured Combinatorial Semi-Bandit
Nonlinear Reward
Signal Dependencies
Optimal Structure Identification
Interconnected Data
Graph Structured Combinatorial Semi-Bandit with Nonlinear Reward Associations through Separable Signals
🤖 AI Summary
This work addresses the sampling and computational challenges posed by nonlinear rewards in graph-structured combinatorial semi-bandits. The authors propose a general adaptive framework that, for the first time, incorporates a separable signal mechanism, integrating graph-based causal reward modeling, reproducing kernel Hilbert space methods, and functional Taylor approximation to efficiently model nonlinear reward structures. Under mild assumptions, they theoretically establish a regret upper bound that is sublinear in time and linear in data volume. Empirical evaluations on both synthetic and real-world traffic datasets demonstrate the method’s effectiveness and robustness.
📝 Abstract
The identification of optimal structures within vast arrays of interconnected data necessitates significant sampling- and computational effort. Learning and leveraging underlying signal dependencies can improve efficiency and predictive capabilities considerably, but the ubiquity of nonlinear statistical relations amplifies the complexity of such undertakings. In this paper, we develop novel generic and adaptive strategies equipped with routines for graph-based causal reward modeling, analytic reproducing kernel methods, and Taylor approximation of functional processes. We establish theoretical performance guarantees sublinear in time and linear in data volume over time. Our analyses cover robustness to a multitude of uncertainties arising from noise interference, gradual model convergence, and solution space mismatch. The framework's general appeal is substantiated by a minimalistic set of conditions or reliance on prior estimates, while various outlined modifications address specific or extended settings. To demonstrate practical effectiveness, we conduct numerical experiments using both benchmarked synthetic and real-world transportation datasets.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Graph-structured bandits
Nonlinear reward
Reproducing kernel methods
Causal reward modeling
Taylor approximation
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