2023/04/26 by Amaury Gouverneur, Gouverneur, Amaury, Borja Rodríguez-Gálvez +5
Computer Science · Decision Sciences · Engineering · #Advanced Bandit Algorithms Research #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Smart Grid Energy Management
paper · pdf · doi:10.48550/arxiv.2304.13593
openalex publication_date 2023/04/26 · openalex created_date 2023/04/28 · openalex updated_date 2026/08/01
In this work, we study the performance of the Thompson Sampling algorithm for Contextual Bandit problems based on the framework introduced by Neu et al. and their concept of lifted information ratio. First, we prove a comprehensive bound on the Thompson Sampling expected cumulative regret that depends on the mutual information of the environment parameters and the history. Then, we introduce new bounds on the lifted information ratio that hold for sub-Gaussian rewards, thus generalizing the results from Neu et al. which analysis requires binary rewards. Finally, we provide explicit regret bounds for the special cases of unstructured bounded contextual bandits, structured bounded contextual bandits with Laplace likelihood, structured Bernoulli bandits, and bounded linear contextual bandits.