We consider a version of the continuum armed bandit where an action induces a filtered realisation of a non-homogeneous Poisson process. Point data in the filtered sample are then revealed to the decision-maker, whose reward is the total number of revealed points. Using knowledge of the function governing the filtering, but without knowledge of the Poisson intensity function, the decision-maker seeks to maximise the expected number of revealed points over T rounds. We propose an upper confidence bound algorithm for this problem utilising data-adaptive discretisation of the action space. This approach enjoys O(T^(2/3)) regret under a Lipschitz assumption on the reward function. We provide lower bounds on the regret of any algorithm for the problem, via new lower bounds for related finite-armed bandits, and show that the orders of the upper and lower bounds match up to a logarithmic factor.
Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update
RIKEN AIP（日本理化学研究所高级研究所）；National Key Laboratory for Novel Software Technology（国家新型软件技术实验室）；School of Artificial Intelligence（人工智能学院）；The University of Tokyo（东京大学）
Self-Concordant Analysis of Generalized Linear Bandits with Forgetting
DI ENS（高等师范学院信息学系）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；ENS（高等师范学院）；Université PSL（巴黎文理研究大学）；Criteo AI Lab（Criteo人工智能实验室）；LTCI（通信与信息处理实验室）；TélécomParis（巴黎电信学院）；UMPA（纯粹数学与应用数学研究所）；ENS Lyon（里昂高等师范学院）
