2017/02/17 by Zifan Li, Ambuj Tewari, Li, Zifan +1
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Search Problems #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.1702.05536
openalex publication_date 2017/02/17 · openalex created_date 2017/03/16 · openalex updated_date 2026/07/28
Recent work on follow the perturbed leader (FTPL) algorithms for the adversarial multi-armed bandit problem has highlighted the role of the hazard rate of the distribution generating the perturbations. Assuming that the hazard rate is bounded, it is possible to provide regret analyses for a variety of FTPL algorithms for the multi-armed bandit problem. This paper pushes the inquiry into regret bounds for FTPL algorithms beyond the bounded hazard rate condition. There are good reasons to do so: natural distributions such as the uniform and Gaussian violate the condition. We give regret bounds for both bounded support and unbounded support distributions without assuming the hazard rate condition. We also disprove a conjecture that the Gaussian distribution cannot lead to a low-regret algorithm. In fact, it turns out that it leads to near optimal regret, up to logarithmic factors. A key ingredient in our approach is the introduction of a new notion called the generalized hazard rate.