Parametric Bandits: The Generalized Linear Case

Sarah L. Filippi · Olivier Cappé · Aurélien Garivier · Csaba Szepesvári

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Advanced Bandit Algorithms Research Reinforcement Learning in Robotics Machine Learning and Algorithms

Abstract

We consider structured multi-armed bandit problems based on the Generalized Linear Model (GLM) framework of statistics. For these bandits, we propose a new algorithm, called GLM-UCB. We derive finite time, high probability bounds on the regret of the algorithm, extending previous analyses developed for the linear bandits to the non-linear case. The analysis highlights a key difficulty in generalizing linear bandit algorithms to the non-linear case, which is solved in GLM-UCB by focusing on the reward space rather than on the parameter space. Moreover, as the actual effectiveness of current parameterized bandit algorithms is often poor in practice, we provide a tuning method based on asymptotic arguments, which leads to significantly better practical performance. We present two numerical experiments on real-world data that illustrate the potential of the GLM-UCB approach.

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References

2002Finite-time Analysis of the Multiarmed Bandit Problem 2006Prediction, Learning, and Games 2003Using confidence bounds for exploitation-exploration trade-offs 2008Stochastic Linear Optimization Under Bandit Feedback 2010Linearly Parameterized Bandits 2007The Epoch-Greedy Algorithm for Multi-armed Bandits with Side Information 2007The Epoch-Greedy algorithm for contextual multi-armed bandits

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2014From Bandits to Monte-Carlo Tree Search: The Optimistic Principle Applied to Optimization and Planning 2012Optimistic bayesian sampling in contextual-bandit problems 2015Cascading Bandits: Learning to Rank in the Cascade Model 2017Linear Thompson sampling revisited 2020Mostly Exploration-Free Algorithms for Contextual Bandits 2019MNL-Bandit: A Dynamic Learning Approach to Assortment Selection 2017From Ads to Interventions: Contextual Bandits in Mobile Health

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