Google Research

Garbage In, Reward Out: Bootstrapping Exploration in Multi-Armed Bandits

  • Branislav Kveton
  • Csaba Szepesvari
  • Sharan Vaswani
  • Zheng Wen
  • Mohammad Ghavamzadeh
  • Tor Lattimore
36th International Conference on Machine Learning (2019)


We propose a bandit algorithm that explores by randomizing its history of rewards. Specifically, it pulls the arm with the highest mean reward in a non-parametric bootstrap sample of its history with pseudo rewards. We design the pseudo rewards such that the bootstrap mean is optimistic with a sufficiently high probability. We call our algorithm Giro, which stands for garbage in, reward out. We analyze Giro in a Bernoulli bandit and derive a $O(K \Delta^{-1} \log n)$ bound on its $n$-round regret, where $\Delta$ is the difference in the expected rewards of the optimal and the best suboptimal arms, and $K$ is the number of arms. The main advantage of our exploration design is that it easily generalizes to structured problems. To show this, we propose contextual Giro with an arbitrary reward generalization model. We evaluate Giro and its contextual variant on multiple synthetic and real-world problems, and observe that it performs well.

Research Areas

Learn more about how we do research

We maintain a portfolio of research projects, providing individuals and teams the freedom to emphasize specific types of work