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arXiv · 1903.09132

Perturbed-History Exploration in Stochastic Linear Bandits

Branislav Kveton·Csaba Szepesvari·Mohammad Ghavamzadeh·Craig Boutilier
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Abstract

We propose a new online algorithm for cumulative regret minimization in a stochastic linear bandit. The algorithm pulls the arm with the highest estimated reward in a linear model trained on its perturbed history. Therefore, we call it perturbed-history exploration in a linear bandit (LinPHE). The perturbed history is a mixture of observed rewards and randomly generated i.i.d. pseudo-rewards. We derive a $\tilde{O}(d \sqrt{n})$ gap-free bound on the $n$-round regret of LinPHE, where $d$ is the number of features. The key steps in our analysis are new concentration and anti-concentration bounds on the weighted sum of Bernoulli random variables. To show the generality of our design, we generalize LinPHE to a logistic model. We evaluate our algorithms empirically and show that they are practical.

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Branislav Kveton, Csaba Szepesvari, Mohammad Ghavamzadeh, Craig Boutilier. 2019-03-21. Perturbed-History Exploration in Stochastic Linear Bandits. https://arxiv.org/abs/1903.09132

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