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arXiv · 1902.10089

Perturbed-History Exploration in Stochastic Multi-Armed Bandits

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

We propose an online algorithm for cumulative regret minimization in a stochastic multi-armed bandit. The algorithm adds $O(t)$ i.i.d. pseudo-rewards to its history in round $t$ and then pulls the arm with the highest average reward in its perturbed history. Therefore, we call it perturbed-history exploration (PHE). The pseudo-rewards are carefully designed to offset potentially underestimated mean rewards of arms with a high probability. We derive near-optimal gap-dependent and gap-free bounds on the $n$-round regret of PHE. The key step in our analysis is a novel argument that shows that randomized Bernoulli rewards lead to optimism. Finally, we empirically evaluate PHE and show that it is competitive with state-of-the-art baselines.

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Branislav Kveton, Csaba Szepesvari, Mohammad Ghavamzadeh, Craig Boutilier. 2019-02-26. Perturbed-History Exploration in Stochastic Multi-Armed Bandits. https://arxiv.org/abs/1902.10089

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