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What is Learnable in Valiant's Theory of the Learnable? 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Regret Analysis of the Finite-Horizon Gittins Index Strategy for Multi-Armed Bandits
Tor Lattimore · 2015-11-19 · via math.ST updates on arXiv.org

I analyse the frequentist regret of the famous Gittins index strategy for multi-armed bandits with Gaussian noise and a finite horizon. Remarkably it turns out that this approach leads to finite-time regret guarantees comparable to those available for the popular UCB algorithm. Along the way I derive finite-time bounds on the Gittins index that are asymptotically exact and may be of independent interest. I also discuss some computational issues and present experimental results suggesting that a particular version of the Gittins index strategy is a modest improvement on existing algorithms with finite-time regret guarantees such as UCB and Thompson sampling.

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