Stochastic Multi-armed Bandits in Constant Space

12/25/2017

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by   David Liau, et al.

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We consider the stochastic bandit problem in the sublinear space setting, where one cannot record the win-loss record for all K arms. We give an algorithm using O(1) words of space with regret ∑_i=1^K1/Δ_iΔ_i/Δ T where Δ_i is the gap between the best arm and arm i and Δ is the gap between the best and the second-best arms. If the rewards are bounded away from 0 and 1, this is within an O( 1/Δ) factor of the optimum regret possible without space constraints.