In the stochastic multi-armed bandit problem we consider a modification of the UCB algorithm of Auer et al. [4]. For this modified algorithm we give an improved bound on the regret with respect to the optimal reward. While for the original UCB algorithm the regret in K-armed bandits after T trials is bounded by const · #xA; #xA;nfrac{{Klog (T)}}n{Delta }n, where Δ measures the distance between a suboptimal arm and the optimal arm, for the modified UCB algorithm we show an upper bound on the regret of const · $nfrac{{Klog (TDelta ^2 )}}n{Delta }n$nfrac{{Klog (TDelta ^2 )}}n{Delta }
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机译：在随机多武装匪徒问题中，我们考虑对Auer等人的UCB算法进行修改。 [4]。对于这种改进的算法，我们给出了关于最佳奖励的遗憾的改进界限。对于原始的UCB算法，T试验后K武装匪徒的遗憾受到const·#xA的限制； #xA; nfrac {{Klog（T）}} n {Delta} n，其中Δ衡量次优臂与最佳臂之间的距离，对于改进的UCB算法，我们在const·$ nfrac的遗憾上显示了上限{{Klog（TDelta ^ 2）}} n {Delta} n $ nfrac {{Klog（TDelta ^ 2）}} n {Delta}。
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