An Empirical Process Approachtothe Union Bound: Practical Algorithmsfor Combinatorialand Linear Bandits

Neural Information Processing Systems 

Theorem 7 impliesthatifT O( log ( 1/ )[ + ] log ( (Z)) log ( log ( (Z)))), then Algorithm 3 returnsz withprobabilityatleast1 . Then, O(' log ( log (d))).

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