# What Doubling Tricks Can and Can't Do for Multi-Armed Bandits

5 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : An online reinforcement learning algorithm is anytime if it does not need to know in advance the horizon T of the experiment. A well-known technique to obtain an anytime algorithm from any non-anytime algorithm is the "Doubling Trick". In the context of adversarial or stochastic multi-armed bandits, the performance of an algorithm is measured by its regret, and we study two families of sequences of growing horizons (geometric and exponential) to generalize previously known results that certain doubling tricks can be used to conserve certain regret bounds. In a broad setting, we prove that a geometric doubling trick can be used to conserve (minimax) bounds in $R_T = O(\sqrt{T})$ but cannot conserve (distribution-dependent) bounds in $R_T = O(\log T)$. We give insights as to why exponential doubling tricks may be better, as they conserve bounds in $R_T = O(\log T)$, and are close to conserving bounds in $R_T = O(\sqrt{T})$.
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Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-01736357
Contributor : Lilian Besson <>
Submitted on : Monday, March 19, 2018 - 11:51:34 AM
Last modification on : Monday, June 3, 2019 - 11:29:47 AM
Long-term archiving on : Tuesday, September 11, 2018 - 7:04:45 AM

### Files

BK__COLT_2018.pdf
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### Identifiers

• HAL Id : hal-01736357, version 1
• ARXIV : 1803.06971

### Citation

Lilian Besson, Emilie Kaufmann. What Doubling Tricks Can and Can't Do for Multi-Armed Bandits. 2018. ⟨hal-01736357⟩

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