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Paper · 1902.00610 · 2019

On the Optimality of Perturbations in Stochastic and Adversarial Multi-armed Bandit Problems

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 3 functions out of this paper's own repositories and ran 3 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
baekjin-kim/Perturbation-Methods-StochasticMAB canonical 3 of 3
FunctionStatusWhere it lives
reward_generate Ran baekjin-kim/Perturbation-Methods-StochasticMAB/experiments.py
pointer only (licence: NONE) · get_code("6ec138954b1de3c6")
reward_generate Ran baekjin-kim/Perturbation-Methods-StochasticMAB/experiments.py
pointer only (licence: NONE) · get_code("99b6a0fdb71529c7")
reward_generate Ran baekjin-kim/Perturbation-Methods-StochasticMAB/experiments.py
pointer only (licence: NONE) · get_code("95d6a7b81669865c")

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Abstract

We investigate the optimality of perturbation based algorithms in the stochastic and adversarial multi-armed bandit problems. For the stochastic case, we provide a unified regret analysis for both sub-Weibull and bounded perturbations when rewards are sub-Gaussian. Our bounds are instance optimal for sub-Weibull perturbations with parameter 2 that also have a matching lower tail bound, and all bounded support perturbations where there is sufficient probability mass at the extremes of the support. For the adversarial setting, we prove rigorous barriers against two natural solution approaches using tools from discrete choice theory and extreme value theory. Our results suggest that the optimal perturbation, if it exists, will be of Frechet-type.

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