
Exploiting Correlation in FiniteArmed Structured Bandits
We consider a correlated multiarmed bandit problem in which rewards of ...
read it

Forcedexploration free Strategies for Unimodal Bandits
We consider a multiarmed bandit problem specified by a set of Gaussian ...
read it

Structure Adaptive Algorithms for Stochastic Bandits
We study reward maximisation in a wide class of structured stochastic mu...
read it

An Optimal Algorithm for Linear Bandits
We provide the first algorithm for online bandit linear optimization who...
read it

Almost Boltzmann Exploration
Boltzmann exploration is widely used in reinforcement learning to provid...
read it

DiversityPreserving KArmed Bandits, Revisited
We consider the banditbased framework for diversitypreserving recommen...
read it
Optimal Strategies for GraphStructured Bandits
We study a structured variant of the multiarmed bandit problem specified by a set of Bernoulli distributions ν= (ν_a,b)_a ∈𝒜, b ∈ℬ with means (μ_a,b)_a ∈𝒜, b ∈ℬ∈[0,1]^𝒜×ℬ and by a given weight matrix ω= (ω_b,b')_b,b' ∈ℬ, where 𝒜 is a finite set of arms and ℬ is a finite set of users. The weight matrix ω is such that for any two users b,b'∈ℬ, max_a∈𝒜μ_a,bμ_a,b' ≤ω_b,b'. This formulation is flexible enough to capture various situations, from highlystructured scenarios (ω∈{0,1}^ℬ×ℬ) to fully unstructured setups (ω≡ 1).We consider two scenarios depending on whether the learner chooses only the actions to sample rewards from or both users and actions. We first derive problemdependent lower bounds on the regret for this generic graphstructure that involves a structure dependent linear programming problem. Second, we adapt to this setting the Indexed Minimum Empirical Divergence (IMED) algorithm introduced by Honda and Takemura (2015), and introduce the IMEDGS^⋆ algorithm. Interestingly, IMEDGS^⋆ does not require computing the solution of the linear programming problem more than about log(T) times after T steps, while being provably asymptotically optimal. Also, unlike existing bandit strategies designed for other popular structures, IMEDGS^⋆ does not resort to an explicit forced exploration scheme and only makes use of local counts of empirical events. We finally provide numerical illustration of our results that confirm the performance of IMEDGS^⋆.
READ FULL TEXT
Comments
There are no comments yet.