Weighted Linear Bandits for Non-Stationary Environments

Yoan Russac 1, 2 Claire Vernade 3 Olivier Cappé 1, 2
2 VALDA - Value from Data
DI-ENS - Département d'informatique de l'École normale supérieure, Inria de Paris
Abstract : We consider a stochastic linear bandit model in which the available actions correspond to arbitrary context vectors whose associated rewards follow a non-stationary linear regression model. In this setting, the unknown regression parameter is allowed to vary in time. To address this problem, we propose D-LinUCB, a novel optimistic algorithm based on discounted linear regression, where exponential weights are used to smoothly forget the past. This involves studying the deviations of the sequential weighted least-squares estimator under generic assumptions. As a by-product, we obtain novel deviation results that can be used beyond non-stationary environments. We provide theoretical guarantees on the behavior of D-LinUCB in both slowly-varying and abruptly-changing environments. We obtain an upper bound on the dynamic regret that is of order d^{2/3} B_T^{1/3}T^{2/3}, where B_T is a measure of non-stationarity (d and T being, respectively, dimension and horizon). This rate is known to be optimal. We also illustrate the empirical performance of D-LinUCB and compare it with recently proposed alternatives in simulated environments.
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Submitted on : Wednesday, September 18, 2019 - 7:35:07 PM
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  • HAL Id : hal-02291460, version 1
  • ARXIV : 1909.09146

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Yoan Russac, Claire Vernade, Olivier Cappé. Weighted Linear Bandits for Non-Stationary Environments. NeurIPS 2019 - 33rd Conference on Neural Information Processing Systems, Dec 2019, Vancouver, Canada. ⟨hal-02291460⟩

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