Thresholded Lasso Bandit

22 Oct 2020  ·  Kaito Ariu, Kenshi Abe, Alexandre Proutière ·

In this paper, we revisit the regret minimization problem in sparse stochastic contextual linear bandits, where feature vectors may be of large dimension $d$, but where the reward function depends on a few, say $s_0\ll d$, of these features only. We present Thresholded Lasso bandit, an algorithm that (i) estimates the vector defining the reward function as well as its sparse support, i.e., significant feature elements, using the Lasso framework with thresholding, and (ii) selects an arm greedily according to this estimate projected on its support. The algorithm does not require prior knowledge of the sparsity index $s_0$ and can be parameter-free under some symmetric assumptions. For this simple algorithm, we establish non-asymptotic regret upper bounds scaling as $\mathcal{O}( \log d + \sqrt{T} )$ in general, and as $\mathcal{O}( \log d + \log T)$ under the so-called margin condition (a probabilistic condition on the separation of the arm rewards). The regret of previous algorithms scales as $\mathcal{O}( \log d + \sqrt{T \log (d T)})$ and $\mathcal{O}( \log T \log d)$ in the two settings, respectively. Through numerical experiments, we confirm that our algorithm outperforms existing methods.

PDF Abstract

Datasets


  Add Datasets introduced or used in this paper

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods


No methods listed for this paper. Add relevant methods here