Why is there no upper confidence bound algorithm for linear stochastic bandits that uses lasso regression in the case that the regression parameters are sparse in the features?
In particular, I don't understand what is hard about lasso regression that makes it hard to be used in a UCB type algorithm whereas there is a lot of work on ridge regression based UCB algorithms see e.g. Yadkori et al.
I looked up some works e.g. Bastani and Bayati, Kim and Paik but they all do not a UCB-type algorithm, instead, they propose forced or probabilistic sampling to satisfy the compatibility condition (see Lemma EC.6. of Bastani and Bayati).
