Online Linear Optimization with Sparsity Constraints

We study the problem of online linear optimization with sparsity constraints in the 1 semi-bandit setting. It can be seen as a marriage between two well-known problems: 2 the online linear optimization problem and the combinatorial bandit problem. For 3 this problem, we provide two algorithms which are efficient and achieve sublinear 4 regret bounds. Moreover, we extend our results to two generalized settings, one 5 with delayed feedbacks and one with costs for receiving feedbacks. Finally, we 6 conduct experiments which show the effectiveness of our methods in practice. 7