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This paper addresses online combinatorial optimization where the set of available actions stochastically varies over time. They introduce a novel loss estimation technique called "Counting Asleep Times" to handle unreliable composite actions. The proposed Follow-The-Perturbed-Leader-based algorithms achieve improved regret bounds in full information, semi-bandit, and a novel restricted information setting, and empirically outperform existing approaches.
Stochastic action availability doesn't have to hamstring online learning: "Counting Asleep Times" unlocks improved regret bounds in combinatorial settings.
Most work on sequential learning assumes a fixed set of actions that are available all the time. However, in practice, actions can consist of picking subsets of readings from sensors that may break from time to time, road segments that can be blocked or goods that are out of stock. In this paper we study learning algorithms that are able to deal with stochastic availability of such unreliable composite actions. We propose and analyze algorithms based on the Follow-The-Perturbed-Leader prediction method for several learning settings differing in the feedback provided to the learner. Our algorithms rely on a novel loss estimation technique that we call Counting Asleep Times. We deliver regret bounds for our algorithms for the previously studied full information and (semi-)bandit settings, as well as a natural middle point between the two that we call the restricted information setting. A special consequence of our results is a significant improvement of the best known performance guarantees achieved by an efficient algorithm for the sleeping bandit problem with stochastic availability. Finally, we evaluate our algorithms empirically and show their improvement over the known approaches.
