• Corpus ID: 252567818

Online Subset Selection using $\alpha$-Core with no Augmented Regret

@inproceedings{Sahoo2022OnlineSS,
  title={Online Subset Selection using \$\alpha\$-Core with no Augmented Regret},
  author={Sourav Sahoo and Samrat Mukhopadhyay and Abhishek Sinha},
  year={2022}
}

• Sourav Sahoo, S. Mukhopadhyay, Abhishek Sinha
• Published 28 September 2022
• Computer Science

We consider the problem of sequential sparse subset selections in an online learning setup. Assume that the set [ N ] consists of N distinct elements. On the t th round, a monotone reward function f t : 2 [ N ] → R + , which assigns a non-negative reward to each subset of [ N ] , is revealed to a learner. The learner selects (perhaps randomly) a subset S t ⊆ [ N ] of k elements before the reward function f t for that round is revealed ( k ≤ N ) . As a consequence of its choice, the learner receives a reward of f t ( S t ) on the t th round. The learner’s goal is to design an online subset selection policy to maximize its expected cumulative reward accrued over a given time horizon. In this connection, we propose an online learning policy called SC ORE ( S ubset Selection with Core ) that solves the problem for a large class of reward functions. The proposed SC ORE policy is based on a new concept of α - C ORE , which is a generalization of the notion of Core from the cooperative game theory literature. We establish a learning guarantee for the SC ORE policy in terms of a new performance metric called α - augmented regret . In this new metric, the power of the offline benchmark is suitably augmented compared to the online policy. We give several illustrative examples to show that a broad class of reward functions, including submodular, can be efficiently learned with the SC ORE policy. We also outline how the SC ORE policy can be used under a semi-bandit feedback model and conclude the paper with a number of open problems.