The greedy algorithm is extensively studied in the field of combinatorial optimization for decades. In this paper, we address the online learning problem when the input to the greedy algorithm is stochastic with unknown parameters that have to be learned over time. We first propose the greedy regret and $\epsilon$-quasi greedy regret as learning metrics comparing with the performance of offline greedy algorithm. We then propose two online greedy learning algorithms with semi-bandit feedbacks, which use multi-armed bandit and pure exploration bandit policies at each level of greedy learning, one for each of the regret metrics respectively. Both algorithms achieve $O(\log T)$ problem-dependent regret bound ($T$ being the time horizon) for a general class of combinatorial structures and reward functions that allow greedy solutions. We further show that the bound is tight in $T$ and other problem instance parameters.

We study the online influence maximization problem in social networks under the independent cascade model. Specifically, we aim to learn the set of "best

To help address these issues, a natural approach is to consider games with special structures. In this paper, we focus on congestion games.

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This paper investigates stochastic and adversarial combinatorial multi-armed bandit problems. In the stochastic setting under semi-bandit feedback, we derive a problem-specific regret lower bound, and discuss its scaling with the dimension of the decision space. We propose ESCB, an algorithm that efficiently exploits the structure of the problem and provide a finite-time analysis of its regret. ESCB has better performance guarantees than existing algorithms, and significantly outperforms these algorithms in practice.

After each decision to choose a particular arm, the learner receives some form of feedback - typically a numerical reward - determined by a feedback mechanism of the chosen arm.

To help address these issues, a natural approach is to consider games with special structures. In this paper, we focus on congestion games.

To help address these issues, a natural approach is to consider games with special structures. In this paper, we focus on congestion games.

Adversarial online learning is a well-studied framework for sequential decision making with numerous applications.