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We investigate the problem of unconstrained combinatorial multi-armed bandits with full-bandit feedback and stochastic rewards for submodular maximization. Previous works investigate the same problem assuming a submodular and monotone reward function. In this work, we study a more general problem, i.e., when the reward function is not necessarily monotone, and the submodularity is assumed only in expectation. We propose Randomized Greedy Learning (RGL) algorithm and theoretically prove that it achieves a $$\frac{1}{2}$$-regret upper bound of $$\Tilde{\mathcal{O}}(n T^{\frac{2}{3}})$$ for horizon $$T$$ and number of arms $$n$$. We also show in experiments that RGL empirically outperforms other full-bandit variants in submodular and non-submodular settings.
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Variance-aware Regret Bounds for Stochastic Contextual Dueling Bandits
Dueling bandits is a prominent framework for decision-making involving preferential feedback, a valuable feature that fits various applications involving human interaction, such as ranking, information retrieval, and recommendation systems. While substantial efforts have been made to minimize the cumulative regret in dueling bandits, a notable gap in the current research is the absence of regret bounds that account for the inherent uncertainty in pairwise comparisons between the dueling arms. Intuitively, greater uncertainty suggests a higher level of difficulty in the problem. To bridge this gap, this paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM). We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound $$\tilde O\big(d\sqrt{\sum_{t=1}^T\sigma_t^2} + d\big)$$, where $$\sigma_t$$ is the variance of the pairwise comparison in round $$t$$, $$d$$ is the dimension of the context vectors, and $$T$$ is the time horizon. Our regret bound naturally aligns with the intuitive expectation in scenarios where the comparison is deterministic, the algorithm only suffers from an $$\tilde O(d)$$ regret. We perform empirical experiments on synthetic data to confirm the advantage of our method over previous variance-agnostic algorithms.
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- Award ID(s):
- 1908544
- PAR ID:
- 10583755
- Publisher / Repository:
- ICLR
- Date Published:
- Format(s):
- Medium: X
- Location:
- Vienna, Austria
- Sponsoring Org:
- National Science Foundation
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