Guanyu Nie

Guanyu Nie, Yididiya Y Nadew, Yanhui Zhu et al.

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear $α$-regret methods that only require bandit feedback, achieving $\mathcal{O}\left(T^\frac{2}{3}\log(T)^\frac{1}{3}\right)$ expected cumulative $α$-regret dependence on the horizon $T$. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as a black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to diverse applications in submodular maximization. The new CMAB algorithms for submodular maximization with knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

Guanyu Nie, Vaneet Aggarwal, Christopher John Quinn

In this paper, we present the first sublinear $α$-regret bounds for online $k$-submodular optimization problems with full-bandit feedback, where $α$ is a corresponding offline approximation ratio. Specifically, we propose online algorithms for multiple $k$-submodular stochastic combinatorial multi-armed bandit problems, including (i) monotone functions and individual size constraints, (ii) monotone functions with matroid constraints, (iii) non-monotone functions with matroid constraints, (iv) non-monotone functions without constraints, and (v) monotone functions without constraints. We transform approximation algorithms for offline $k$-submodular maximization problems into online algorithms through the offline-to-online framework proposed by Nie et al. (2023a). A key contribution of our work is analyzing the robustness of the offline algorithms.