Part of Advances in Neural Information Processing Systems 37 (NeurIPS 2024) Main Conference Track
Guanyu Nie, Vaneet Aggarwal, Christopher Quinn
In this paper, we consider the problem of online monotone DR-submodular maximization subject to long-term stochastic constraints. Specifically, at each round $t\in [T]$, after committing an action $\mathbf{x}_t$, a random reward $f_t(\mathbf{x}_t)$ and an unbiased gradient estimate of the point $\widetilde{\nabla}f_t(\mathbf{x}_t)$ (semi-bandit feedback) are revealed. Meanwhile, a budget of $g_t(\mathbf{x}_t)$, which is linear and stochastic, is consumed of its total allotted budget $B_T$. We propose a gradient ascent based algorithm that achieves $\frac{1}{2}$-regret of $\mathcal{O}(\sqrt{T})$ with $\mathcal{O}(T^{3/4})$ constraint violation with high probability. Moreover, when first-order full-information feedback is available, we propose an algorithm that achieves $(1-1/e)$-regret of $\mathcal{O}(\sqrt{T})$ with $\mathcal{O}(T^{3/4})$ constraint violation. These algorithms significantly improve over the state-of-the-art in terms of query complexity.