More Like this

1. Randomized Greedy Learning for Non-monotone Stochastic Submodular Maximization Under Full-bandit Feedback

   Fares Fourati, Vaneet Aggarwal (January 2023, Proceedings of Machine Learning Research)

   We investigate the problem of unconstrained combinatorial multi-armed bandits with fullbandit 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 1 2 -regret upper bound of O˜(nT 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. 

   more » « less
2. An explore-then-commit algorithm for submodular maximization under full-bandit feedback

   Nie, Guanyu; Agarwal, Mridul; Umrawal, Abhishek Kumar; Aggarwal, Vaneet; Quinn, Christopher John (January 2022, Uncertainty in Artificial Intelligence)

   Cussens, James; Zhang, Kun (Ed.)

   We investigate the problem of combinatorial multi-armed bandits with stochastic submodular (in expectation) rewards and full-bandit feedback, where no extra information other than the reward of selected action at each time step $$t$$ is observed. We propose a simple algorithm, Explore-Then-Commit Greedy (ETCG) and prove that it achieves a $(1-1/e)$-regret upper bound of $$\mathcal{O}(n^\frac{1}{3}k^\frac{4}{3}T^\frac{2}{3}\log(T)^\frac{1}{2})$$ for a horizon $$T$$, number of base elements $$n$$, and cardinality constraint $$k$$. We also show in experiments with synthetic and real-world data that the ETCG empirically outperforms other full-bandit methods. 

   more » « less
3. Gradient Methods for Online DR-Submodular Maximization with Stochastic Long-Term Constraints

   Nie, Guanyu; Aggarwal, Vaneet; Quinn, Christopher John (December 2024, The Thirty-Eighth Annual Conference on Neural Information Processing Systems)

   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 $$\bx_t$$, a random reward $$f_t(\bx_t)$$ and an unbiased gradient estimate of the point $$\widetilde{\nabla}f_t(\bx_t)$$ (semi-bandit feedback) are revealed. Meanwhile, a budget of $$g_t(\bx_t)$$, 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. 

   more » « less
4. Combinatorial Stochastic-Greedy Bandit

   https://doi.org/10.1609/aaai.v38i11.29093  

   Fourati, Fares; Quinn, Christopher John; Alouini, Mohamed-Slim; Aggarwal, Vaneet (March 2024, Proceedings of the AAAI Conference on Artificial Intelligence)

   We propose a novel combinatorial stochastic-greedy bandit (SGB) algorithm for combinatorial multi-armed bandit problems when no extra information other than the joint reward of the selected set of n arms at each time step t in [T] is observed. SGB adopts an optimized stochastic-explore-then-commit approach and is specifically designed for scenarios with a large set of base arms. Unlike existing methods that explore the entire set of unselected base arms during each selection step, our SGB algorithm samples only an optimized proportion of unselected arms and selects actions from this subset. We prove that our algorithm achieves a (1-1/e)-regret bound of O(n^(1/3) k^(2/3) T^(2/3) log(T)^(2/3)) for monotone stochastic submodular rewards, which outperforms the state-of-the-art in terms of the cardinality constraint k. Furthermore, we empirically evaluate the performance of our algorithm in the context of online constrained social influence maximization. Our results demonstrate that our proposed approach consistently outperforms the other algorithms, increasing the performance gap as k grows. 

   more » « less
5. An Explore-then-Commit Algorithm for Submodular Maximization Under Full-bandit Feedback

   Guanyu Nie, Mridul Agarwal (January 2022, Uncertainty in artificial intelligence)

   We investigate the problem of combinatorial multi-armed bandits with stochastic submodular (in expectation) rewards and full-bandit feedback, where no extra information other than the reward of selected action at each time step is observed. We propose a simple algorithm, Explore-Then-Commit Greedy (ETCG) and prove that it achieves a -regret upper bound of for a horizon , number of base elements , and cardinality constraint . We also show in experiments with synthetic and real-world data that the ETCG empirically outperforms other full-bandit methods. 

   more » « less