# Stochastic Submodular Bandits with Delayed Composite Anonymous Bandit Feedback

arXiv: https://arxiv.org/abs/2303.13604 · HTML: https://mlsanity.com/paper/2303.13604/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 23 Mar 2023.

## Builds on (most cited first, 10 of 10)

- [Online Learning under Delayed Feedback](https://mlsanity.com/paper/1306.0686/) (2013)
- [Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization](https://mlsanity.com/paper/2102.11050/) (2021)
- [Online Continuous Submodular Maximization: From Full-Information to Bandit Feedback](https://mlsanity.com/paper/1910.12424/) (2019)
- [Projection-Free Online Optimization with Stochastic Gradient: From Convexity to Submodularity](https://mlsanity.com/paper/1802.08183/) (2018)
- [Top-k Combinatorial Bandits with Full-Bandit Feedback](https://mlsanity.com/paper/1905.12624/) (2019)
- [A Framework for Adapting Offline Algorithms to Solve Combinatorial Multi-Armed Bandit Problems with Bandit Feedback](https://mlsanity.com/paper/2301.13326/) (2023)
- [Nonstochastic Bandits with Composite Anonymous Feedback](https://mlsanity.com/paper/2112.02866/) (2021)
- [Submodular Bandit Problem Under Multiple Constraints](https://mlsanity.com/paper/2006.00661/) (2020)
- [Adaptive Algorithms for Multi-armed Bandit with Composite and Anonymous Feedback](https://mlsanity.com/paper/2012.07048/) (2020)
- [Stochastic Bandits with Delayed Composite Anonymous Feedback](https://mlsanity.com/paper/1910.01161/) (2019)

## Built on by (most cited first, 2 of 2)

- [Nearly Minimax Optimal Submodular Maximization with Bandit Feedback](https://mlsanity.com/paper/2310.18465/) (2023)
- [Reinforcement Learning with Delayed, Composite, and Partially Anonymous Reward](https://mlsanity.com/paper/2305.02527/) (2023)

## Abstract (arXiv)

This paper investigates the problem of combinatorial multiarmed bandits with stochastic submodular (in expectation) rewards and full-bandit delayed feedback, where the delayed feedback is assumed to be composite and anonymous. In other words, the delayed feedback is composed of components of rewards from past actions, with unknown division among the sub-components. Three models of delayed feedback: bounded adversarial, stochastic independent, and stochastic conditionally independent are studied, and regret bounds are derived for each of the delay models. Ignoring the problem dependent parameters, we show that regret bound for all the delay models is tildeO(T2/3 + T1/3 nu) for time horizon T, where nu is a delay parameter defined differently in the three cases, thus demonstrating an additive term in regret with delay in all the three delay models. The considered algorithm is demonstrated to outperform other full-bandit approaches with delayed composite anonymous feedback.