Adaptive Algorithms for Multi-armed Bandit with Composite and Anonymous Feedback
This work is significant for researchers and practitioners in multi-armed bandit problems, particularly when the reward interval is unknown, by providing algorithms that do not require prior knowledge of this parameter.
This paper addresses the multi-armed bandit problem where rewards are composite and anonymous, spreading over an unknown reward interval. The authors propose adaptive algorithms for both stochastic and adversarial scenarios, achieving regret bounds that match lower bounds for the stochastic case and outperforming existing benchmarks in simulations.
We study the multi-armed bandit (MAB) problem with composite and anonymous feedback. In this model, the reward of pulling an arm spreads over a period of time (we call this period as reward interval) and the player receives partial rewards of the action, convoluted with rewards from pulling other arms, successively. Existing results on this model require prior knowledge about the reward interval size as an input to their algorithms. In this paper, we propose adaptive algorithms for both the stochastic and the adversarial cases, without requiring any prior information about the reward interval. For the stochastic case, we prove that our algorithm guarantees a regret that matches the lower bounds (in order). For the adversarial case, we propose the first algorithm to jointly handle non-oblivious adversary and unknown reward interval size. We also conduct simulations based on real-world dataset. The results show that our algorithms outperform existing benchmarks.