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This content will become publicly available on June 27, 2024

Title: Stochastic Contextual Bandits with Long Horizon Rewards
The growing interest in complex decision-making and language modeling problems highlights the importance of sample-efficient learning over very long horizons. This work takes a step in this direction by investigating contextual linear bandits where the current reward depends on at most s prior actions and contexts (not necessarily consecutive), up to a time horizon of h. In order to avoid polynomial dependence on h, we propose new algorithms that leverage sparsity to discover the dependence pattern and arm parameters jointly. We consider both the data-poor (T= h) regimes and derive respective regret upper bounds O(d square-root(sT) +min(q, T) and O( square-root(sdT) ), with sparsity s, feature dimension d, total time horizon T, and q that is adaptive to the reward dependence pattern. Complementing upper bounds, we also show that learning over a single trajectory brings inherent challenges: While the dependence pattern and arm parameters form a rank-1 matrix, circulant matrices are not isometric over rank-1 manifolds and sample complexity indeed benefits from the sparse reward dependence structure. Our results necessitate a new analysis to address long-range temporal dependencies across data and avoid polynomial dependence on the reward horizon h. Specifically, we utilize connections to the restricted isometry property of circulant matrices formed by dependent sub-Gaussian vectors and establish new guarantees that are also of independent interest.  more » « less
Award ID(s):
2023166 2007036
NSF-PAR ID:
10443285
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Proceedings of the AAAI Conference on Artificial Intelligence
Volume:
37
Issue:
8
ISSN:
2159-5399
Page Range / eLocation ID:
9525 to 9533
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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