2024-06-30-guo24a.md

title	section	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Stochastic Constrained Contextual Bandits via Lyapunov Optimization Based Estimation to Decision Framework	Original Papers	This paper studies the problem of stochastic constrained contextual bandits (CCB) under general realizability condition where the expected rewards and costs are within general function classes. We propose LOE2D, a Lyapunov Optimization Based Estimation to Decision framework with online regression oracles for learning reward/constraint. LOE2D establishes $\Tilde O(T^{\frac{3}{4}}U^{\frac{1}{4}})$ regret and constraint violation, which can be further refined to $\Tilde O(\min\{\sqrt{TU}/\varepsilon^2, T^{\frac{3}{4}}U^{\frac{1}{4}}\})$ when the Slater condition holds in the underlying offline problem with the Slater “constant” $ \varepsilon=\Omega(\sqrt{U/T}),$ where $U$ denotes the error bounds of online regression oracles. These results improve LagrangeCBwLC in two aspects: i) our results hold without any prior information while LagrangeCBwLC requires the knowledge of Slater constant to design a proper learning rate; ii) our results hold when $\varepsilon=\Omega(\sqrt{U/T})$ while LagrangeCBwLC requires a constant margin $\varepsilon=\Omega(1).$ These improvements stem from two novel techniques: violation-adaptive learning in E2D module and multi-step Lyapunov drift analysis in bounding constraint violation. The experiments further justify LOE2D outperforms the baseline algorithm.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	guo24a	0	Stochastic Constrained Contextual Bandits via Lyapunov Optimization Based Estimation to Decision Framework	2204	2231	2204-2231	2204	false	Guo, Hengquan and Liu, Xin	given family Hengquan Guo given family Xin Liu	2024-06-30		Proceedings of Thirty Seventh Conference on Learning Theory	247	inproceedings	date-parts 2024 6 30	https://proceedings.mlr.press/v247/guo24a/guo24a.pdf