Almost Optimal Variance-Constrained Best Arm Identification

Hou, Yunlong; Tan, Vincent Y. F.; Zhong, Zixin

doi:10.1109/tit.2022.3222231

Cited by 3 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Under the risk-constrained pure exploration framework, Hou et al (2023) and David et al (2018) attempted to identify the optimal arm within those low-risk (based on their variances or α-quantiles) arms with probability at least 1 − δ.…”

Section: Introductionmentioning

confidence: 99%

Probably Anytime-Safe Stochastic Combinatorial Semi-Bandits

Hou¹,

Tan²,

Zhong³

2023

Preprint

View full text Add to dashboard Cite

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1 − δ, over the entire horizon of time T , each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm PASCOMBUCB that minimizes the regret over the horizon of time T . By developing accompanying information-theoretic lower bounds, we show under both the problem-dependent and problem-independent paradigms, PASCOMBUCB is almost asymptotically optimal. Our problem setup, the proposed PASCOMBUCB algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.Literature review. There is a large body of works that take risk into account while conducting the exploration and/or

show abstract

Section: Introductionmentioning

confidence: 99%