2025/04/23 by Arghavan Zibaie, Spencer Hutchinson, Zibaie, Arghavan +5
Decision Sciences · #Advanced Bandit Algorithms Research #Differential privacy #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Measure (data warehouse) #Optimization and Control (math.OC) #Order (exchange) #Probability measure #Regret #Set (abstract data type)
paper · pdf · doi:10.48550/arxiv.2504.16371
openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/08/05
We consider a collection of linear stochastic bandit problems, each modeling the random response of different agents to proposed interventions, coupled together by a global safety constraint. We assume a central coordinator must choose actions to play on each bandit with the objective of regret minimization, while also ensuring that the expected response of all agents satisfies the global safety constraints at each round, in spite of uncertainty about the bandits' parameters. The agents consider their observed responses to be private and in order to protect their sensitive information, the data sharing with the central coordinator is performed under local differential privacy (LDP). However, providing higher level of privacy to different agents would have consequences in terms of safety and regret. We formalize these tradeoffs by building on the notion of the sharpness of the safety set - a measure of how the geometric properties of the safe set affects the growth of regret - and propose a unilaterally unimprovable vector of privacy levels for different agents given a maximum regret budget.