The Safety-Privacy Tradeoff in Linear Bandits
This work addresses the tradeoff between safety and privacy in multi-agent bandit systems, which is an incremental contribution to the field of online learning with constraints.
The paper tackles the problem of balancing safety constraints and privacy in linear bandit settings, where a central coordinator minimizes regret while ensuring global safety and protecting agent data with local differential privacy, and it formalizes tradeoffs by analyzing the safety set's sharpness to propose optimal privacy levels given a regret budget.
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.