Distributed Differential Privacy in Multi-Armed Bandits
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We consider the standard K-armed bandit problem under a distributed trust model of differential privacy (DP), which enables to guarantee privacy without a trustworthy server. Under this trust model, previous work largely focus on achieving privacy using a shuffle protocol, where a batch of users data are randomly permuted before sending to a central server. This protocol achieves (ϵ,δ) or approximate-DP guarantee by sacrificing an additional additive O(Klog T√(log(1/δ))/ϵ) cost in T-step cumulative regret. In contrast, the optimal privacy cost for achieving a stronger (ϵ,0) or pure-DP guarantee under the widely used central trust model is only Θ(Klog T/ϵ), where, however, a trusted server is required. In this work, we aim to obtain a pure-DP guarantee under distributed trust model while sacrificing no more regret than that under central trust model. We achieve this by designing a generic bandit algorithm based on successive arm elimination, where privacy is guaranteed by corrupting rewards with an equivalent discrete Laplace noise ensured by a secure computation protocol. We also show that our algorithm, when instantiated with Skellam noise and the secure protocol, ensures Rényi differential privacy – a stronger notion than approximate DP – under distributed trust model with a privacy cost of O(K√(log T)/ϵ).
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