When Privacy Meets Partial Information: A Refined Analysis of Differentially Private Bandits

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Achraf Azize, Debabrota Basu


We study the problem of multi-armed bandits with ε-global Differential Privacy (DP). First, we prove the minimax and problem-dependent regret lower bounds for stochastic and linear bandits that quantify the hardness of bandits with ε-global DP. These bounds suggest the existence of two hardness regimes depending on the privacy budget ε. In the high-privacy regime (small ε), the hardness depends on a coupled effect of privacy and partial information about the reward distributions. In the low-privacy regime (large ε), bandits with ε-global DP are not harder than the bandits without privacy. For stochastic bandits, we further propose a generic framework to design a near-optimal ε global DP extension of an index-based optimistic bandit algorithm. The framework consists of three ingredients: the Laplace mechanism, arm-dependent adaptive episodes, and usage of only the rewards collected in the last episode for computing private statistics. Specifically, we instantiate ε-global DP extensions of UCB and KL-UCB algorithms, namely AdaP-UCB and AdaP-KLUCB. AdaP-KLUCB is the first algorithm that both satisfies ε-global DP and yields a regret upper bound that matches the problem-dependent lower bound up to multiplicative constants.