Differential Privacy in the Extensive-Form Bandit Problem

TL;DR

This paper introduces a differentially private algorithm for the extensive-form bandit problem, achieving low regret while preserving local differential privacy, a novel contribution in this domain.

Contribution

It presents the first study of differential privacy in the extensive-form bandit setting, with an algorithm that balances privacy, regret, and computational efficiency.

Findings

Achieves regret of O(\u221a{A \u22ef (S) T}/) under -local differential privacy.

Algorithm's time complexity is comparable to transmitting the reduced strategy.

First work to address differential privacy in the extensive-form bandit problem.

Abstract

We consider the extensive-form bandit problem, where on each trial the learner (a user coordinated by a server) plays an extensive-form game against an oblivious adversary, observing the information sets it finds itself in as well as the resulting payoff/loss. We give an algorithm for this problem that satisfies $\epsilon$-local differential privacy and attains a regret of $\tilde{O}(\sqrt{A\ln(S)T}/\epsilon)$, where $A$ is the total number of actions that the learner can possibly take, $S$ is the number of the learner's possible reduced strategies, and $T$ is the number of trials. On each trial, the time complexity of our algorithm is, up to a factor logarithmic in the maximum number of actions at an infoset, equal to the time required for the server to transmit the reduced strategy to the user. We note that local differential privacy is the strongest version of differential privacy and, to the best of our knowledge, this is the first work to study differential privacy of any form in the extensive-form bandit problem.