${\upvarepsilon }$-Strong Privacy Preserving Multi-agent Planning

Abstract

Multi-agent planning can solve various sequential decision problems comprising multiple entities. In contrast to classical planning, the agents are interested in maintaining privacy while planning with each other. Therefore they have to reason about what information they can share. Although privacy is one of the crucial aspects of multi-agent planning, formal and algorithmic treatment of privacy is rather sparse in literature. No domain-independent strong privacy preserving multi-agent planner was proposed so far. Moreover, our recent results indicate that an efficient variant of such planner may not exist at all. Such strong privacy preserving planner would not allow to leak any private information during planning neither directly nor indirectly. Especially the indirect leakage is hard to assess as it can be based on any possible deduction principle from the non-private information along the planning process.

Here, we propose a refined version of a multi-agent planning principle, based on our previous work published as the conference version of this paper. The planning principle is designed so that it can get arbitrarily close to the general strong privacy preserving planning for the price of decreased planning efficiency. We have tighten the bounds on the privacy leakage and proved the strong privacy can be achieved by a finite number of additional plans, in contrast to the previous algorithm, where the number had to be infinite in general. We newly illustrate the principle on an additional synthetic planning problem, which shows the general privacy leakage upper bound. As in the previous variant of the algorithm, the strong privacy assurances are under computational tractability assumptions commonly used in secure computation research.