Quantifying privacy in multiagent planning

Abstract

Privacy is often cited as the main reason to adopt a multiagent approach for a certain problem. This also holds true for multiagent planning. Still, a metric to evaluate the privacy performance of planners is virtually non-existent. This makes it hard to compare dierent algorithms on their performance with regards to privacy. Moreover, it prevents multiagent planning methods from being designed specically for this aspect. This paper introduces such a measure for privacy. It is based on Shannon's theory of information and revolves around counting the number of alternative plans that are consistent with information that is gained during, for example, a negotiation step, or the complete planning episode. To accurately obtain this measure, one should have intimate knowledge of the agent's domain. It is unlikely (although not impossible) that an opponent who learns some information on a target agent has this knowledge. Therefore, it is not meant to be used by an opponent to understand how much he has learned. Instead, the measure is aimed at agents who want to know how much privacy they have given up, or are about to give up, in the planning process. They can then use this to decide whether or not to engage in a proposed negotiation, or to limit the options they are willing to negotiate upon.

Efficient approaches for multi-agent planning

“…We assume that both the complete initial state, I = ∪ m i=1 I i , and set of goals, G = ∪ m i=1 G i are consistent; that is, they are conflict-free (there are no mutex). In other MAP approaches, they allow conflicts among goals [70].…”

“…A related question is how much privacy we are loosing by sharing obfuscated augmented plans among agents. One alternative would be to use the approach proposed by van der Krogt [70], where he proposes to measure the loss of privacy using Shannon information theory. They propose to take into account the number of plans that could potentially be generated, and the number of plans that each agent observed.…”

FMAP: Distributed cooperative multi-agent planning

“…Besides the need for computational or information distribution, privacy is also one of the reasons to adopt a multi-agent approach. This aspect, however, has been traditionally relegated in MAP, particularly by the planning community [21]. While some approaches define a basic notion of privacy [2,25], others allow agents to share detailed parts of their plans or do not take private information into account at all [22].…”