Action dependencies in privacy-preserving multi-agent planning

Collaborative privacy-preserving planning (CPPP) is a multi-agent planning task in which agents need to achieve a common set of goals without revealing certain private information. In many CPPP algorithms, the individual agents reason about a projection of the multi-agent problem onto a single-agent classical planning problem. For example, an agent can plan as if it controls the public actions of other agents, ignoring any private preconditions and effects theses actions may have, and use the cost of this plan as a heuristic estimate of the cost of the full, multi-agent plan. Using such a projection, however, ignores some dependencies between agents' public actions. In particular, it does not contain dependencies between public actions of other agents caused by their private facts. We propose a projection in which these private dependencies are maintained. The benefit of our dependency-preserving projection is demonstrated by using it to produce high-level plans in a new privacy-preserving planner, and as a heuristic for guiding forward search privacy-preserving algorithms. Both are able to solve more benchmark problems than any other state-of-the-art privacy-preserving planner. This more informed projection does not explicitly expose any private fact, action, or precondition. In addition, we show that even if an adversary agent knows that an agent has some private objects of a given type (e.g., trucks), it cannot infer the number of such private objects that the agent controls. This introduces a novel form of strong privacy, which we call object-cardinality privacy, that is motivated by real-world requirements.