Action dependencies in privacy-preserving multi-agent planning

Abstract

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.

Appendix: Deferred heuristic evaluation and globally preferred operators

In our implementation of MAFS, we used two heuristic techniques that are known to be helpful in single-agent planning. The first technique is deferred heuristic evaluation [31], which means that the heuristic value of a state is computed only when a state is expanded (i.e., when it is extracted from the open list), as oppose to when it is generated (i.e., when inserted into the open list). Newly generated states are inserted into the open list with the heuristic value of their parent—the state that is currently expanded. This is extremely useful in the case of heuristics that require relatively costly computations, which is often the case in single and multi-agent domain independant planning. The benefit of deferred heuristic evaluation specifically for privacy-preserving MA-STRIPS has been established in prior work [23].

Table 8 The percentage of messages sent and states expanded during planning when using the global preferred operators, compared to using the regular preferred operators mechanism

Table 9 Coverage over the CoDMAP domains when using the global preferred operators

The second helpful technique we used is preferred operators [31], which means that we prioritize some actions—referred to as the preferred operators—over others. Which actions we prioritize depend on the specific heuristic being used. For the full DP heuristic, these are the actions that appear in the solution to the DP projection that is computed by the heuristic. For the $DP^{{ FF}}$ heuristic and the Joint FF heuristic, the preferred actions are those that achieve preconditions of actions in the relaxed plan. Following [31], we use two queues, one for states that were generated following a preferred operator, and one for states that were generated using other actions. Priority is given to the preferred operators, expanding more often states from that list.

We implemented a global form of preferred operators, in which an agent expands states from their non-preferred operators list only if all agents report that they do not have states in their preferred operator queue. We implement this by adding to the broadcast messages a flag, notifying other agents whether the sending agent has states in its preferred operator queue. Of course, due to synchronization issues, it is possible that one agent is expanding non-preferred states while another agent has already inserted new states into its preferred operators list. Empirically, however, we observed that this global approach for using preferred operators significantly reduces the number of expanded states, and hence, the number of broadcasted messages and overall coverage.

Table 8 shows the percentage of messages sent and states expanded during planning when using the global preferred operators, compared to using the regular preferred operators mechanism. We can see here that MAFS with the full DP heuristic benefits the most from the global preferred operators. By contrast, Joint FF and $DP^{{ FF}}$ gain less, and in some domains even perform better without the global preferred operators list. This occurs because when using global preferred operators, some agents may be idle waiting for others to expand states from their preferred operators queue. While this is usually worthwhile for the more informed full DP heuristic, it is sometimes not worthwhile for the weaker heuristics.

The use of the global preferred operators in the full DP heuristic also resulted in a much better coverage results, as can be seen in Table 9. Using the global preferred operators, MAFS with the full DP heuristic has the best coverage over all the heuristics that we tried, although still slightly less than the DPP planner. The reason why using global preferred operators has a stronger impact on the full DP heuristic is mainly because planning over the DP projection is relatively costly to planning over the delete relaxation problem, as done by the FF heuristic. Hence, reducing the number of heuristic computations, through reducing the number of state expansions, is most influential for the projection planning approach. Moreover, without the global preferred operators, full DP actually has a lower coverage compared to the other heuristics.