[Paper Review] Finding plans subject to stipulations on what information they divulge

Yulin Zhang, Dylan A. Shell+1 more|arXiv (Cornell University)|Sep 25, 2018

Optimization and Search Problems10 references4 citations

TL;DR

This paper proposes a novel framework for robot planning under privacy constraints, where a robot must execute a task while strategically controlling what information it reveals to an observer. It introduces a joint synthesis of plans and disclosure policies using procrustean graphs and a worst-case observer model, ensuring sensitive information (e.g., facility type) remains hidden while still achieving task goals.

ABSTRACT

Motivated by applications where privacy is important, we consider planning problems for robots acting in the presence of an observer. We first formulate and then solve planning problems subject to stipulations on the information divulged during plan execution --- the appropriate solution concept being both a plan and an information disclosure policy. We pose this class of problem under a worst-case model within the framework of procrustean graphs, formulating the disclosure policy as a particular type of map on edge labels. We devise algorithms that, given a planning problem supplemented with an information stipulation, can find a plan, associated disclosure policy, or both if some exists. Both the plan and associated disclosure policy may depend subtlety on additional information available to the observer, such as whether the observer knows the robot's plan (e.g., leaked via a side-channel). Our implementation finds a plan and a suitable disclosure policy, jointly, when any such pair exists, albeit for small problem instances.

Motivation & Objective

• To address privacy concerns in robot applications where sensitive information may be leaked through actions, observations, or state disclosures.
• To formalize planning under stipulations that require certain information to be revealed (e.g., task-relevant data) and other information to be concealed (e.g., facility type).
• To develop a joint synthesis method that computes both a valid plan and a disclosure policy that satisfies the stipulated privacy constraints.
• To model the observer’s knowledge using a worst-case inference model, ensuring that even an adversarial observer cannot deduce sensitive information.
• To implement and evaluate the approach on small-scale problems, demonstrating feasibility despite high computational complexity.

Proposed method

• Formalizes the planning problem using procrustean graphs, where edges are labeled with actions and observations, and a disclosure policy is modeled as a partial label map on edge labels.
• Introduces a worst-case observer model that infers the robot’s state based on the history of observed labels, ensuring privacy by limiting what the observer can deduce.
• Uses a hybrid and–or search algorithm to explore plan and policy combinations, with pruning based on safe partitions of observations that preserve privacy constraints.
• Employs a recursive tree expansion strategy: action vertices are expanded by considering all possible action choices and observation partitions, while observation vertices are expanded based on possible label mappings.
• Computes the disclosure policy as a map that groups actions and observations such that sensitive distinctions (e.g., facility type) are obscured from the observer.
• Implements the algorithm in Python and validates it using both custom search and model checking via nuXmv for comparison.

Experimental results

Research questions

• RQ1 Can a robot be guided to execute a task while ensuring that an observer cannot infer sensitive information such as facility type, even when observing actions and observations?
• RQ2 How can a plan and a disclosure policy be jointly synthesized so that the robot achieves its goal while satisfying privacy stipulations?
• RQ3 What is the computational complexity of solving such privacy-constrained planning problems, and how does it scale with problem size?
• RQ4 How does the observer’s background knowledge (e.g., awareness of the robot’s plan) affect the feasibility and design of disclosure policies?
• RQ5 Can the approach be effectively implemented and verified on realistic, albeit small-scale, scenarios such as nuclear facility inspection?

Key findings

• The proposed method successfully computes a plan and disclosure policy pair that satisfies privacy stipulations in the nuclear inspection scenario, where the robot must determine radioactivity levels without revealing the facility type.
• For the nuclear inspection task, the and–or search algorithm found a valid solution in 11 seconds, while the CTL-based approach took 24 seconds, though it prioritized shorter plans.
• In a smaller pentagonal world, the Seek x,λ problem returned a solution where the robot loops at least once to obscure its position, with a disclosure policy mapping actions and observations to hide state distinctions.
• The disclosure policy was designed such that h(a₂) = h(a₃) and h(o₁) = h(o₃), ensuring the observer cannot distinguish between different paths or states.
• The computational complexity is high, bounded by O(2^{d|U||V|}) for depth d, due to the exponential number of action choices and observation partitions.
• The implementation confirms the feasibility of the approach on small instances, though scalability remains a major challenge, suggesting the need for heuristic or cost-aware extensions in future work.