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Goal Recognition via Linear Programming

Felipe Meneguzzi, Luísa R. de A. Santos, Ramon Fraga Pereira, André G. Pereira

TL;DR

This work advances goal recognition by embedding it into an Operator-Counting framework with Linear Programming constraints. It proves lower bounds on the cost of observation-compliant plans and introduces observation-counting and landmark-based LP constraints to strengthen recognition under partial and noisy observations. A formalism for computing a reference solution set via LP-based estimates (Gamma^{LP}) is proposed, and a comprehensive empirical evaluation across multiple domains demonstrates improved agreement with ground truth and robustness relative to prior RG approaches. The results highlight a practical, scalable approach to goal recognition that balances accuracy and efficiency, even in challenging sensing conditions.

Abstract

Goal Recognition is the task by which an observer aims to discern the goals that correspond to plans that comply with the perceived behavior of subject agents given as a sequence of observations. Research on Goal Recognition as Planning encompasses reasoning about the model of a planning task, the observations, and the goals using planning techniques, resulting in very efficient recognition approaches. In this article, we design novel recognition approaches that rely on the Operator-Counting framework, proposing new constraints, and analyze their constraints' properties both theoretically and empirically. The Operator-Counting framework is a technique that efficiently computes heuristic estimates of cost-to-goal using Integer/Linear Programming (IP/LP). In the realm of theory, we prove that the new constraints provide lower bounds on the cost of plans that comply with observations. We also provide an extensive empirical evaluation to assess how the new constraints improve the quality of the solution, and we found that they are especially informed in deciding which goals are unlikely to be part of the solution. Our novel recognition approaches have two pivotal advantages: first, they employ new IP/LP constraints for efficiently recognizing goals; second, we show how the new IP/LP constraints can improve the recognition of goals under both partial and noisy observability.

Goal Recognition via Linear Programming

TL;DR

This work advances goal recognition by embedding it into an Operator-Counting framework with Linear Programming constraints. It proves lower bounds on the cost of observation-compliant plans and introduces observation-counting and landmark-based LP constraints to strengthen recognition under partial and noisy observations. A formalism for computing a reference solution set via LP-based estimates (Gamma^{LP}) is proposed, and a comprehensive empirical evaluation across multiple domains demonstrates improved agreement with ground truth and robustness relative to prior RG approaches. The results highlight a practical, scalable approach to goal recognition that balances accuracy and efficiency, even in challenging sensing conditions.

Abstract

Goal Recognition is the task by which an observer aims to discern the goals that correspond to plans that comply with the perceived behavior of subject agents given as a sequence of observations. Research on Goal Recognition as Planning encompasses reasoning about the model of a planning task, the observations, and the goals using planning techniques, resulting in very efficient recognition approaches. In this article, we design novel recognition approaches that rely on the Operator-Counting framework, proposing new constraints, and analyze their constraints' properties both theoretically and empirically. The Operator-Counting framework is a technique that efficiently computes heuristic estimates of cost-to-goal using Integer/Linear Programming (IP/LP). In the realm of theory, we prove that the new constraints provide lower bounds on the cost of plans that comply with observations. We also provide an extensive empirical evaluation to assess how the new constraints improve the quality of the solution, and we found that they are especially informed in deciding which goals are unlikely to be part of the solution. Our novel recognition approaches have two pivotal advantages: first, they employ new IP/LP constraints for efficiently recognizing goals; second, we show how the new IP/LP constraints can improve the recognition of goals under both partial and noisy observability.
Paper Structure (17 sections, 5 theorems, 15 equations, 4 figures, 6 tables)

This paper contains 17 sections, 5 theorems, 15 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Planning
  4. Operator-Counting Framework
  5. Goal Recognition as Planning
  6. Cost Difference-Based Goal Recognition
  7. Linear Programming-Based Goal Recognition
  8. Computing the Solution Set.
  9. Noisy Observations.
  10. Novel LP Constraints for Goal Recognition
  11. Experiments and Evaluation
  12. Experimental Setting
  13. Evaluation and Comparison of the Novel LP-Based Approaches
  14. Comparison with Previous Recognition Approaches
  15. Related Work
  16. ...and 2 more sections

Key Result

Proposition 1

Let $C$, $C'$ be functions that map states $s$ of a planning task $\Pi$ to constraint sets for $s$ such that $C(s) \subset C'(s)$ for each $s$. Then the heuristic $h^{\textup{IP/LP}}$ for $C'$dominates the respective heuristic for $C$: $h^{IP/LP}_{C} \leq h^{IP/LP}_{C'}$.

Figures (4)

  • Figure 1: A goal recognition task example.
  • Figure 2: A goal recognition task example considering cost differences.
  • Figure 3: Example of landmark heuristic for a goal recognition task. States $s_1$ and $s_2$ and their corresponding disjunctive landmarks highlighted in red and blue, respectively.
  • Figure 4: Scatter plot comparing the heuristic values of $h^{\text{LMC}}_{\Omega}$ with $h^{\text{LMC}_\Omega}_{\Omega,s^{*}}$, for observability levels 10%, 30%, 50%, 70% and 100%. We take into consideration all goal hypotheses from all instances, and all four data sets. Red indicates the value for the reference goal, blue indicates the value for all other goal hypotheses.

Theorems & Definitions (26)

  • Definition 1: Operator-Counting Constraint
  • Definition 2: Operator-Counting $\textup{IP}$/$\textup{LP}$ Heuristic
  • Proposition 1: Dominance
  • Definition 3: Landmark Constraint
  • Definition 4: Goal Recognition Task
  • Definition 5: Observation Compliance
  • Definition 6: Sequence of Observations
  • Definition 7: Noisy Observations
  • Definition 8: Reference Solution Set
  • Example 1
  • ...and 16 more