Satisficing and Optimal Generalised Planning via Goal Regression (Extended Version)

TL;DR

This paper tackles generalized planning (GP) by introducing Moose, a bottom-up approach that learns generalised plans from training problems through optimal singleton-goal planning, goal regression, and lifting into first-order rules. Moose yields a generalised plan that can be instantiated on new problems or used to prune search by encoding rules as axioms in PDDL, enabling pruning without new solvers. The authors formalise soundness and completeness under goal-independence notions (TGI/SGI/OGI) and demonstrate significant empirical gains in synthesis cost, instantiation cost, and solution quality across classical and numeric domains, including optimal planning settings. The work also shows that learned Moose rules can speed up existing optimal planners, achieving competitive or superior performance relative to state-of-the-art baselines and offering practical impact for scalable, reusable planning policies.

Abstract

Generalised planning (GP) refers to the task of synthesising programs that solve families of related planning problems. We introduce a novel, yet simple method for GP: given a set of training problems, for each problem, compute an optimal plan for each goal atom in some order, perform goal regression on the resulting plans, and lift the corresponding outputs to obtain a set of first-order $\textit{Condition} \rightarrow \textit{Actions}$ rules. The rules collectively constitute a generalised plan that can be executed as is or alternatively be used to prune the planning search space. We formalise and prove the conditions under which our method is guaranteed to learn valid generalised plans and state space pruning axioms for search. Experiments demonstrate significant improvements over state-of-the-art (generalised) planners with respect to the 3 metrics of synthesis cost, planning coverage, and solution quality on various classical and numeric planning domains.

Figures (27)

• Figure 1: A common GP setup consisting of a planning domain $\mathcal{D}$, and a set of training problems $\mathscr{P}_{\text{train}}$ and testing problems $\mathscr{P}_{\text{test}}$. A generalised planner consists of two modules: (1) synthesis and (2) instantiation. See text for details.
• Figure 2: Left: a simplified STRIPS transportation domain. Middle: state progression (purple) and goal regression (yellow) via a putDown action. Right: the generalised plan created by lifting the regressed states, goal condition, and plan actions.
• Figure 3: Left: average time and memory usage for synthesis ($\downarrow$). Lowest values are indicated in colour and bold font. Right: cumulative coverage ($y$-axis) of planners over time ($x$-axis) for different planning settings. Higher values are better ($\uparrow$).
• Figure 4: A planning problem illustrating the necessity of the OGI assumption for learning provably optimal policies in \ref{['thm:opt']}. Nodes represent states and arrows represent transitions between states.
• Figure 5: Average time (left) and plan length (right) of planners across solved problems for Numeric Ferry. Planning problem difficulty increases across the $x$-axis. Lower $y$-axis values are better ($\downarrow$). Note the $y$-axis log scale for runtime. Only points for which all seeds solve the problem are displayed.

Theorems & Definitions (35)

• Example 1: Transportation Domain
• Example 2: Transportation Problem
• Definition 1: Moose Rule
• Definition 2: Grounding
• Definition 3: Moose Program
• Definition 4: Lifting
• Example 3: Transportation Program Synthesis
• Definition 5: True Goal Independence
• Definition 6: Serialisable Goal Independence
• Definition 7: Optimal Goal Independence