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

2025-11-14

AI Summary

This work addresses generalized planning—synthesizing domain-independent programs that solve a family of related planning tasks. We propose a first-order condition-action rule synthesis method grounded in goal regression: optimal plans are first computed on training instances; then, symbolic reasoning lifts atomic goal dependencies into executable first-order logical rules, yielding generalized plans that support both direct execution and search-space pruning. We provide the first formal correctness proof for such rules and establish sufficient conditions for sound state-space pruning, unifying execution and heuristic-guided search. Empirical evaluation on classical and numeric planning benchmarks demonstrates that our approach significantly outperforms current state-of-the-art planners across three key metrics: synthesis cost, planning coverage, and solution quality.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Multiagent Systems: Multiagent Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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 $ extit{Condition} ightarrow extit{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.

Problem

• Synthesizing programs for families of related planning problems
• Computing optimal plans and performing goal regression
• Generating generalised plans to improve synthesis cost and solution quality

Innovation

• Goal regression for generalised planning synthesis
• Lifting plans to first-order Condition-Action rules
• Rules enable execution and search space pruning