LLMs have recently been used to generate Python programs representing generalized plans in PDDL planning, i.e., plans that generalize across the tasks of a given PDDL domain. Previous work proposed a framework consisting of three steps: the LLM first generates a summary and then a strategy for the domain, both in natural language, and then implements that strategy as a Python program, that gets debugged on example planning tasks. In that work, only one strategy is generated and passed directly to the program generation. If the strategy is incorrect, its implementation will therefore result in an incorrect generalized plan. Here, we introduce an approach that generates the strategy in the form of pseudocode and enables automatic debugging of the pseudocode, hence allowing us to identify and fix errors prior to the generation of the generalized plan itself. Additionally, we extend the Python debugging phase with a reflection step prompting the LLM to pinpoint the reason for the observed plan failure. Finally, we take inspiration from LLM code generation to produce several program variants and pick the best one. Running experiments on 17 benchmark domains, we show that these extensions substantially improve (and never deteriorate) the quality of the generalized plans. In 12 of the domains, our best Python programs solve all tasks that can be generated with the respective instance generator.

This paper presents new methods for analyzing and evaluating generalized plans that can solve broad classes of related planning problems. Although synthesis and learning of generalized plans has been a longstanding goal in AI, it remains challenging due to fundamental gaps in methods for analyzing the scope and utility of a given generalized plan. This paper addresses these gaps by developing a new conceptual framework along with proof techniques and algorithmic processes for assessing termination and goal-reachability related properties of generalized plans. We build upon classic results from graph theory to decompose generalized plans into smaller components that are then used to derive hierarchical termination arguments. These methods can be used to determine the utility of a given generalized plan, as well as to guide the synthesis and learning processes for generalized plans. We present theoretical as well as empirical results illustrating the scope of this new approach. Our analysis shows that this approach significantly extends the class of generalized plans that can be assessed automatically, thereby reducing barriers in the synthesis and learning of reliable generalized plans.

This paper presents new methods for analyzing and evaluating generalized plans that can solve broad classes of related planning problems. Although synthesis and learning of generalized plans has been a longstanding goal in AI, it remains challenging due to fundamental gaps in methods for analyzing the scope and utility of a given generalized plan. This paper addresses these gaps by developing a new conceptual framework along with proof techniques and algorithmic processes for assessing termination and goal-reachability related properties of generalized plans. We build upon classic results from graph theory to decompose generalized plans into smaller components that are then used to derive hierarchical termination arguments. These methods can be used to determine the utility of a given generalized plan, as well as to guide the synthesis and learning processes for generalized plans. We present theoretical as well as empirical results illustrating the scope of this new approach. Our analysis shows that this approach significantly extends the class of generalized plans that can be assessed automatically, thereby reducing barriers in the synthesis and learning of reliable generalized plans.

Planning as heuristic search is one of the most successful approaches to classical planning but unfortunately, it does not extend trivially to Generalized Planning (GP). GP aims to compute algorithmic solutions that are valid for a set of classical planning instances from a given domain, even if these instances differ in the number of objects, the number of state variables, their domain size, or their initial and goal configuration. The generalization requirements of GP make it impractical to perform the state-space search that is usually implemented by heuristic planners. This paper adapts the planning as heuristic search paradigm to the generalization requirements of GP, and presents the first native heuristic search approach to GP. First, the paper introduces a new pointer-based solution space for GP that is independent of the number of classical planning instances in a GP problem and the size of those instances (i.e. the number of objects, state variables and their domain sizes). Second, the paper defines a set of evaluation and heuristic functions for guiding a combinatorial search in our new GP solution space. The computation of these evaluation and heuristic functions does not require grounding states or actions in advance. Therefore our GP as heuristic search approach can handle large sets of state variables with large numerical domains, e.g.~integers. Lastly, the paper defines an upgraded version of our novel algorithm for GP called Best-First Generalized Planning (BFGP), that implements a best-first search in our pointer-based solution space, and that is guided by our evaluation/heuristic functions for GP.

Finite State Controllers (FSCs) are an effective way to represent sequential plans compactly. By imposing appropriate conditions on transitions, FSCs can also represent generalized plans that solve a range of planning problems from a given domain. In this paper we introduce the concept of hierarchical FSCs for planning by allowing controllers to call other controllers. We show that hierarchical FSCs can represent generalized plans more compactly than individual FSCs. Moreover, our call mechanism makes it possible to generate hierarchical FSCs in a modular fashion, or even to apply recursion. We also introduce a compilation that enables a classical planner to generate hierarchical FSCs that solve challenging generalized planning problems. The compilation takes as input a set of planning problems from a given domain and outputs a single classical planning problem, whose solution corresponds to a hierarchical FSC. 1 Introduction Finite state controllers (FSCs) are a compact and effective representation commonly used in AI; prominent examples include robotics [ Brooks, 1989 ] and video-games [ Buckland, 2004] . In planning, FSCs offer two main benefits: 1) solution compactness [ B ackstr om et al., 2014 ]; and 2) the ability to represent generalized plans that solve a range of similar planning problems. This generalization capacity allows FSCs to represent solutions to arbitrarily large problems, as well as problems with partial observability and non-deterministic actions [ Bonet et al., 2010; Hu and Levesque, 2011; Srivastava et al., 2011; Hu and De Giacomo, 2013 ] .

Generalized planning is the task of generating a single solution that is valid for a set of planning problems. In this paper we show how to represent and compute generalized plans using procedural Domain Control Knowledge (DCK). We define a {\it divide and conquer} approach that first generates the procedural DCK solving a set of planning problems representative of certain subtasks and then compile it as callable procedures of the overall generalized planning problem. Our procedure calling mechanism allows nested and recursive procedure calls and is implemented in PDDL so that classical planners can compute and exploit procedural DCK. Experiments show that an off-the-shelf classical planner, using procedural DCK as callable procedures, can compute generalized plans in a wide range of domains including non-trivial ones, such as sorting variable-size lists or DFS traversal of binary trees with variable size.

In this paper we introduce a novel approach for unsupervised classification of planning instances based on the recent formalism of planning programs. Our approach is inspired by structured prediction in machine learning, which aims at predicting structured information about a given input rather than a scalar value. In our case, each input is an unlabelled classical planning instance, and the associated structured information is the planning program that solves the instance. We describe a method that takes as input a set of planning instances and outputs a set of planning programs, classifying each instance according to the program that solves it. Our results show that automated planning can be successfully used to solve structured unsupervised classification tasks, and invites further exploration of the connection between automated planning and structured prediction.

In a dynamic environment, an intelligent agent must consider unexpected changes to the world and plan for them. We aim to address this key issue by building more robust artificial agents through the generalization of plan representations. Our research focuses on the process of generalizing various plan forms and the development of a compact representation which embodies a generalized plan as a policy. Our techniques allow an agent to execute efficiently in an online setting. We have, to date, demonstrated our approach for sequential and partial order plans and are pursuing similar techniques for representations such as Hierarchical Task Networks and GOLOG programs

The utility of including cyclic flows of control in plans has been long recognized by the planning community. Loops in a plan help increase both its applicability and the compactness of representation. However, progress in finding such plans has been limited largely due to lack of methods for reasoning about the correctness and safety properties of loops of actions. We present an overview of recent results for determining the class of problems that a plan with loops can solve. These methods can be used to direct the construction of a rich new form of generalized plans that solve a desired class of problems.

We consider the problem of finding generalized plans for situations where the number of objects may be unknown and unbounded during planning. The input is a domain specification, a goal condition, and a class of concrete problem instances or initial states to be solved, expressed in an abstract first-order representation. Starting with an empty generalized plan, our overall approach is to incrementally increase the applicability of the plan by identifying a problem instance that it cannot solve, invoking a classical planner to solve that problem, generalizing the obtained solution and merging it back into the generalized plan. The main contributions of this paper are methods for (a) generating and solving small problem instances not yet covered by an existing generalized plan, (b) translating between concrete classical plans and abstract plan representations, and (c) extending partial generalized plans and increasing their applicability. We analyze the theoretical properties of these methods, prove their correctness, and illustrate experimentally their scalability. The resulting hybrid approach shows that solving only a few, small, classical planning problems can be sufficient to produce a generalized plan that applies to infinitely many problems with unknown numbers of objects.