Abstract Interpretation for Generalized Heuristic Search in Model-Based Planning (2208.02938v1)

Abstract: Domain-general model-based planners often derive their generality by constructing search heuristics through the relaxation or abstraction of symbolic world models. We illustrate how abstract interpretation can serve as a unifying framework for these abstraction-based heuristics, extending the reach of heuristic search to richer world models that make use of more complex datatypes and functions (e.g. sets, geometry), and even models with uncertainty and probabilistic effects. These heuristics can also be integrated with learning, allowing agents to jumpstart planning in novel world models via abstraction-derived information that is later refined by experience. This suggests that abstract interpretation can play a key role in building universal reasoning systems.

• The paper presents a generalized heuristic framework that applies abstract interpretation to derive abstraction-based heuristics for complex planning models.
• It introduces methodologies like widening, predicate abstraction, and CEGAR to compute lower bounds and refine estimates across diverse data types including geometric and probabilistic effects.
• The approach bridges formal symbolic methods with learning-based systems, enabling robust handling of uncertainty and facilitating backward as well as forward search in autonomous planning.

Abstract Interpretation for Generalized Heuristic Search in Model-Based Planning

The paper "Abstract Interpretation for Generalized Heuristic Search in Model-Based Planning" addresses the application of abstract interpretation to enhance heuristic search methods in domain-general model-based planning. The work is situated in the context of classical symbolic planning, which traditionally views planning and decision-making as theorem-proving over symbolic world models. The authors suggest that abstract interpretation, a well-established technique in program analysis, can unify and generalize heuristic approaches in these models to incorporate more complex data types, such as sets and geometric operations, as well as uncertainty and probabilistic effects.

Core Contributions

1. Generalized Heuristic Framework: The utilization of abstract interpretation provides a formal framework for deriving abstraction-based heuristics. This framework enables planners to handle richer world models than traditionally possible. By abstracting the elements of these models, the heuristic search can operate efficiently despite increased complexity.
2. Novel Heuristic Derivations: The paper outlines methodologies for generating several planning heuristics based on abstract interpretation:
   • Relaxed Reachability via Widening: Using widening-based abstract actions over Cartesian abstractions, the proposed technique computes heuristic estimates as lower bounds on the cost to achieve a goal. This approach generalizes the $h_\text{max}$ heuristic, extending it to numerous data types.
   • Predicate Abstractions: By leveraging both Cartesian and predicate abstraction, the paper illustrates improved methodologies for calculating heuristic estimations. This extension moves beyond existing propositional-variable approaches and can incorporate numeric and geometric abstractions.
   • Counterexample Guided Abstraction Refinement (CEGAR): The authors adapt CEGAR techniques from model-checking to planning, paving the way for heuristics that iteratively refine abstract models to obtain reliable search guidance.
3. Uncertainty and Integration with Learning Systems: Abstract interpretation isn't limited to deterministic environments. The authors discuss probabilistic domains and suggest employing abstraction heuristics to influence Real Time Dynamic Programming and similar algorithms, thereby initializing value functions with reliable estimates.
4. Exploration of Reverse Abstract Interpretation: The research acknowledges the potential of reverse abstract interpretation techniques as a means to facilitate backward search, complementing forward heuristic search methodologies.

Implications and Future Directions

The application of abstract interpretation to model-based planning embodies a significant theoretical advance, equipping planners with tools to engage with a broader spectrum of problems. The prospects include accommodating various data types and managing stochastic effects, thereby bridging a gap between formal symbolic methods and learning-based systems. This integration opens up possible collaborations with neural estimators, which can leverage heuristics as learning targets, enhancing the rapid acquisition of value estimates in unfamiliar environments.

In future work, exploring the hinted connections between generalized planning, abstraction-guided program synthesis, and AI planning could further optimize plans expressed as symbolic programs with control flow. Such collaborations may lead to robust algorithms capable of generating policy-like plans adaptable to diverse domains.

In conclusion, this research contributes significantly to the theoretical foundation of heuristic search in model-based planning, offering practitioners new possibilities for solving complex, varied planning problems with abstract interpretation as a cornerstone. The interdisciplinarity of this work prompts further exploration in combining techniques from program analysis and AI planning, potentially influencing the design of more versatile autonomous systems.