Compiling Uncertainty Away in Conformant Planning Problems with Bounded Width (1401.3468v1)

Abstract: Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where good belief representations and heuristics are critical for scaling up. In this work, a different formulation is introduced for conformant problems with deterministic actions where they are automatically converted into classical ones and solved by an off-the-shelf classical planner. The translation maps literals L and sets of assumptions t about the initial situation, into new literals KL/t that represent that L must be true if t is initially true. We lay out a general translation scheme that is sound and establish the conditions under which the translation is also complete. We show that the complexity of the complete translation is exponential in a parameter of the problem called the conformant width, which for most benchmarks is bounded. The planner based on this translation exhibits good performance in comparison with existing planners, and is the basis for T0, the best performing planner in the Conformant Track of the 2006 International Planning Competition.

• The paper introduces the KT,M translation scheme to convert conformant planning problems into classical ones, allowing their resolution using standard techniques.
• The translation is shown to be complete and sound under conditions related to conformant width, a parameter indicating problem complexity and translation tractability.
• Empirical evaluation shows the derived planner T0 performs favorably against existing conformant planners, especially in benchmarks with bounded conformant width.

Overview of "Compiling Uncertainty Away in Conformant Planning Problems with Bounded Width"

In the domain of conformant planning, the paper "Compiling Uncertainty Away in Conformant Planning Problems with Bounded Width" by Hector Palacios and Hector Geffner offers a methodical approach to transforming conformant planning issues into classical ones, thereby facilitating their resolution using standard classical planning techniques. Conformant planning involves identifying a sequence of actions to achieve a specific goal despite uncertainty in the initial state or action effects being present. Traditional approaches tackle conformant planning by searching in belief space, which presents challenges in representing beliefs compactly and developing efficient heuristics. This paper proposes an alternative approach by translating conformant problems into classical problems.

Key Contributions

• Translation Scheme KT,M: The authors introduce a general translation mechanism KT,M, which translates literals and assumptions about the initial situation into conditionals represented by literals KL/t. This translation is foundational for converting conformant planning problems with deterministic actions into classical planning instances that plan with certainty.
• Completeness and Soundness: The paper establishes conditions under which the translation is complete, ensuring it accurately encodes solutions to conformant planning problems, and sound, guaranteeing that the translation does not exceed the capabilities of the original problem. Completeness relies on the concept of conformant width—a parameter of the problem indicating the complexity of the translation, where lower widths imply more tractable translations.
• Performance Evaluation: Empirical results demonstrate that the planner developed from this translation scheme, T0, performs favorably against existing conformant planners, particularly in benchmarks from the Conformant Track of the 2006 International Planning Competition. The translation exhibits superior scalability in benchmark domains typically having bounded conformant width.

Theoretical and Practical Implications

The paper underscores the potential for substantial improvements in conformant planning by leveraging classical planners through effective translations. The approach resolves intrinsic limitations encountered when directly seeking solutions in belief space, such as inefficient heuristic searches and cumbersome belief representation. Conformant problems with deterministic actions are verifiably reduced to well-defined classical planning instances, shifting computational complexities typically associated with belief-space methods.

Future Directions

The exploration of translation techniques in the broader context of contingent planning or planning with non-deterministic effects suggests avenues for further extending these methodologies. A deeper integration with advanced classical planning paradigms could yield additional optimizations, especially in terms of heuristics and plan quality. Enhancing computational capabilities in handling broader and more ambiguous state spaces could reinforce the robustness and applicability of these approaches in various AI applications.

This research contributes significantly to advancing the field of AI planning by bridging conformant and classical planning realms, effectively addressing uncertainty in planning tasks through computationally viable translations. The notion of conformant width and the exploration of corresponding bases also invite further academic inquiry into their role and optimization in translating complex problems across planning domains.