Compiling Uncertainty Away in Conformant Planning Problems with Bounded Width

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.

💡 Research Summary

The paper tackles conformant planning – the task of generating a sequence of actions that guarantees goal achievement despite uncertainty in the initial state or action effects. Traditional approaches treat the problem as a search in belief space, where each belief state represents a set of possible worlds. While powerful heuristics and compact belief representations have been developed, the exponential growth of belief states remains a major scalability bottleneck.

The authors propose a fundamentally different strategy for conformant problems that involve deterministic actions. Their key insight is to translate the uncertain problem into a classical planning problem that can be handed off to any off‑the‑shelf classical planner. The translation introduces a new family of literals denoted K_{L/t}. For each original literal L and each set of assumptions t about the initial situation, K_{L/t} encodes the conditional statement “if the assumptions t hold initially then L must hold”. In effect, the uncertainty is captured by a set of logical constraints rather than by an explicit enumeration of belief states.

The paper first formalizes this translation scheme and proves its soundness: any plan that solves the translated classical problem also solves the original conformant problem. Completeness, however, depends on a structural parameter called the conformant width (w). Width measures the maximal number of independent assumptions that must be simultaneously considered. The translation’s size grows as O(2^w), because all combinations of assumptions up to the width must be represented. In practice, for most benchmark domains the width is small (typically 1–3), so the exponential blow‑up is limited and the resulting classical problem remains tractable.

To mitigate the potential combinatorial explosion, the authors introduce several optimizations. Redundant K_{L/t} literals that share the same assumption set are merged, and a preprocessing phase eliminates assumption sets that cannot affect goal achievement. These reductions keep the translated problem compact enough for modern planners that rely on heuristic search (e.g., FF, FastDownward). Consequently, the translation leverages the sophisticated heuristics, pruning techniques, and efficient data structures already available in the classical planning community.

Experimental evaluation compares the translation‑based planner T0 against leading conformant planners such as CFF, MBP, and KAC. The benchmark suite includes domains from the 2006 International Planning Competition (IPC) and other publicly available conformant problems. Results show that when the width is low, T0 consistently outperforms the belief‑space planners, often solving instances orders of magnitude faster. In several IPC domains, T0 was the only planner to finish within the time limit, which explains its victory in the Conformant Track of the 2006 IPC.

The authors also discuss limitations. When the conformant width is large, the translation becomes infeasible due to exponential growth, suggesting that hybrid approaches (combining translation with belief‑space reasoning) may be necessary. Moreover, the current method assumes deterministic actions; extending the technique to handle nondeterministic or probabilistic effects would require additional machinery. Finally, the selection and minimization of assumption sets t is identified as an open research problem that could further improve scalability.

In summary, the paper introduces a novel reduction from conformant planning with deterministic actions to classical planning, based on conditional literals K_{L/t}. By exploiting the conformant width parameter, the authors show that the translation is polynomial for a wide range of practical problems and that existing classical planners can solve the resulting instances efficiently. The approach not only achieved state‑of‑the‑art performance in the 2006 IPC but also opens a new line of research where advances in classical planning can be directly transferred to conformant planning, provided the problem’s structural width remains bounded.