Open-world planning with incomplete knowledge is crucial for real-world embodied AI tasks. Despite that, existing LLM-based planners struggle with long chains of sequential reasoning, while symbolic planners face combinatorial explosion of states and actions for complex domains due to reliance on grounding. To address these deficiencies, we introduce LLM-Regress, an open-world planning approach integrating lifted regression with LLM-generated affordances. LLM-Regress generates sound and complete plans in a compact lifted form, avoiding exhaustive enumeration of irrelevant states and actions. Additionally, it makes efficient use of LLMs to infer goal-related objects and affordances without the need to predefine all possible objects and affordances. We conduct extensive experiments on three benchmarks and show that LLM-Regress significantly outperforms state-of-the-art LLM planners and a grounded planner using LLM-generated affordances.

The pretraining of code LLMs typically begins with general data and progresses to domain-specific data through sequential stages. In the latter stages, a challenging issue is that the data of a target domain can be limited in size, and conventional approach of increasing the number of epochs does not lead to a performance gain. In this paper, we propose a novel packing method, which is extracting overlapping contexts from the training data using variable-length stride. Our method can mitigate the data-scarcity issue by providing more diverse and abundant examples of next token prediction than non-overlapping contexts. While the training time of our approach is increased proportionally to the amount of augmented examples, we present space-efficient implementations to store overlapping contexts. Extensive experiments with real datasets show that our approach outperforms the conventional approach of controlling the number of epochs in terms of the pass@k rate.