Logical Regression for Planning with Axioms

The paper investigates the use of logical regression in automated planning, particularly in domains that include axioms. Logical regression is a technique used to determine the most general conditions necessary for an action to achieve a specific formula. The research introduces a methodology for approximating logical regression in such domains, focusing on limiting conditions to partial states to maintain computational efficiency.

The authors propose a novel method for efficiently computing approximate logical regression over actions in the presence of axioms. This method involves three approaches with varying granularity: a naive method, a relevant variables method, and a post-processing method. The naive method retains all basic variables, while the relevant variables method focuses on variables directly influencing derived variables. The post-processing method further refines the regression by selecting specific axioms to achieve the desired result.

The study applies these methods within an execution monitoring framework, demonstrating that the approximate regression can significantly reduce the number of variables considered during execution monitoring. This reduction can be as much as 70%, allowing for more robust plan execution in environments with unexpected changes. The execution monitor was shown to recover frequently, with some domains achieving recovery rates over 50%.

The research identifies limitations in handling stratified axioms and suggests that the current benchmarks may not fully capture the potential of the proposed methods. The paper highlights the need for further exploration of heuristic improvements and the expansion of datasets to include more complex domains with axioms.

Future work is suggested to extend the algorithm to handle conditional and non-deterministic effects, expand the datasets used, and explore the impact of different heuristics. The authors also emphasize the need for more comprehensive benchmarks that include axioms to better evaluate the capabilities of the proposed methods.