Research in planning has sought to broaden the scope of planning problems by incorporating numeric parameters into action descriptions to condition both continuous and discrete change. Focusing on the latter, this work studies the problem of numeric planning with control variables, a reformulation of actions with infinite domain parameters. To tackle the challenge of handling an infinite decision space driven by control variables, we incorporate sampling into a forward state-space search. The resulting search framework (1) partially expands nodes by sampling their successors and (2) implements a re-expansion strategy to sample additional successors if a node shows promise in future evaluations. We perform a deep probe into this concept that materializes into a new algorithm called Sampling Greedy Best-First Search (S-GBFS). Our empirical evaluation of S-GBFS across various domains shows significant improvements over existing planning approaches.

In automated planning, control parameters extend standard action representations through the introduction of continuous numeric decision variables. Existing state-of-the-art approaches have primarily handled control parameters as embedded constraints alongside other temporal and numeric restrictions, and thus have implicitly treated them as additional constraints rather than as decision points in the search space. In this paper, we propose an efficient alternative that explicitly handles control parameters as true decision points within a systematic search scheme. We develop a best-first, heuristic search algorithm that operates over infinite decision spaces defined by control parameters and prove a notion of completeness in the limit under certain conditions. Our algorithm leverages the concept of delayed partial expansion, where a state is not fully expanded but instead incrementally expands a subset of its successors. Our results demonstrate that this novel search algorithm is a competitive alternative to existing approaches for solving planning problems involving control parameters.

In this article, we propose a centralized Multi-Agent Learning framework for learning a policy that models the simultaneous behavior of multiple agents that need to coordinate to solve a certain task. Centralized approaches often suffer from the explosion of an action space that is defined by all possible combinations of individual actions, known as joint actions. Our approach addresses the coordination problem via a sequential abstraction, which overcomes the scalability problems typical to centralized methods. It introduces a meta-agent, called supervisor, which abstracts joint actions as sequential assignments of actions to each agent. This sequential abstraction not only simplifies the centralized joint action space but also enhances the framework's scalability and efficiency. Our experimental results demonstrate that the proposed approach successfully coordinates agents across a variety of Multi-Agent Learning environments of diverse sizes.