Let G beacausalQ = Pr.

While most heuristics studied in heuristic search depend only on the state, some accumulate information during search and thus also depend on the search history. Various existing approaches use such dynamic heuristics in $\mathrm{A}^*$-like algorithms and appeal to classic results for $\mathrm{A}^*$ to show optimality. However, doing so ignores the complexities of searching with a mutable heuristic. In this paper we formalize the idea of dynamic heuristics and use them in a generic algorithm framework. We study a particular instantiation that models $\mathrm{A}^*$ with dynamic heuristics and show general optimality results. Finally we show how existing approaches from classical planning can be viewed as special cases of this instantiation, making it possible to directly apply our optimality results.

Planning is one of the most critical tasks in autonomous systems, where even a small error can lead to major failures or million-dollar losses. Current state-of-the-art neural planning approaches struggle with complex domains, producing plans with missing preconditions, inconsistent goals, and hallucinations. While classical planners provide logical guarantees, they lack the flexibility and natural language understanding capabilities needed for modern autonomous systems. Existing neuro-symbolic approaches use one-shot translation from natural language to formal plans, missing the opportunity for neural and symbolic components to work and refine solutions together. To address this gap, we develop LOOP -- a novel neuro-symbolic planning framework that treats planning as an iterative conversation between neural and symbolic components rather than simple translation. LOOP integrates 13 coordinated neural features including graph neural networks for spatial relationships, multi-agent validation for consensus-based correctness, hierarchical decomposition for complex task management, and causal memory that learns from both successes and failures. Unlike existing approaches, LOOP generates PDDL specifications, refines them iteratively based on symbolic feedback, and builds a causal knowledge base from execution traces. LOOP was evaluated on six standard IPC benchmark domains, where it achieved 85.8% success rate compared to LLM+P (55.0%), LLM-as-Planner (19.2%), and Tree-of-Thoughts (3.3%). This work shows that the key to reliable planning is not in choosing between neural networks or symbolic reasoners but it lies in making them actually ``talk'' to each other during the entire process. LOOP provides a thorough blueprint for building autonomous systems that can finally be trusted with critical real-world applications.

In over sixty years since its inception, the field of planning has made significant contributions to both the theory and practice of building planning software that can solve a never-before-seen planning problem. This was done through established practices of rigorous design and evaluation of planning systems. It is our position that this rigor should be applied to the current trend of work on planning with large language models. One way to do so is by correctly incorporating the insights, tools, and data from the automated planning community into the design and evaluation of LLM-based planners. The experience and expertise of the planning community are not just important from a historical perspective; the lessons learned could play a crucial role in accelerating the development of LLM-based planners. This position is particularly important in light of the abundance of recent works that replicate and propagate the same pitfalls that the planning community has encountered and learned from. We believe that avoiding such known pitfalls will contribute greatly to the progress in building LLM-based planners and to planning in general.

Classical planning asks for a sequence of operators reaching a given goal. While the most common case is to compute a plan, many scenarios require more than that. However, quantitative reasoning on the plan space remains mostly unexplored. A fundamental problem is to count plans, which relates to the conditional probability on the plan space. Indeed, qualitative and quantitative approaches are well-established in various other areas of automated reasoning. We present the first study to quantitative and qualitative reasoning on the plan space. In particular, we focus on polynomially bounded plans. On the theoretical side, we study its complexity, which gives rise to rich reasoning modes. Since counting is hard in general, we introduce the easier notion of facets, which enables understanding the significance of operators. On the practical side, we implement quantitative reasoning for planning. Thereby, we transform a planning task into a propositional formula and use knowledge compilation to count different plans. This framework scales well to large plan spaces, while enabling rich reasoning capabilities such as learning pruning functions and explainable planning.

One key decision for heuristic search algorithms is how to balance exploration and exploitation. In classical planning, novelty search has come out as the most successful approach in this respect. The idea is to favor states that contain previously unseen facts when searching for a plan. This is done by maintaining a record of the tuples of facts observed in previous states. Then the novelty of a state is the size of the smallest previously unseen tuple. The most successful version of novelty search is best-first width search (BFWS), which combines novelty measures with heuristic estimates. An orthogonal approach to balance exploration-exploitation is to use several open-lists. These open-lists are ordered using different heuristic estimates, which diversify the information used in the search. The search algorithm then alternates between these open-lists, trying to exploit these different estimates. This is the approach used by LAMA, a classical planner that, a decade after its release, is still considered state-of-the-art in agile planning. In this paper, we study how to combine LAMA and BFWS. We show that simply adding the strongest open-list used in BFWS to LAMA harms performance. However, we show that combining only parts of each planner leads to a new state-of-the-art agile planner.

The ability to generate multiple plans is central to using planning in real-life applications. Top-quality planners generate sets of such top-cost plans, allowing flexibility in determining equivalent ones. In terms of the order between actions in a plan, the literature only considers two extremes -- either all orders are important, making each plan unique, or all orders are unimportant, treating two plans differing only in the order of actions as equivalent. To allow flexibility in selecting important orders, we propose specifying a subset of actions the orders between which are important, interpolating between the top-quality and unordered top-quality planning problems. We explore the ways of adapting partial order reduction search pruning techniques to address this new computational problem and present experimental evaluations demonstrating the benefits of exploiting such techniques in this setting.

GNN-based approaches for learning general policies across planning domains are limited by the expressive power of $C_2$, namely; first-order logic with two variables and counting. This limitation can be overcomed by transitioning to $k$-GNNs, for $k=3$, wherein object embeddings are substituted with triplet embeddings. Yet, while $3$-GNNs have the expressive power of $C_3$, unlike $1$- and $2$-GNNs that are confined to $C_2$, they require quartic time for message exchange and cubic space for embeddings, rendering them impractical. In this work, we introduce a parameterized version of relational GNNs. When $t$ is infinity, R-GNN[$t$] approximates $3$-GNNs using only quadratic space for embeddings. For lower values of $t$, such as $t=1$ and $t=2$, R-GNN[$t$] achieves a weaker approximation by exchanging fewer messages, yet interestingly, often yield the $C_3$ features required in several planning domains. Furthermore, the new R-GNN[$t$] architecture is the original R-GNN architecture with a suitable transformation applied to the input states only. Experimental results illustrate the clear performance gains of R-GNN[$1$] and R-GNN[$2$] over plain R-GNNs, and also over edge transformers that also approximate $3$-GNNs.

The growing utilization of planning tools in practical scenarios has sparked an interest in generating multiple high-quality plans. Consequently, a range of computational problems under the general umbrella of top-quality planning were introduced over a short time period, each with its own definition. In this work, we show that the existing definitions can be unified into one, based on a dominance relation. The different computational problems, therefore, simply correspond to different dominance relations. Given the unified definition, we can now certify the top-quality of the solutions, leveraging existing certification of unsolvability and optimality. We show that task transformations found in the existing literature can be employed for the efficient certification of various top-quality planning problems and propose a novel transformation to efficiently certify loopless top-quality planning.

The field of urban spatial-temporal prediction is advancing rapidly with the development of deep learning techniques and the availability of large-scale datasets. However, challenges persist in accessing and utilizing diverse urban spatial-temporal datasets from different sources and stored in different formats, as well as determining effective model structures and components with the proliferation of deep learning models. This work addresses these challenges and provides three significant contributions. Firstly, we introduce "atomic files", a unified storage format designed for urban spatial-temporal big data, and validate its effectiveness on 40 diverse datasets, simplifying data management. Secondly, we present a comprehensive overview of technological advances in urban spatial-temporal prediction models, guiding the development of robust models. Thirdly, we conduct extensive experiments using diverse models and datasets, establishing a performance leaderboard and identifying promising research directions. Overall, this work effectively manages urban spatial-temporal data, guides future efforts, and facilitates the development of accurate and efficient urban spatial-temporal prediction models. It can potentially make long-term contributions to urban spatial-temporal data management and prediction, ultimately leading to improved urban living standards.