Combinatorial methods for learning general policies that solve large collections of planning problems have been recently developed. One of their strengths, in relation to deep learning approaches, is that the resulting policies can be understood and shown to be correct. A weakness is that the methods do not scale up and learn only from small training instances and feature pools that contain a few hundreds of states and features at most. In this work, we propose a new symbolic method for learning policies based on the generalization of sampled plans that ensures structural termination and hence acyclicity. The proposed learning approach is not based on SA T/ASP, as previous symbolic methods, but on a hitting set algorithm that can effectively handle problems with millions of states, and pools with hundreds of thousands of features. The formal properties of the approach are analyzed, and its scalability is tested on a number of benchmarks.

Recent work has shown that successful per-domain generalizing action policies can be learned. Scaling behavior, from small training instances to large test instances, is the key objective; and the use of validation instances larger than training instances is one key to achieve it. Prior work has used fixed validation sets. Here, we introduce a method generating the validation set dynamically, on the fly, increasing instance size so long as informative and feasible. We also introduce refined methodology for evaluating scaling behavior, generating test instances systematically to guarantee a given confidence in coverage performance for each instance size. In experiments, dynamic validation improves scaling behavior of GNN policies in all 9 domains used.

Automated decision-making is a fundamental topic that spans multiple sub-disciplines in AI: reinforcement learning (RL), AI planning (AP), foundation models, and operations research, among others. Despite recent efforts to ``bridge the gaps'' between these communities, there remain many insights that have not yet transcended the boundaries. Our goal in this paper is to provide a brief and non-exhaustive primer on ideas well-known in AP, but less so in other sub-disciplines. We do so by introducing the classical AP problem and representation, and extensions that handle uncertainty and time through the Markov Decision Process formalism. Next, we survey state-of-the-art techniques and ideas for solving AP problems, focusing on their ability to exploit problem structure. Lastly, we cover subfields within AP for learning structure from unstructured inputs and learning to generalise to unseen scenarios and situations.

Goal instructions for autonomous AI agents cannot assume that objects have unique names. Instead, objects in goals must be referred to by providing suitable descriptions. However, this raises problems in both classical planning and generalized planning. The standard approach to handling existentially quantified goals in classical planning involves compiling them into a DNF formula that encodes all possible variable bindings and adding dummy actions to map each DNF term into the new, dummy goal. This preprocessing is exponential in the number of variables. In generalized planning, the problem is different: even if general policies can deal with any initial situation and goal, executing a general policy requires the goal to be grounded to define a value for the policy features. The problem of grounding goals, namely finding the objects to bind the goal variables, is subtle: it is a generalization of classical planning, which is a special case when there are no goal variables to bind, and constraint reasoning, which is a special case when there are no actions. In this work, we address the goal grounding problem with a novel supervised learning approach. A GNN architecture, trained to predict the cost of partially quantified goals over small domain instances is tested on larger instances involving more objects and different quantified goals. The proposed architecture is evaluated experimentally over several planning domains where generalization is tested along several dimensions including the number of goal variables and objects that can bind such variables. The scope of the approach is also discussed in light of the known relationship between GNNs and C2 logics.

State symmetries play an important role in planning and generalized planning. In the first case, state symmetries can be used to reduce the size of the search; in the second, to reduce the size of the training set. In the case of general planning, however, it is also critical to distinguish non-symmetric states, i.e., states that represent non-isomorphic relational structures. However, while the language of first-order logic distinguishes non-symmetric states, the languages and architectures used to represent and learn general policies do not. In particular, recent approaches for learning general policies use state features derived from description logics or learned via graph neural networks (GNNs) that are known to be limited by the expressive power of C_2, first-order logic with two variables and counting. In this work, we address the problem of detecting symmetries in planning and generalized planning and use the results to assess the expressive requirements for learning general policies over various planning domains. For this, we map planning states to plain graphs, run off-the-shelf algorithms to determine whether two states are isomorphic with respect to the goal, and run coloring algorithms to determine if C_2 features computed logically or via GNNs distinguish non-isomorphic states. Symmetry detection results in more effective learning, while the failure to detect non-symmetries prevents general policies from being learned at all in certain domains.

Current approaches for learning for planning have yet to achieve competitive performance against classical planners in several domains, and have poor overall performance. In this work, we construct novel graph representations of lifted planning tasks and use the WL algorithm to generate features from them. These features are used with classical machine learning methods which have up to 2 orders of magnitude fewer parameters and train up to 3 orders of magnitude faster than the state-of-the-art deep learning for planning models. Our novel approach, WL-GOOSE, reliably learns heuristics from scratch and outperforms the $h^{\text{FF}}$ heuristic in a fair competition setting. It also outperforms or ties with LAMA on 4 out of 10 domains on coverage and 7 out of 10 domains on plan quality. WL-GOOSE is the first learning for planning model which achieves these feats. Furthermore, we study the connections between our novel WL feature generation method, previous theoretically flavoured learning architectures, and Description Logic Features for planning.

Recently, a simple but powerful language for expressing and learning general policies and problem decompositions (sketches) has been introduced in terms of rules defined over a set of Boolean and numerical features. In this work, we consider three extensions of this language aimed at making policies and sketches more flexible and reusable: internal memory states, as in finite state controllers; indexical features, whose values are a function of the state and a number of internal registers that can be loaded with objects; and modules that wrap up policies and sketches and allow them to call each other by passing parameters. In addition, unlike general policies that select state transitions rather than ground actions, the new language allows for the selection of such actions. The expressive power of the resulting language for policies and sketches is illustrated through a number of examples.

There is a growing interest in the application of Reinforcement Learning (RL) techniques to AI planning with the aim to come up with general policies. Typically, the mapping of the transition model of AI planning to the state transition system of a Markov Decision Process is established by assuming a one-to-one correspondence of the respective action spaces. In this paper, we introduce the concept of meta-operator as the result of simultaneously applying multiple planning operators, and we show that including meta-operators in the RL action space enables new planning perspectives to be addressed using RL, such as parallel planning. Our research aims to analyze the performance and complexity of including meta-operators in the RL process, concretely in domains where satisfactory outcomes have not been previously achieved using usual generalized planning models. The main objective of this article is thus to pave the way towards a redefinition of the RL action space in a manner that is more closely aligned with the planning perspective.

While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such spaces have not received much attention. The main OT tool on these spaces is the Wasserstein distance which suffers from a heavy computational burden. On Euclidean spaces, a popular alternative is the Sliced-Wasserstein distance, which leverages a closed-form solution of the Wasserstein distance in one dimension, but which is not readily available on manifolds. In this work, we derive general constructions of Sliced-Wasserstein distances on Cartan-Hadamard manifolds, Riemannian manifolds with non-positive curvature, which include among others Hyperbolic spaces or the space of Symmetric Positive Definite matrices. Then, we propose different applications. Additionally, we derive non-parametric schemes to minimize these new distances by approximating their Wasserstein gradient flows.

Many problems in science and engineering involve optimizing an expensive black-box function over a high-dimensional space. For such black-box optimization (BBO) problems, we typically assume a small budget for online function evaluations, but also often have access to a fixed, offline dataset for pretraining. Prior approaches seek to utilize the offline data to approximate the function or its inverse but are not sufficiently accurate far from the data distribution. We propose BONET, a generative framework for pretraining a novel black-box optimizer using offline datasets. In BONET, we train an autoregressive model on fixed-length trajectories derived from an offline dataset. We design a sampling strategy to synthesize trajectories from offline data using a simple heuristic of rolling out monotonic transitions from low-fidelity to high-fidelity samples. Empirically, we instantiate BONET using a causally masked Transformer and evaluate it on Design-Bench, where we rank the best on average, outperforming state-of-the-art baselines.