Unsupervised Grounding of Plannable First-Order Logic Representation
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Abstract

Recently, there is an increasing interest in obtaining the relational structures of the environment in the Reinforcement Learning community. However, the resulting "relations" are not the discrete, logical predicates compatible to the symbolic reasoning such as classical planning or goal recognition. Meanwhile, Latplan (Asai and Fukunaga 2018) bridged the gap between deep-learning perceptual systems and symbolic classical planners. One key component of the system is a Neural Network called State AutoEncoder (SAE), which encodes an image-based input into a propositional representation compatible to classical planning. To get the best of both worlds, we propose First-Order State AutoEncoder, an unsupervised architecture for grounding the first-order logic predicates and facts. Each predicate models a relationship between objects by taking the interpretable arguments and returning a propositional value. In the experiment using 8-Puzzle and a photo-realistic Blocksworld environment, we show that (1) the resulting predicates capture the interpretable relations (e.g. spatial), (2) they help obtaining the compact, abstract model of the environment, and finally, (3) the resulting model is compatible to symbolic classical planning.

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The graph neural network model.

F. Scarselli, M. Gori, Ah Chung Tsoi … (2009)

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.