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What Planning Problems Can A Relational Neural Network Solve?

Jiayuan Mao · Tomás Lozano-Pérez · Josh Tenenbaum · Leslie Kaelbling

Great Hall & Hall B1+B2 (level 1) #433
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[ Paper [ Poster [ OpenReview
Thu 14 Dec 8:45 a.m. PST — 10:45 a.m. PST


Goal-conditioned policies are generally understood to be "feed-forward" circuits, in the form of neural networks that map from the current state and the goal specification to the next action to take. However, under what circumstances such a policy can be learned and how efficient the policy will be are not well understood. In this paper, we present a circuit complexity analysis for relational neural networks (such as graph neural networks and transformers) representing policies for planning problems, by drawing connections with serialized goal regression search (S-GRS). We show that there are three general classes of planning problems, in terms of the growth of circuit width and depth as a function of the number of objects and planning horizon, providing constructive proofs. We also illustrate the utility of this analysis for designing neural networks for policy learning.

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