Implicit planning has emerged as an elegant technique for combining learned models of the world with end-to-end model-free reinforcement learning. We study the class of implicit planners inspired by value iteration, an algorithm that is guaranteed to yield perfect policies in fully-specified tabular environments. We find that prior approaches either assume that the environment is provided in such a tabular form---which is highly restrictive---or infer local neighbourhoods of states to run value iteration over---for which we discover an algorithmic bottleneck effect. This effect is caused by explicitly running the planning algorithm based on scalar predictions in every state, which can be harmful to data efficiency if such scalars are improperly predicted. We propose eXecuted Latent Value Iteration Networks (XLVINs), which alleviate the above limitations. Our method performs all planning computations in a high-dimensional latent space, breaking the algorithmic bottleneck. It maintains alignment with value iteration by carefully leveraging neural graph-algorithmic reasoning and contrastive self-supervised learning. Across seven low-data settings---including classical control, navigation and Atari---XLVINs provide significant improvements to data efficiency against value iteration-based implicit planners, as well as relevant model-free baselines. Lastly, we empirically verify that XLVINs can closely align with value iteration.

--The development and application of large language models (LLM) have demonstrated that foundational models can be utilized to solve a wide array of tasks. However, their performance in multi-agent path finding (MAPF) tasks has been less than satisfactory, with only a few studies exploring this area. MAPF is a complex problem requiring both planning and multi-agent coordination. T o improve the performance of LLM in MAPF tasks, we propose a novel framework, LLM-NAR, which leverages neural algorithmic reasoners (NAR) to inform LLM for MAPF . LLM-NAR consists of three key components: an LLM for MAPF, a pre-trained graph neural network-based NAR, and a cross-attention mechanism. This is the first work to propose using a neural algorithmic reasoner to integrate GNNs with the map information for MAPF, thereby guiding LLM to achieve superior performance. LLM-NAR can be easily adapted to various LLM models. Both simulation and real-world experiments demonstrate that our method significantly outperforms existing LLM-based approaches in solving MAPF problems.

Implicit planning has emerged as an elegant technique for combining learned models of the world with end-to-end model-free reinforcement learning. We study the class of implicit planners inspired by value iteration, an algorithm that is guaranteed to yield perfect policies in fully-specified tabular environments. We find that prior approaches either assume that the environment is provided in such a tabular form---which is highly restrictive---or infer "local neighbourhoods" of states to run value iteration over---for which we discover an algorithmic bottleneck effect. This effect is caused by explicitly running the planning algorithm based on scalar predictions in every state, which can be harmful to data efficiency if such scalars are improperly predicted. We propose eXecuted Latent Value Iteration Networks (XLVINs), which alleviate the above limitations.

Neural Algorithmic Reasoning (NAR) is a research area focused on designing neural architectures that can reliably capture classical computation, usually by learning to execute algorithms. A typical approach is to rely on Graph Neural Network (GNN) architectures, which encode inputs in high-dimensional latent spaces that are repeatedly transformed during the execution of the algorithm. In this work we perform a detailed analysis of the structure of the latent space induced by the GNN when executing algorithms. We identify two possible failure modes: (i) loss of resolution, making it hard to distinguish similar values; (ii) inability to deal with values outside the range observed during training. We propose to solve the first issue by relying on a softmax aggregator, and propose to decay the latent space in order to deal with out-of-range values. We show that these changes lead to improvements on the majority of algorithms in the standard CLRS-30 benchmark when using the state-of-the-art Triplet-GMPNN processor. Our code is available at \href{https://github.com/mirjanic/nar-latent-spaces}{https://github.com/mirjanic/nar-latent-spaces}.