Iterative Deepening Sampling for Large Language Models

The recent release of OpenAI's o1 models and other similar frameworks showcasing test-time scaling laws has demonstrated their exceptional capability to tackle complex reasoning tasks. Inspired by this, subsequent research has revealed that such test-time scaling laws hinge on the model's ability to search both within a single response (intra-response) and across multiple responses (inter-response) during training. Crucially, beyond selecting a single optimal response, the model must also develop robust self-correction capabilities within its own outputs. However, training models to achieve effective self-evaluation and self-correction remains a significant challenge, heavily dependent on the quality of self-reflection data. In this paper, we address this challenge by focusing on enhancing the quality of self-reflection data generation for complex problem-solving, which can subsequently improve the training of next-generation large language models (LLMs). Specifically, we explore how manually triggering a model's self-correction mechanisms can improve performance on challenging reasoning tasks. To this end, we propose a novel iterative deepening sampling algorithm framework designed to enhance self-correction and generate higher-quality samples. Through extensive experiments on Math500 and AIME benchmarks, we demonstrate that our method achieves a higher success rate on difficult tasks and provide detailed ablation studies to analyze its effectiveness across diverse settings.

Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models

Recent advances in diffusion models hold significant potential in robotics, enabling the generation of diverse and smooth trajectories directly from raw representations of the environment. Despite this promise, applying diffusion models to motion planning remains challenging due to their difficulty in enforcing critical constraints, such as collision avoidance and kinematic feasibility. These limitations become even more pronounced in Multi-Robot Motion Planning (MRMP), where multiple robots must coordinate in shared spaces. To address this challenge, this work proposes Simultaneous MRMP Diffusion (SMD), a novel approach integrating constrained optimization into the diffusion sampling process to produce collision-free, kinematically feasible trajectories. Additionally, the paper introduces a comprehensive MRMP benchmark to evaluate trajectory planning algorithms across scenarios with varying robot densities, obstacle complexities, and motion constraints. Experimental results show SMD consistently outperforms classical and learning-based motion planners, achieving higher success rates and efficiency in complex multi-robot environments.

Enhancing Lifelong Multi-Agent Path Finding with Cache Mechanism

Multi-Agent Path Finding (MAPF), which focuses on finding collision-free paths for multiple robots, is crucial in autonomous warehouse operations. Lifelong MAPF (L-MAPF), where agents are continuously reassigned new targets upon completing their current tasks, offers a more realistic approximation of real-world warehouse scenarios. While cache storage systems can enhance efficiency and reduce operational costs, existing approaches primarily rely on expectations and mathematical models, often without adequately addressing the challenges of multi-robot planning and execution. In this paper, we introduce a novel mechanism called Lifelong MAPF with Cache Mechanism (L-MAPF-CM), which integrates high-level cache storage with low-level path planning. We have involved a new type of map grid called cache for temporary item storage. Additionally, we involved a task assigner (TA) with a locking mechanism to bridge the gap between the new cache grid and L-MAPF algorithm. The TA dynamically allocates target locations to agents based on their status in various scenarios. We evaluated L-MAPF-CM using different cache replacement policies and task distributions. L-MAPF-CM has demonstrated performance improvements particularly with high cache hit rates and smooth traffic conditions.

Multi-Agent Path Finding in Continuous Spaces with Projected Diffusion Models

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics, requiring the computation of collision-free paths for multiple agents moving from their respective start to goal positions. Coordinating multiple agents in a shared environment poses significant challenges, especially in continuous spaces where traditional optimization algorithms struggle with scalability. Moreover, these algorithms often depend on discretized representations of the environment, which can be impractical in image-based or high-dimensional settings. Recently, diffusion models have shown promise in single-agent path planning, capturing complex trajectory distributions and generating smooth paths that navigate continuous, high-dimensional spaces. However, directly extending diffusion models to MAPF introduces new challenges since these models struggle to ensure constraint feasibility, such as inter-agent collision avoidance. To overcome this limitation, this work proposes a novel approach that integrates constrained optimization with diffusion models for MAPF in continuous spaces. This unique combination directly produces feasible multi-agent trajectories that respect collision avoidance and kinematic constraints. The effectiveness of our approach is demonstrated across various challenging simulated scenarios of varying dimensionality.

Anytime Multi-Agent Path Finding with an Adaptive Delay-Based Heuristic

Anytime multi-agent path finding (MAPF) is a promising approach to scalable path optimization in multi-agent systems. MAPF-LNS, based on Large Neighborhood Search (LNS), is the current state-of-the-art approach where a fast initial solution is iteratively optimized by destroying and repairing selected paths of the solution. Current MAPF-LNS variants commonly use an adaptive selection mechanism to choose among multiple destroy heuristics. However, to determine promising destroy heuristics, MAPF-LNS requires a considerable amount of exploration time. As common destroy heuristics are non-adaptive, any performance bottleneck caused by these heuristics cannot be overcome via adaptive heuristic selection alone, thus limiting the overall effectiveness of MAPF-LNS in terms of solution cost. In this paper, we propose Adaptive Delay-based Destroy-and-Repair Enhanced with Success-based Self-Learning (ADDRESS) as a single-destroy-heuristic variant of MAPF-LNS. ADDRESS applies restricted Thompson Sampling to the top-K set of the most delayed agents to select a seed agent for adaptive LNS neighborhood generation. We evaluate ADDRESS in multiple maps from the MAPF benchmark set and demonstrate cost improvements by at least 50% in large-scale scenarios with up to a thousand agents, compared with the original MAPF-LNS and other state-of-the-art methods.

RePrompt: Planning by Automatic Prompt Engineering for Large Language Models Agents

In this past year, large language models (LLMs) have had remarkable success in domains outside the traditional natural language processing, and people are starting to explore the usage of LLMs in more general and close to application domains like code generation, travel planning, and robot controls. Connecting these LLMs with great capacity and external tools, people are building the so-called LLM agents, which are supposed to help people do all kinds of work in everyday life. In all these domains, the prompt to the LLMs has been shown to make a big difference in what the LLM would generate and thus affect the performance of the LLM agents. Therefore, automatic prompt engineering has become an important question for many researchers and users of LLMs. In this paper, we propose a novel method, \textsc{RePrompt}, which does "gradient descent" to optimize the step-by-step instructions in the prompt of the LLM agents based on the chat history obtained from interactions with LLM agents. By optimizing the prompt, the LLM will learn how to plan in specific domains. We have used experiments in PDDL generation and travel planning to show that our method could generally improve the performance for different reasoning tasks when using the updated prompt as the initial prompt.

ITA-ECBS: A Bounded-Suboptimal Algorithm for Combined Target-Assignment and Path-Finding Problem

Multi-Agent Path Finding (MAPF), i.e., finding collision-free paths for multiple robots, plays a critical role in many applications. Sometimes, assigning a specific target to each agent also presents a challenge. The Combined Target-Assignment and Path-Finding (TAPF) problem, a variant of MAPF, requires simultaneously assigning targets to agents and planning collision-free paths. Several algorithms, including CBM, CBS-TA, and ITA-CBS, can optimally solve the TAPF problem, with ITA-CBS being the leading method of flowtime. However, the only existing suboptimal method ECBS-TA, is derived from CBS-TA rather than ITA-CBS, and adapting the optimal ITA-CBS method to its bounded-suboptimal variant is a challenge due to the variability of target assignment solutions in different search nodes. We introduce ITA-ECBS as the first bounded-suboptimal variant of ITA-CBS. ITA-ECBS employs focal search to enhance efficiency and determines target assignments based on a new lower bound matrix. We show that ITA-ECBS outperforms the baseline method ECBS-TA in 87.42% of 54,033 test cases.

MARL-LNS: Cooperative Multi-agent Reinforcement Learning via Large Neighborhoods Search

Cooperative multi-agent reinforcement learning (MARL) has been an increasingly important research topic in the last half-decade because of its great potential for real-world applications. Because of the curse of dimensionality, the popular "centralized training decentralized execution" framework requires a long time in training, yet still cannot converge efficiently. In this paper, we propose a general training framework, MARL-LNS, to algorithmically address these issues by training on alternating subsets of agents using existing deep MARL algorithms as low-level trainers, while not involving any additional parameters to be trained. Based on this framework, we provide three algorithm variants based on the framework: random large neighborhood search (RLNS), batch large neighborhood search (BLNS), and adaptive large neighborhood search (ALNS), which alternate the subsets of agents differently. We test our algorithms on both the StarCraft Multi-Agent Challenge and Google Research Football, showing that our algorithms can automatically reduce at least 10% of training time while reaching the same final skill level as the original algorithm.

Caching-Augmented Lifelong Multi-Agent Path Finding

Multi-Agent Path Finding (MAPF), which involves finding collision-free paths for multiple robots, is crucial in various applications. Lifelong MAPF, where targets are reassigned to agents as soon as they complete their initial targets, offers a more accurate approximation of real-world warehouse planning. In this paper, we present a novel mechanism named Caching-Augmented Lifelong MAPF (CAL-MAPF), designed to improve the performance of Lifelong MAPF. We have developed a new type of map grid called cache for temporary item storage and replacement, and designed a locking mechanism for it to improve the stability of the planning solution. This cache mechanism was evaluated using various cache replacement policies and a spectrum of input task distributions. We identified three main factors significantly impacting CAL-MAPF performance through experimentation: suitable input task distribution, high cache hit rate, and smooth traffic. In general, CAL-MAPF has demonstrated potential for performance improvements in certain task distributions, maps, and agent configurations.

Why Solving Multi-agent Path Finding with Large Language Model has not Succeeded Yet

With the explosive influence caused by the success of large language models (LLM) like ChatGPT and GPT-4, there has been an extensive amount of recent work showing that foundation models can be used to solve a large variety of tasks. However, there is very limited work that shares insights on multi-agent planning. Multi-agent planning is different from other domains by combining the difficulty of multi-agent coordination and planning, and making it hard to leverage external tools to facilitate the reasoning needed. In this paper, we focus on the problem of multi-agent path finding (MAPF), which is also known as multi-robot route planning, and study how to solve MAPF with LLMs. We first show the motivating success on an empty room map without obstacles, then the failure to plan on a slightly harder room map. We present our hypothesis of why directly solving MAPF with LLMs has not been successful yet, and we use various experiments to support our hypothesis.