PARCO: Learning Parallel Autoregressive Policies for Efficient Multi-Agent Combinatorial Optimization

Multi-agent combinatorial optimization problems such as routing and scheduling have great practical relevance but present challenges due to their NP-hard combinatorial nature, hard constraints on the number of possible agents, and hard-to-optimize objective functions. This paper introduces PARCO (Parallel AutoRegressive Combinatorial Optimization), a novel approach that learns fast surrogate solvers for multi-agent combinatorial problems with reinforcement learning by employing parallel autoregressive decoding. We propose a model with a Multiple Pointer Mechanism to efficiently decode multiple decisions simultaneously by different agents, enhanced by a Priority-based Conflict Handling scheme. Moreover, we design specialized Communication Layers that enable effective agent collaboration, thus enriching decision-making. We evaluate PARCO in representative multi-agent combinatorial problems in routing and scheduling and demonstrate that our learned solvers offer competitive results against both classical and neural baselines in terms of both solution quality and speed. We make our code openly available at https://github.com/ai4co/parco.

RouteFinder: Towards Foundation Models for Vehicle Routing Problems

Vehicle Routing Problems (VRPs) are optimization problems with significant real-world implications in logistics, transportation, and supply chain management. Despite the recent progress made in learning to solve individual VRP variants, there is a lack of a unified approach that can effectively tackle a wide range of tasks, which is crucial for real-world impact. This paper introduces RouteFinder, a framework for developing foundation models for VRPs. Our key idea is that a foundation model for VRPs should be able to model variants by treating each variant as a subset of a larger VRP problem, equipped with different attributes. We introduce a parallelized environment that can handle any combination of attributes at the same time in a batched manner, and an efficient sampling procedure to train on a mix of problems at each optimization step that can greatly improve convergence robustness. We also introduce novel Global Feature Embeddings that project instance-wise attributes efficiently onto the latent space and help the model understand different VRP variants. Finally, we introduce Efficient Adapter Layers, a simple yet effective technique to finetune pre-trained RouteFinder models to solve novel variants with previously unseen attributes outside of the original feature space. We validate our approach through extensive experiments on 24 VRP variants, demonstrating competitive results over recent multi-task learning models. We make our code openly available at https://github.com/ai4co/routefinder.

Ensembling Prioritized Hybrid Policies for Multi-agent Pathfinding

Multi-Agent Reinforcement Learning (MARL) based Multi-Agent Path Finding (MAPF) has recently gained attention due to its efficiency and scalability. Several MARL-MAPF methods choose to use communication to enrich the information one agent can perceive. However, existing works still struggle in structured environments with high obstacle density and a high number of agents. To further improve the performance of the communication-based MARL-MAPF solvers, we propose a new method, Ensembling Prioritized Hybrid Policies (EPH). We first propose a selective communication block to gather richer information for better agent coordination within multi-agent environments and train the model with a Q-learning-based algorithm. We further introduce three advanced inference strategies aimed at bolstering performance during the execution phase. First, we hybridize the neural policy with single-agent expert guidance for navigating conflict-free zones. Secondly, we propose Q value-based methods for prioritized resolution of conflicts as well as deadlock situations. Finally, we introduce a robust ensemble method that can efficiently collect the best out of multiple possible solutions. We empirically evaluate EPH in complex multi-agent environments and demonstrate competitive performance against state-of-the-art neural methods for MAPF.

HiMAP: Learning Heuristics-Informed Policies for Large-Scale Multi-Agent Pathfinding

Large-scale multi-agent pathfinding (MAPF) presents significant challenges in several areas. As systems grow in complexity with a multitude of autonomous agents operating simultaneously, efficient and collision-free coordination becomes paramount. Traditional algorithms often fall short in scalability, especially in intricate scenarios. Reinforcement Learning (RL) has shown potential to address the intricacies of MAPF; however, it has also been shown to struggle with scalability, demanding intricate implementation, lengthy training, and often exhibiting unstable convergence, limiting its practical application. In this paper, we introduce Heuristics-Informed Multi-Agent Pathfinding (HiMAP), a novel scalable approach that employs imitation learning with heuristic guidance in a decentralized manner. We train on small-scale instances using a heuristic policy as a teacher that maps each single agent observation information to an action probability distribution. During pathfinding, we adopt several inference techniques to improve performance. With a simple training scheme and implementation, HiMAP demonstrates competitive results in terms of success rate and scalability in the field of imitation-learning-only MAPF, showing the potential of imitation-learning-only MAPF equipped with inference techniques.

Learning Efficient Surrogate Dynamic Models with Graph Spline Networks

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this paper, we present GraphSplineNets, a novel deep-learning method to speed up the forecasting of physical systems by reducing the grid size and number of iteration steps of deep surrogate models. Our method uses two differentiable orthogonal spline collocation methods to efficiently predict response at any location in time and space. Additionally, we introduce an adaptive collocation strategy in space to prioritize sampling from the most important regions. GraphSplineNets improve the accuracy-speedup tradeoff in forecasting various dynamical systems with increasing complexity, including the heat equation, damped wave propagation, Navier-Stokes equations, and real-world ocean currents in both regular and irregular domains.

RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmark

We introduce RL4CO, an extensive reinforcement learning (RL) for combinatorial optimization (CO) benchmark. RL4CO employs state-of-the-art software libraries as well as best practices in implementation, such as modularity and configuration management, to be efficient and easily modifiable by researchers for adaptations of neural network architecture, environments, and algorithms. Contrary to the existing focus on specific tasks like the traveling salesman problem (TSP) for performance assessment, we underline the importance of scalability and generalization capabilities for diverse optimization tasks. We also systematically benchmark sample efficiency, zero-shot generalization, and adaptability to changes in data distributions of various models. Our experiments show that some recent state-of-the-art methods fall behind their predecessors when evaluated using these new metrics, suggesting the necessity for a more balanced view of the performance of neural CO solvers. We hope RL4CO will encourage the exploration of novel solutions to complex real-world tasks, allowing to compare with existing methods through a standardized interface that decouples the science from the software engineering. We make our library publicly available at https://github.com/kaist-silab/rl4co.

Bootstrapped Training of Score-Conditioned Generator for Offline Design of Biological Sequences

We study the problem of optimizing biological sequences, e.g., proteins, DNA, and RNA, to maximize a black-box score function that is only evaluated in an offline dataset. We propose a novel solution, bootstrapped training of score-conditioned generator (BootGen) algorithm. Our algorithm repeats a two-stage process. In the first stage, our algorithm trains the biological sequence generator with rank-based weights to enhance the accuracy of sequence generation based on high scores. The subsequent stage involves bootstrapping, which augments the training dataset with self-generated data labeled by a proxy score function. Our key idea is to align the score-based generation with a proxy score function, which distills the knowledge of the proxy score function to the generator. After training, we aggregate samples from multiple bootstrapped generators and proxies to produce a diverse design. Extensive experiments show that our method outperforms competitive baselines on biological sequential design tasks. We provide reproducible source code: \href{https://github.com/kaist-silab/bootgen}{https://github.com/kaist-silab/bootgen}.

Transform Once: Efficient Operator Learning in Frequency Domain

Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this work, we study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time: frequency-domain models (FDMs). Existing FDMs are based on complex-valued transforms i.e. Fourier Transforms (FT), and layers that perform computation on the spectrum and input data separately. This design introduces considerable computational overhead: for each layer, a forward and inverse FT. Instead, this work introduces a blueprint for frequency domain learning through a single transform: transform once (T1). To enable efficient, direct learning in the frequency domain we derive a variance-preserving weight initialization scheme and investigate methods for frequency selection in reduced-order FDMs. Our results noticeably streamline the design process of FDMs, pruning redundant transforms, and leading to speedups of 3x to 10x that increase with data resolution and model size. We perform extensive experiments on learning the solution operator of spatio-temporal dynamics, including incompressible Navier-Stokes, turbulent flows around airfoils and high-resolution video of smoke. T1 models improve on the test performance of FDMs while requiring significantly less computation (5 hours instead of 32 for our large-scale experiment), with over 20% reduction in average predictive error across tasks.

Meta-SysId: A Meta-Learning Approach for Simultaneous Identification and Prediction

In this paper, we propose Meta-SysId, a meta-learning approach to model sets of systems that have behavior governed by common but unknown laws and that differentiate themselves by their context. Inspired by classical modeling-and-identification approaches, Meta-SysId learns to represent the common law through shared parameters and relies on online optimization to compute system-specific context. Compared to optimization-based meta-learning methods, the separation between class parameters and context variables reduces the computational burden while allowing batch computations and a simple training scheme. We test Meta-SysId on polynomial regression, time-series prediction, model-based control, and real-world traffic prediction domains, empirically finding it outperforms or is competitive with meta-learning baselines.

Neural Solvers for Fast and Accurate Numerical Optimal Control

Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive but accurate numerical routines are replaced by fast and inaccurate methods, trading inference time for solution accuracy. This paper provides techniques to improve the quality of optimized control policies given a fixed computational budget. We achieve the above via a hypersolvers approach, which hybridizes a differential equation solver and a neural network. The performance is evaluated in direct and receding-horizon optimal control tasks in both low and high dimensions, where the proposed approach shows consistent Pareto improvements in solution accuracy and control performance.