Task Specialization Fine-Tuning for Contextual Reinforcement Learning

Contextual Reinforcement Learning (CRL) seeks to generalize classical RL by maximizing task coverage across a context space of related tasks. While prior works often train from scratch and rely on either multi-task learning for a single policy or strategically training multiple policies, we advocate for a unified alternative: pretraining a single policy with good initial performance, followed by fine-tuning multiple policies for task specialization. This new paradigm, however, introduces unique challenges, such as heterogeneous marginal returns and sample inefficiency. This raises a critical research question: given a pretrained policy and a constrained budget, how much fine-tuning should each task region receive to enable sample-efficient CRL? To this end, we propose Task Specialization Fine-Tuning (TSFT), an online framework that predicts fine-tuning performance with a simple parametric model and exactly solves the resulting discrete budget allocation problem via integer linear programming. Extensive experiments across diverse decision domains, including combinatorial optimization, continuous control, and LLM fine-tuning, demonstrate that TSFT significantly outperforms baselines in task coverage and approaches oracle performance. Our work charts a new direction for model-based CRL, aligning with the modern pretrain-finetune era.

ToolAnchor: Anchoring Counterfactual Context to Boost Agentic Tool-use Capability

Tool-augmented large language model agents excel at long-horizon tasks, yet they are typically post-trained on fixed toolsets. When tasks demand new tools, these agents struggle to incorporate them effectively, and retraining from scratch is often impractical. We identify the core obstacle in such toolset expansion problem as behavioral inertia: the tendency of agents to fall back on familiar tools and established reasoning patterns despite having access to new ones. We demonstrate that injecting counterfactual anchor contexts at critical decision points can break this inertia, recovering failed trajectories by eliciting suppressed agent capabilities. To scale this insight, we propose ToolAnchor, a framework that uses teacher models to hypothesize these counterfactual contexts, verifies them via student rollouts, and internalizes the successful interventions through agentic post-training. Extensive evaluations across general AI assistant (GAIA), textual search (BrowseComp), and visual search (VDR-Bench) tasks demonstrate that ToolAnchor consistently exhibits competitive performance under expanded toolsets. Our work bridges the gap between static post-training and dynamic adaptation, charting a new path for scalable agentic reinforcement learning.

Interpreting Neural Combinatorial Optimization via Evolving Programmatic Bottlenecks

Neural Combinatorial Optimization (NCO) achieves strong performance, yet its black-box nature remains a key roadblock to deployment and scientific diagnosis. Standard interpretability tools, such as Concept Bottleneck Models (CBMs), are ill-equipped for NCO, whose decisions are dynamic, state-dependent, and lack proper concept vocabulary definition. To close this gap, we introduce Evolving Programmatic Bottlenecks (EPB), to our knowledge, the first framework for interpreting NCO policies by distilling black-box NCO models into human-readable program portfolios. EPB employs an LLM to autonomously evolve a bank of programs, where each program's per-step action distribution serves as the bottleneck. EPB works through an iterative framework: Block I fixes program bank capacity and introduces a hybrid textual-numerical gradient descent scheme that couples numerical gradients for student router updates and textual gradients for LLM-based program revision; Block II dynamically adapts bank capacity via fault-targeted expansion and redundancy pruning. Extensive experiments demonstrate EPB's effectiveness and broad applicability, where the distilled program portfolios largely match original performance. EPB also reveals that NCO behavior shifts across optimization stages and can be approximated as a composition of classic heuristic variants. Our work advances interpretable NCO and establishes EPB as a promising tool for interpreting sequential decision-making models.

Beyond Static Priors: Dynamic Neural Guidance for Large-Scale Ant Colony Optimization

Neural-guided Ant Colony Optimization (ACO) suffers from a fundamental training-inference misalignment: policies are typically trained to generate static priors (e.g., heatmaps), yet deployed to guide iterative, long-horizon search processes. In this paper, we present DyNACO, a novel framework that achieves dynamic neural guidance by periodically observing the pheromone distribution and the incumbent solution. To make DyNACO tractable at scale, we pair the policy with a perturbation-based ACO backend and a scope-restricted refinement mechanism that jointly ensure efficacy and stable credit assignment. On TSP, DyNACO scales to 100,000-node instances and outperforms neural baselines while often reducing total runtime compared to the unguided solver. We extend DyNACO to CVRP via a capacity-aware backend, consistently improving the unguided baseline with less than 1% neural overhead. We further provide in-depth analysis validating the model's generalization capabilities and elucidating why dynamic guidance outperforms static priors. Our work underscores the necessity of aligning neural training with iterative search dynamics in learning-guided optimization. The code is available at https://github.com/shoraaa/DyNACO.

Rethinking Positional Encoding for Neural Vehicle Routing

Transformer-based models have become the dominant paradigm for neural combinatorial optimization (NCO) of vehicle routing problems (VRPs), yet the role of positional encoding (PE) in these architectures remains largely unexplored. Unlike natural language, where tokens are uniformly spaced on a line, routing solutions exhibit several properties that render standard NLP positional encodings inadequate. In this work, we formalize three such structural properties that a routing-aware PE should respect, namely anisometric node distances, cyclic and direction-aware topology, and hierarchical depot-anchored global multi-route structure, combining them with a unifying design principle of geometric grounding. Guided by these criteria, we analyze and compare PE methods spanning NLP, graph-transformer, and routing-specific families, and propose a hierarchical anisometric PE that combines a distance-indexed, circularly consistent in-route encoding with a depot-anchored angular cross-route encoding. Extensive experiments across diverse VRP variants demonstrate that geometry-grounded PE consistently outperforms index-based alternatives, with gains that transfer across problem variants, model architectures, and distribution shifts.

Learning-guided Prioritized Planning for Lifelong Multi-Agent Path Finding in Warehouse Automation

Lifelong Multi-Agent Path Finding (MAPF) is critical for modern warehouse automation, which requires multiple robots to continuously navigate conflict-free paths to optimize the overall system throughput. However, the complexity of warehouse environments and the long-term dynamics of lifelong MAPF often demand costly adaptations to classical search-based solvers. While machine learning methods have been explored, their superiority over search-based methods remains inconclusive. In this paper, we introduce Reinforcement Learning (RL) guided Rolling Horizon Prioritized Planning (RL-RH-PP), the first framework integrating RL with search-based planning for lifelong MAPF. Specifically, we leverage classical Prioritized Planning (PP) as a backbone for its simplicity and flexibility in integrating with a learning-based priority assignment policy. By formulating dynamic priority assignment as a Partially Observable Markov Decision Process (POMDP), RL-RH-PP exploits the sequential decision-making nature of lifelong planning while delegating complex spatial-temporal interactions among agents to reinforcement learning. An attention-based neural network autoregressively decodes priority orders on-the-fly, enabling efficient sequential single-agent planning by the PP planner. Evaluations in realistic warehouse simulations show that RL-RH-PP achieves the highest total throughput among baselines and generalizes effectively across agent densities, planning horizons, and warehouse layouts. Our interpretive analyses reveal that RL-RH-PP proactively prioritizes congested agents and strategically redirects agents from congestion, easing traffic flow and boosting throughput. These findings highlight the potential of learning-guided approaches to augment traditional heuristics in modern warehouse automation.

RADAR: Learning to Route with Asymmetry-aware DistAnce Representations

Recent neural solvers have achieved strong performance on vehicle routing problems (VRPs), yet they mainly assume symmetric Euclidean distances, restricting applicability to real-world scenarios. A core challenge is encoding the relational features in asymmetric distance matrices of VRPs. Early attempts directly encoded these matrices but often failed to produce compact embeddings and generalized poorly at scale. In this paper, we propose RADAR, a scalable neural framework that augments existing neural VRP solvers with the ability to handle asymmetric inputs. RADAR addresses asymmetry from both static and dynamic perspectives. It leverages Singular Value Decomposition (SVD) on the asymmetric distance matrix to initialize compact and generalizable embeddings that inherently encode the static asymmetry in the inbound and outbound costs of each node. To further model dynamic asymmetry in embedding interactions during encoding, it replaces the standard softmax with Sinkhorn normalization that imposes joint row and column distance awareness in attention weights. Extensive experiments on synthetic and real-world benchmarks across various VRPs show that RADAR outperforms strong baselines on both in-distribution and out-of-distribution instances, demonstrating robust generalization and superior performance in solving asymmetric VRPs.

Towards Efficient Constraint Handling in Neural Solvers for Routing Problems

Neural solvers have achieved impressive progress in addressing simple routing problems, particularly excelling in computational efficiency. However, their advantages under complex constraints remain nascent, for which current constraint-handling schemes via feasibility masking or implicit feasibility awareness can be inefficient or inapplicable for hard constraints. In this paper, we present Construct-and-Refine (CaR), the first general and efficient constraint-handling framework for neural routing solvers based on explicit learning-based feasibility refinement. Unlike prior construction-search hybrids that target reducing optimality gaps through heavy improvements yet still struggle with hard constraints, CaR achieves efficient constraint handling by designing a joint training framework that guides the construction module to generate diverse and high-quality solutions well-suited for a lightweight improvement process, e.g., 10 steps versus 5k steps in prior work. Moreover, CaR presents the first use of construction-improvement-shared representation, enabling potential knowledge sharing across paradigms by unifying the encoder, especially in more complex constrained scenarios. We evaluate CaR on typical hard routing constraints to showcase its broader applicability. Results demonstrate that CaR achieves superior feasibility, solution quality, and efficiency compared to both classical and neural state-of-the-art solvers.

A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention

Mixed-integer linear programming (MILP), a widely used modeling framework for combinatorial optimization, are central to many scientific and engineering applications, yet remains computationally challenging at scale. Recent advances in deep learning address this challenge by representing MILP instances as variable-constraint bipartite graphs and applying graph neural networks (GNNs) to extract latent structural patterns and enhance solver efficiency. However, this architecture is inherently limited by the local-oriented mechanism, leading to restricted representation power and hindering neural approaches for MILP. Here we present an attention-driven neural architecture that learns expressive representations beyond the pure graph view. A dual-attention mechanism is designed to perform parallel self- and cross-attention over variables and constraints, enabling global information exchange and deeper representation learning. We apply this general backbone to various downstream tasks at the instance level, element level, and solving state level. Extensive experiments across widely used benchmarks show consistent improvements of our approach over state-of-the-art baselines, highlighting attention-based neural architectures as a powerful foundation for learning-enhanced mixed-integer linear optimization.

SHIELD: Multi-task Multi-distribution Vehicle Routing Solver with Sparsity and Hierarchy

Recent advances toward foundation models for routing problems have shown great potential of a unified deep model for various VRP variants. However, they overlook the complex real-world customer distributions. In this work, we advance the Multi-Task VRP (MTVRP) setting to the more realistic yet challenging Multi-Task Multi-Distribution VRP (MTMDVRP) setting, and introduce SHIELD, a novel model that leverages both sparsity and hierarchy principles. Building on a deeper decoder architecture, we first incorporate the Mixture-of-Depths (MoD) technique to enforce sparsity. This improves both efficiency and generalization by allowing the model to dynamically select nodes to use or skip each decoder layer, providing the needed capacity to adaptively allocate computation for learning the task/distribution specific and shared representations. We also develop a context-based clustering layer that exploits the presence of hierarchical structures in the problems to produce better local representations. These two designs inductively bias the network to identify key features that are common across tasks and distributions, leading to significantly improved generalization on unseen ones. Our empirical results demonstrate the superiority of our approach over existing methods on 9 real-world maps with 16 VRP variants each.