Agentic ESOpt: Fine-Tuning Long-Horizon LLM Agents with Minimal GPU Requirements

Reinforcement Learning (RL) has been promising in single-turn LLM fine-tuning. However, long-horizon agentic reasoning introduces increasingly branching interactions and sparse rewards, exposing several limitations of RL: its heavyweight backpropagation-based training stack makes it impractical to fine-tune larger LLMs, and longer-horizon trajectories make credit assignment in RL substantially harder. This paper argues that evolution strategies (ES) can be a better choice for fine-tuning long-horizon LLM agents. Compared with agentic RL, ES offers three key advantages: 1) Model Scalability: ES enables full-parameter optimization with only minimal, inference-level GPU memory, making it possible to fine-tune large LLMs. 2) Flexibility: its lightweight, black-box feedback interface makes ES fine-tuning easy to compose with prompt-space evolution (e.g., skill optimization & test-time compute); and 3) Long-Horizon Scalability: ES performs trajectory-level parameter attribution without decomposing rewards across horizons, yielding better scalability than Agentic RL as the horizon length grows. Based on this insight, we propose Agentic ESOpt, a full-parameter agentic fine-tuning framework tailored to flexible parameter--context co-evolution. At each step, Agentic ESOpt samples perturbations around the current LLM parameters, evaluates the resulting agents with rewards, and applies an online reward-weighted update. To improve the exploration--adaptation trade-off, Agentic ESOpt further introduces a cosine decay schedule of the perturbation scale $σ$. On WebArena-Lite, full-parameter optimization of Qwen-3.5-27B improves the No Skill baseline by 6.69%. In test-time automatic heuristic design, Agentic ESOpt performs online prompt--parameter co-evolution, improving its matched baseline in 28 of 36 settings.

SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver

Generalist neural routing solvers have shown great potential in solving diverse vehicle routing problems (VRPs) with a unified model. However, existing solvers are typically limited to symmetric settings or degrade in performance when switching to asymmetric settings due to input inconsistencies or inherent structural differences, substantially limiting their practicality in real-world scenarios that encompass both scenarios. To address this limitation, we define the spatial position of each node based on the relative distances to a specific set of pivots and further propose a Spatial Pivot-Aligned Coordinate-free Embedding (SPACE) framework that unifies node representation and solution generation across symmetric and asymmetric VRPs. Specifically, we construct a bidirectional Frechet representation using a novel furthest pivot sampling strategy to enable invariant node representations across distinct problem settings. Furthermore, we introduce a weight-decomposed adaptive decoding mechanism that decouples geometric perception from problem representations, mitigating the overfitting of constraint decisions to a specific geometry setting. Extensive experiments on 110 VRP variants, comprising 55 symmetric problems and their asymmetric counterparts, demonstrate that SPACE achieves promising zero-shot generalization in both symmetric and asymmetric VRPs.

Rethinking Constraint Awareness for Efficient State Embedding of Neural Routing Solver

Heavy-Encoder-Light-Decoder (HELD) neural routing solvers have emerged as a promising paradigm due to their broad applicability across multiple vehicle routing problems (VRPs). However, they typically struggle with VRP variants with complex constraints. To address this limitation, this paper systematically revisits existing neural solvers from the perspective of the generation mechanism for state embeddings (i.e., query vector prior to compatibility calculation) during decoding. We identify that current mechanisms restrict the observation space during attention computation, introducing a key bottleneck to achieving high-quality solutions. Through detailed empirical analysis, we demonstrate the necessity of preserving a global observation space. To overcome the constraint-agnostic drawback inherent to global observation spaces, we propose a simple yet powerful Constraint-Aware Residual Modulation (CARM) module. By adaptively modulating the context embedding with constraint-relevant variables, CARM effectively enhances constraint awareness, enabling the neural solver to fully leverage the global observation space and generate an efficient state embedding. Extensive experimental results across two single-task and five multi-task neural routing solvers confirm that the CARM module consistently boosts baseline performance. Notably, solvers equipped with our CARM achieve substantial improvements in scaling to large-scale instances and in generalizing to unseen VRP variants. These findings provide valuable insights for the architectural design of neural routing solvers.