HyCO: A Hybrid Neural Solver for Combinatorial Optimization

• URL: http://arxiv.org/abs/2609.07990v1
• Date: Mon, 07 Sep 2026 21:11:09 GMT
• Title: HyCO: A Hybrid Neural Solver for Combinatorial Optimization
• Abstract summary: We propose a hybrid inference algorithm that constructs a solution prefix with an RL solver and adaptively to a conditional DM switches to complete the remaining decisions.<n> Experimental results on diverse benchmarks demonstrate that HyCO achieves consistent improvements over both backbones.
• Score: 19.59560767239393
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sequential reinforcement learning (RL) solvers and global diffusion model (DM) solvers for neural combinatorial optimization exhibit complementary failure modes under an optimization-regret view. The former enjoys small marginal regret in the early construction stage, but suffers from horizon-wise compounding errors with super-linear regret growth; the latter avoids horizon compounding but incurs linear or sublinear regret w.r.t. the dimension of the remaining unsolved subspace. We propose Hybrid Neural Solver for Combinatorial Optimization (HyCO), a hybrid inference algorithm that constructs a solution prefix with an RL solver and adaptively switches to a conditional DM to complete the remaining decisions. To characterize why such hybridization helps, when to trigger the handover, and how to realize it in practice, we first develop a unified error-scaling theoretical framework and prove that, under explicit error-scaling assumptions, i) the hybrid structure achieves strictly lower expected regret than either backbone alone, and ii) there exists a unique optimal trigger step that minimizes the hybrid regret. We then design a lightweight adaptive trigger that combines policy entropy and RL-DM disagreement to detect trajectory-level signals of the regime shift as a practical proxy, since the optimal trigger step is defined at the expected-regret level and is not directly computable on individual trajectories. Experimental results on diverse benchmarks demonstrate that HyCO achieves consistent improvements over both backbones and support the empirical effectiveness of adaptive triggering.

Related papers

• Closed-Form Spectral Regularization for Multi-Task Model Merging [96.82449201305234]
  Model merging combines several independently fine-tuned experts into a single multi-task model without any training data.<n>State-of-the-art merging methods formulate merging as a layer-wise interference problem.<n>We propose SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent.
  arXiv  Detail & Related papers  (2026-06-05T14:00:47Z)
• Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations [0.0]
  HIN-LRI is a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error.<n>A lightweight neural network, operating on a low-dimensional latent manifold, learns the residual defect that analytical methods cannot close.<n>Experiments show that HIN-LRI improves accuracy over analytical, splitting methods, and neural PDE surrogates, with stable spatial refinement, effective out-of-distribution transfer, and modest online overhead.
  arXiv  Detail & Related papers  (2026-05-06T12:50:36Z)
• Towards The Implicit Bias on Multiclass Separable Data Under Norm Constraints [3.421126849736858]
  We introduce NucGD, a geometry-aware geometry designed to enforce low rank structures through nuclear norm constraints.<n>To enable scalable training, we derive an efficient SVD-free update rule via asynchronous power iteration.<n>We empirically dissect the impact of gradient optimization dynamics, characterizing how varying levels of gradient noise induced by mini-batch sampling and momentum modulate the convergence toward the expected maximum margin solutions.
  arXiv  Detail & Related papers  (2026-03-24T05:51:50Z)
• ODELoRA: Training Low-Rank Adaptation by Solving Ordinary Differential Equations [54.886931928255564]
  Low-rank adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning method in deep transfer learning.<n>We propose a novel continuous-time optimization dynamic for LoRA factor matrices in the form of an ordinary differential equation (ODE)<n>We show that ODELoRA achieves stable feature learning, a property that is crucial for training deep neural networks at different scales of problem dimensionality.
  arXiv  Detail & Related papers  (2026-02-07T10:19:36Z)
• Parallel Diffusion Solver via Residual Dirichlet Policy Optimization [88.7827307535107]
  Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature.<n>Existing solver-based acceleration methods often face significant image quality degradation under a low-dimensional budget.<n>We propose the Ensemble Parallel Direction solver (dubbed as EPD-EPr), a novel ODE solver that mitigates these errors by incorporating multiple gradient parallel evaluations in each step.
  arXiv  Detail & Related papers  (2025-12-28T05:48:55Z)
• SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion [0.8594140167290097]
  SPREAD is a generative framework based on Denoising Diffusion Probabilistic Models (DDPMs)<n>It learns a conditional diffusion process over points sampled from the decision space.<n>It refines candidates via a sampling scheme that uses an adaptive multiple gradient descent-inspired update for fast convergence.
  arXiv  Detail & Related papers  (2025-09-25T12:09:37Z)
• Stable Nonconvex-Nonconcave Training via Linear Interpolation [51.668052890249726]
  This paper presents a theoretical analysis of linearahead as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear can help by leveraging the theory of nonexpansive operators.
  arXiv  Detail & Related papers  (2023-10-20T12:45:12Z)
• Meta-Learning Adversarial Bandit Algorithms [55.72892209124227]
  We study online meta-learning with bandit feedback. We learn to tune online mirror descent generalization (OMD) with self-concordant barrier regularizers.
  arXiv  Detail & Related papers  (2023-07-05T13:52:10Z)
• A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution [50.13564338607482]
  We propose a novel optimization framework for the hyperspectral deconvolution problem, called DeepMix.<n>It consists of three distinct modules, namely, a data consistency module, a module that enforces the effect of the handcrafted regularizers, and a denoising module.<n>This work proposes a context aware denoising module designed to sustain the advancements achieved by the cooperative efforts of the other modules.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Distributed Online Non-convex Optimization with Composite Regret [31.53784277195043]
  We propose a novel composite regret with a new network regret for distributed online general bounds losses. To our knowledge, is the first regret bound for distributed online nonlinear learning.
  arXiv  Detail & Related papers  (2022-09-21T04:16:33Z)
• Cogradient Descent for Bilinear Optimization [124.45816011848096]
  We introduce a Cogradient Descent algorithm (CoGD) to address the bilinear problem. We solve one variable by considering its coupling relationship with the other, leading to a synchronous gradient descent. Our algorithm is applied to solve problems with one variable under the sparsity constraint.
  arXiv  Detail & Related papers  (2020-06-16T13:41:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.