Test-Time Adaptation for Unsupervised Combinatorial Optimization

TL;DR

This paper addresses the gap between generalization-focused unsupervised NCO and per-instance optimization by introducing TACO, a model-agnostic test-time adaptation framework that uses a shrink-perturb warm-start to enable effective instance-level refinement with minimal overhead. TACO is compatible with existing backbones (EGN and Meta-EGN) and is evaluated on canonical graph problems (Minimum Vertex Cover and Maximum Clique) under static, distribution-shifted, and dynamic conditions, where it consistently improves solution quality over baselines. The work demonstrates that principled warm-starting can unlock rapid adaptation without sacrificing learned inductive bias, offering a practical bridge between two major NCO paradigms. The results suggest that TACO improves robustness to shifts and dynamics while maintaining efficient runtimes, highlighting its potential for real-world deployment of unsupervised NCO solvers.

Abstract

Unsupervised neural combinatorial optimization (NCO) enables learning powerful solvers without access to ground-truth solutions. Existing approaches fall into two disjoint paradigms: models trained for generalization across instances, and instance-specific models optimized independently at test time. While the former are efficient during inference, they lack effective instance-wise adaptability; the latter are flexible but fail to exploit learned inductive structure and are prone to poor local optima. This motivates the central question of our work: how can we leverage the inductive bias learned through generalization while unlocking the flexibility required for effective instance-wise adaptation? We first identify a challenge in bridging these two paradigms: generalization-focused models often constitute poor warm starts for instance-wise optimization, potentially underperforming even randomly initialized models when fine-tuned at test time. To resolve this incompatibility, we propose TACO, a model-agnostic test-time adaptation framework that unifies and extends the two existing paradigms for unsupervised NCO. TACO applies strategic warm-starting to partially relax trained parameters while preserving inductive bias, enabling rapid and effective unsupervised adaptation. Crucially, compared to naively fine-tuning a trained generalizable model or optimizing an instance-specific model from scratch, TACO achieves better solution quality while incurring negligible additional computational cost. Experiments on canonical CO problems, Minimum Vertex Cover and Maximum Clique, demonstrate the effectiveness and robustness of TACO across static, distribution-shifted, and dynamic combinatorial optimization problems, establishing it as a practical bridge between generalizable and instance-specific unsupervised NCO.

Figures (5)

• Figure 1: Performance ($\uparrow$) of trained and randomly initialized (rand) EGN models with respect to the number of fine-tuning (FT) steps. Detailed setup is explained in Section \ref{['sec:res']}.
• Figure 2: Two versions of TACO: standard vs. online.
• Figure 3: Mean ApR of methods using EGN as the backbone on static MVC ($\downarrow$) and MC ($\uparrow$) problems with respect to the number of update steps. "FT" stands for fine-tuning; "rand" means models are freshly initialized. The wall clock time factors in the decoding operations. Subplots not showing results of "EGN-rand-FT" are zoomed in for better illustration (i.e., freshly initialized models perform much worse). Figure \ref{['fig:egn_show_all']} in Appendix \ref{['app:add-res']} shows all results.
• Figure 4: Mean ApR of methods using Meta-EGN as the backbone on static MVC ($\downarrow$) and MC ($\uparrow$) problems with respect to the number of update steps. "FT" stands for fine-tuning. The wall clock time factors in the decoding operations.
• Figure 5: Mean ApR of methods using EGN as the backbone on static MVC ($\downarrow$) and MC ($\uparrow$) problems with respect to the number of update steps. "FT" stands for fine-tuning; "rand" means models are freshly initialized. The wall clock time factors in the decoding operations.