Feasible by Construction: Constrained Rule Search Yields Robust, Readable Offloading Policies Where a Learned Baseline Violates Hard Constraints –- and LLM Structure Proposals Add No Reliable Gain

Abstract

Large language models are increasingly proposed as proposers of deployable decision rules, and vehicular edge (VEC) offloading is a natural target: a rule maps normalized task features to the fraction of a task's compute offloaded to an edge node, under four hard properties (safety isolation, per-task deadline, per-task energy allowance, per-edge capacity). We report a pre-registered, two-phase study on real GPS trajectories (Beijing T-Drive taxis) that drives mobility and channel quality, with a frozen protocol: an exploratory day, criteria frozen before a confirmatory run on a fresh day, and a post-hoc multi-day robustness extension. Three findings. (i) A constrained grammar searched by numerical optimization (differential evolution over a small, readable rule template with the safety guard enforced by construction) produces rules that are feasible on every holdout instance, while a discrete-action DQN baseline violates at least one hard property on $5$ of $12$ instances; feasibility-aware $J$ is $0.638$ vs.\ $0.369$ (paired Wilcoxon $p=0.0012$, $11/12$). (ii) A reimplementation of the domain-standard continuous-action D4PG baseline is unstable on this scenario –- across a $12$-configuration sweep it either plateaus at the conservative all-local policy or collapses to saturation –- and the grammar dominates it on every one of five day-cells (pooled $0.642$ vs.\ $0.585$/$0.377$; $p 8 10^-10$). (iii) Letting the LLM propose rule structures (subsets of a term pool) yields no reliable gain over random structure search at an identical budget ($+0.0015$, within seed noise). We state the honest scope: the grammar's edge is feasibility rather than raw objective value –- on instances where both methods are feasible, $J$ is comparable –- and the trace-to-workload mapping is a derived assumption. Post-hoc stress tests support deployment realism: under lognormal channel shadowing up to $ =0.4$, the champion rule remains feasible in $99.6$–$100\ $720$ re-verifications ($J$ degradation $<1\ victory lap, is the contribution: constrain the search space and the verifier becomes a floor the learned baselines keep failing.