Title:Certified Predictive Value-of-Advice Gating for Cost-Aware Language-Model Guidance in Reinforcement Learning

Abstract:Language-model advice can accelerate reinforcement learning, but calls are costly and returned actions may be stale or wrong. We formulate advice acquisition as a response-contingent metareasoning problem: before querying, the controller predicts possible parsed responses, evaluates the decision and declared continuation that would follow each response, and queries only when a lower confidence bound on predictive value exceeds the priced cost. Execution is governed separately by an action-specific certificate. Under explicit assumptions, certified advice is near-optimal, a wrapped learner inherits fallback regret only under intervention stability, and conservative allocation loses at most the declared query-value estimation error relative to a myopic oracle. On BabyAI, a proxy-calibrated controller with Qwen2.5-1.5B and 7B advisors improves GoToObj return over no querying by 0.029 +/- 0.016 and 0.030 +/- 0.015 across 20 seeds while reducing calls by more than 97% relative to always-query. GoToLocal is a null result. Exactly matched-call tests show an advantage over random placement only for the 1.5B advisor and no advantage over an equal-budget early schedule. Mondrian calibration improves decision-relevant empirical coverage from 0.47 to 0.85, still below the 0.90 target, while the formally covered radius is vacuous. The demonstrated benefit is therefore robust sparse advice volume on a useful task, not a proven per-state placement advantage.

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