For large language models deployed through black-box APIs, recurring inference costs often exceed one-time training costs. This motivates composed agentic systems that amortize expensive reasoning into reusable intermediate representations. We study a broad class of such systems, termed Guide-Core Policies (GCoP), in which a guide model generates a structured strategy that is executed by a black-box core model. This abstraction subsumes base, supervised, and advisor-style approaches, which differ primarily in how the guide is trained. We formalize GCoP under a cost-sensitive utility objective and show that end-to-end performance is governed by guide-averaged executability: the probability that a strategy generated by the guide can be faithfully executed by the core. Our analysis shows that existing GCoP instantiations often fail to optimize executability under deployment constraints, resulting in brittle strategies and inefficient computation. Motivated by these insights, we propose ExecTune, a principled training recipe that combines teacher-guided acceptance sampling, supervised fine-tuning, and structure-aware reinforcement learning to directly optimize syntactic validity, execution success, and cost efficiency. Across mathematical reasoning and code-generation benchmarks, GCoP with ExecTune improves accuracy by up to 9.2% over prior state-of-the-art baselines while reducing inference cost by up to 22.4%. It enables Claude Haiku 3.5 to outperform Sonnet 3.5 on both math and code tasks, and to come within 1.7% absolute accuracy of Sonnet 4 at 38% lower cost. Beyond efficiency, GCoP also supports modular adaptation by updating the guide without retraining the core.
Figures & tables
Figure 1: Reward–cost trade-off. Test performance versus total inference cost on GSM8K (left; core= Haiku-3.5 ) and KodCode (right; core= Haiku-3.0 ). A small ExecTune guide ( Qwen3-1.7B ) yields the best accuracy–cost trade-off among GCoP variants, outperforming prompting/ICL and GCoP (Base/SFT/Advisor) while remaining far cheaper than frontier baselines. GCoP (ExecTune) matches or exceeds Sonnet-3.5 and approaches Sonnet-4 at substantially lower cost, showing that executable strategies can reliably steer black-box cores toward large-model performance.
Figure 2: SFT dataset curation pipeline. A strong model (LLM-1; e.g., Claude Sonnet 4.5) extracts a high-level strategy from a (problem, solution) pair. A weaker frontier model (LLM-2; e.g., Claude Haiku 3) generates a solution conditioned on the problem and strategy. An environment provides reward and feedback; unsuccessful strategies are iteratively refined by LLM-1. The resulting (problem, strategy) pairs form the SFT corpus.
Figure 3: Effect of iterative strategy refinement during acceptance sampling: additional refinement iterations increase the probability that the target core solves the problem when conditioned on the proposed strategy.
Table 1: Performance on math and code benchmarks. Guided generation with ExecTune achieves the strongest results, demonstrating that optimizing guides for executability improves black-box core performance. FT Recipe denotes the guide fine-tuning recipe.
Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University · Department of Data and Systems Engineering, The University of Hong Kong · College of Economics and Management, Zhejiang Normal University +3