Title: Conformal Arbitrage: Risk-Controlled Balancing of Competing Objectives in Language Models
Venue: NeurIPS 2025
Accepted: yes
Keywords: Large Language Model

LLM

Alignment

Trustworthy AI

Model Routing

Conformal Prediction

Conformal Risk Control
Abstract: Modern language‑model deployments must often balance competing objectives—for example, helpfulness versus harmlessness, cost versus accuracy, and reward versus safety. We introduce Conformal Arbitrage, a post‑hoc framework that learns a data‑driven threshold to mediate between a Primary model optimized for a primary objective and a more conservative Guardian—which could be another model or a human domain expert—aligned with a guardrail objective. The threshold is calibrated with conformal risk control, yielding finite‑sample, distribution‑free guarantees that the long‑run frequency of undesirable events (such as factual errors or safety violations) does not exceed a user‑specified quota. Because Conformal Arbitrage operates wholly at the API level—without requiring access to model logits or updating model weights—it complements weight‑based alignment techniques and integrates seamlessly with existing cost‑aware cascades. Empirically, Conformal Arbitrage traces an efficient frontier, allowing users to define an acceptable performance level for one objective while maximizing utility in another. We observe that our method outperforms (in terms of accuracy) cost-matched random routing between models. These properties make Conformal Arbitrage a practical, theoretically grounded tool for trustworthy and economical deployment of large language models across a broad range of potentially competing objectives.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a new method based on conformal risk control for multiple-choice tasks to defer instances from a primary model to a secondary \"Guardian\" model in order to guarantee a desired safeguard objective while maximizing a primary objective (e.g., accuracy vs. cost). The authors motivate the usage of this method in the context of LLMs and show experimentally that it outperforms random deferral of instances at the same cost.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n- I think the application of conformal risk control for deferring to specialized (language) models in order to guarantee a certain objective is interesting\n- The methodology/theory seems sound to me (up to a minor question see below)\n- The experiment setup is in general well chosen for the methodology and the results are convincing, but the random baseline is a weak comparison\n\n**Weaknesses**\n- The framework requires specialized models (or a human expert) for each of the objectives. It (implicitly) assumes that in general the specialized model (guardian model) will make less mistakes than the non-specialized one. However, in practice this might not always be the case for all types of inputs, e.g., when the \"guardian model\" is a human expert. (The experimental setup was chosen such that the assumption holds so it is unclear how beneficial it is when it doesn't.)\n- I find the paper lacks coherence in the presentation which makes the paper unclear at times. The introduction and related work section refers broadly to the application of conformal arbitrage to LLMs. However, the methodology section uses the terminology \"action\" and \"action sets\" to refer to the output without connecting it to the context of LLMs. The experiments then only handle multiple choice questions with this limitation not being explicitly mentioned earlier.\n- the application possibilities/significance in the context of LLMs is narrow due to the method only being applicable to multiple-choice tasks.\n\nQUESTIONS:\n- I think it should be made explicitly clear much earlier that the methodological contributions only apply to multiple-choice tasks. This is only stated explicitly in the last paragraph under limitations. In particular, it would make it clearer why in the methodology section the framework is presented in terms of actions and action sets and how you can obtain a score for the actions from the LLM (but this should ideally also be clarified explicitly in this section).\n- It seems the methodology and the experiments treat the LLM as a basic classifier (multiple-choice tasks and confidence score output). In this case, could you compare how your method differs from methods in the learning to defer literature?\n- Theorem 1 requires $R$ to be continuous and strictly decreasing but to me it seems that both do not hold given the definition of $L_i(\\lambda)$ in Equation 2 (Eq. 2 looks like a decreasing piecewise constant function). Could you explain if the theorem would still hold?\n\n**Minor Comments**\n- line 53: twice \"the the\" written\n- line 164: \"any black-box predictor attains ($1-\\alpha$) coverage\" this is confusing, the conformal predictor attains the coverage not the black-box classifier.\n- line 221: \"$\\lambda$-relaxed set\" should be \"$\\hat{\\lambda}$-relaxed set\"?\n- Algorithm 1 line 7: \"G(a)\" should be \"g(x,a)\"?\n- line 241: \"$\\lambda$ can only shrink the set of contexts\" should be \"set of actions\"?\n\nLIMITATIONS:\nThe authors have very briefly addressed limitations. However, I think the main limitation of their method being only applicable in multiple-choice tasks should be mentioned much earlier, such as in the introduction.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper is focusing on the problem of tensions between potentially competing objectives in LLM models (for example, helpfulness versus harmlessness, cost versus accuracy, and reward versus safety). The authors propose Conformal Arbitrage, a post-hoc API framework based on conformal risk control that learns a data-driven threshold to mediate between a model optimized for a primary objective and a more conservative guardian (another model or a human domain expert). The authors test their framework in two trade-off settings, i.e., cost-accuracy axis and helpfulness-harmlessness axis on TruthfulQA, PKU-SafeRLHFand MMLU datasets. Comparisons against single-model baselines and random routers show that the proposed framework outperforms cost- and  risk-matched random routing, recovers most gains of the stronger model at a fraction of the cost, and works with closed-API deployments without accessing weights or logits.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThe proposed algorithm is logical, elegant and theoretically grounded - instead of rejecting an uncertain instance, escalate it to a more conservative model. The Conformal Arbitrage framework  works with black box APIs, requires no access to logits or probabilities, and only makes one call to the primary model, and when the call is routed just one call to the guardian model.\n\nThe authors include ablation analysis which shows that the Conformal Arbitrage frontier is stable overall. Results demonstrate that the framework traces an efficient frontier between helpfulness and harmlessness. \n\nExtensive review of related work, the framework is well placed in the context of the literature. \n\nThe paper is well written and argumented, and addresses an important open problem in the literature.\n \n\nWeaknesses:\n\nThe framework can only be applied to multiple choice tasks and does not work with free-form text generation, which is a limitation of the proposed approach. \n\nThe authors do not explain why they focus only on single-step, two-model router  (Primary and Guardian); while they acknowledge that deeper cascades are possible, they do not explore this in the paper - it is likely this could yield improved results or finer control.\n\nWhile Conformal Arbitrage is a lightweight and theoretically grounded approach, its current form is best suited for structured tasks and simple model pairs. The authors leave enhancements in generalization to complex tasks and richer model configurations for future work.\n\nQUESTIONS:\nHow would you design a task specific loss function for applying your framework to free-form text generation?\n\nLIMITATIONS:\nThe authors acknowledge the limitations of their work and important directions to further explore for extending their framework to varied tasks.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

comments: SUMMARY:
This paper presents a data-driven approach called Conformal Arbitrage (CA), rooted in conformal risk control theory. This method allows for precise control over trade-offs, enabling users to explicitly specify how much they are willing to compromise on one objective in order to gain on another. Notably, CA operates entirely at the API level, without the need for access to model logits or adjustments to model weights. Experiments conducted with the GPT-4.1 series demonstrate Pareto improvements of CA over random model selection strategies.

STRENGTHS AND WEAKNESSES:
1. CA functions as a lightweight router that mediates between a primary model optimized for a specific objective and a more conservative Guardian model.
2. The promising results indicate that the proposed method effectively leverages the performance gap between specialized models, yielding superior outcomes compared to naive model selection.

QUESTIONS:
1. In Algorithm 1, how can we choose an appropriate lambda value based on different data distributions and tasks?
2. Regarding the first cost versus accuracy task, can similar results be achieved for long-to-short tasks? For instance, in "Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning" (2025). For the second task, instead of assigning a score to a response candidate, can the method be extended to safety generation tasks?
3. In Figure 1, when alpha = 0.25, could you explain why the performance of CA is lower than that of random routing?

LIMITATIONS:
Please see my questions.
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-05