Authors: Arlen Dean, Zijin Zhang, Stefanus Jasin, Yuqing Liu
Organizations: Washington University in St. Louis, Olin Business School · Boston College, Carroll School of Management · University of Michigan, Stephen M. Ross School of Business · University of Michigan, Industrial and Operations Engineering
Deploying multiple large language models (LLMs) in parallel to classify an unknown ground-truth label is a common practice, yet the problem of optimally allocating queries across heterogeneous models remains poorly understood. In this paper, we formulate a robust, offline query-planning problem that minimizes total query cost subject to statewise error constraints which guarantee reliability for every possible ground-truth label. We first establish that this problem is NP-hard via a reduction from the minimum-weight set cover problem. To overcome this intractability, we develop a surrogate by combining a union bound decomposition of the multi-class error into pairwise comparisons with Chernoff-type concentration bounds. The resulting surrogate admits a closed-form, multiplicatively separable expression in the query counts and is guaranteed to be feasibility-preserving. We further show that the surrogate is asymptotically tight at the optimization level: the ratio of surrogate-optimal cost to true optimal cost converges to one as error tolerances shrink, with an explicit rate of O(loglog(1/αmin)/log(1/αmin)). Finally, we design an asymptotic fully polynomial-time approximation scheme (AFPTAS) that returns a surrogate-feasible query plan within a (1+ε) factor of the surrogate optimum.
Multi-LLM collaboration studies how large language models share work, exchange information, and combine outputs to improve capability, reliability, or cost.
Language models make it easy to build classifiers by simply prompting a model with the sample to classify. However, their predictions are neither deterministic nor uniformly reliable across samples. How can we combine predictions from different models to improve reliability? We view LLM classifiers as noisy measurement instruments of an underlying target label. Our goal is to maximize average classification accuracy at a given average query cost. To this end, we introduce circuits that organize LLM classifiers into an adaptive sequence of queries and decisions. We then characterize the optimal circuit, obtain the fundamental limits of achievable accuracy, and provide practical insights on realizing the optimal circuit. Across seven classification tasks spanning safety, health, political science, human preference, agent evaluation, decision-making and reasoning, our method improves the cost-accuracy frontier over routing and cascading baselines.
Hadi Khalaf, Sajani Vithana, Kunal Talreja +3
Harvard School of Engineering and Applied Science · Kempner Institute for the Study of Natural & Artificial Intelligence · School of Electrical and Computer Engineering, Georgia Institute of Technology +2
We study the problem of routing queries to large language models (LLMs) under cost, GPU resources, and concurrency constraints. Prior per-query routing methods often fail to control batch-level cost, especially under non-uniform or adversarial batching. To address this, we propose a batch-level, resource-aware routing framework that jointly optimizes model assignment for each batch while respecting cost and model capacity limits. We further introduce a robust variant that accounts for uncertainty in predicted LLM performance, along with an offline instance allocation procedure that balances quality and throughput across multiple models. Experiments on two multi-task LLM benchmarks show that robustness improves accuracy by 1-14% over non-robust counterparts (depending on the performance estimator), batch-level routing outperforms per-query methods by up to 24% under adversarial batching, and optimized instance allocation yields additional gains of up to 3% compared to a non-optimized allocation, all while strictly controlling cost and GPU resource constraints.
Jelena Markovic-Voronov, Kayhan Behdin, Yuanda Xu +3
Statistical estimation often involves tradeoffs between expensive, high-quality measurements and a variety of lower-quality proxies. We introduce Multiple-Prediction-Powered Inference (MultiPPI): a general framework for constructing statistically efficient estimates by optimally allocating resources across these diverse data sources. This work provides theoretical guarantees about the minimax optimality, finite-sample performance, and asymptotic normality of the MultiPPI estimator. Through experiments across three diverse large language model (LLM) evaluation scenarios, we show that MultiPPI consistently achieves lower estimation error than existing baselines. This advantage stems from its budget-adaptive allocation strategy, which strategically combines subsets of models by learning their complex cost and correlation structures.
Charlie Cowen-Breen, Alekh Agarwal, Stephen Bates +4
Massachusetts Institute of Technology · Google Research · Google DeepMind