# Opti-Q: A Constraint-Based Optimization Framework for Multi-LLM Question Planning

arXiv: https://arxiv.org/abs/2607.22621 · HTML: https://mlsanity.com/paper/2607.22621/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 30 of 39)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [BERTopic: Neural topic modeling with a class-based TF-IDF procedure](https://mlsanity.com/paper/2203.05794/) (2022)
- [Reading Wikipedia to Answer Open-Domain Questions](https://mlsanity.com/paper/1704.00051/) (2017)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [The Carbon Footprint of Machine Learning Training Will Plateau, Then Shrink](https://mlsanity.com/paper/2204.05149/) (2022)
- [Benchmarking LLMs via Uncertainty Quantification](https://mlsanity.com/paper/2401.12794/) (2024)
- [The rising costs of training frontier AI models](https://mlsanity.com/paper/2405.21015/) (2024)
- [ChatQA: Surpassing GPT-4 on Conversational QA and RAG](https://mlsanity.com/paper/2401.10225/) (2024)
- [Harnessing Multiple Large Language Models: A Survey on LLM Ensemble](https://mlsanity.com/paper/2502.18036/) (2025)
- [Zeus: Understanding and Optimizing GPU Energy Consumption of DNN Training](https://mlsanity.com/paper/2208.06102/) (2022)
- [Bao: Learning to Steer Query Optimizers](https://mlsanity.com/paper/2004.03814/) (2020)
- [Prompt Design and Engineering: Introduction and Advanced Methods](https://mlsanity.com/paper/2401.14423/) (2024)
- [LLM-TOPLA: Efficient LLM Ensemble by Maximising Diversity](https://mlsanity.com/paper/2410.03953/) (2024)
- [Towards Optimizing the Costs of LLM Usage](https://mlsanity.com/paper/2402.01742/) (2024)
- [Cardinality Estimation in DBMS: A Comprehensive Benchmark Evaluation](https://mlsanity.com/paper/2109.05877/) (2021)
- [When One LLM Drools, Multi-LLM Collaboration Rules](https://mlsanity.com/paper/2502.04506/) (2025)

## Abstract (arXiv)

While large language models (LLMs) enable strong question answering (QA), budgeted deployment is complicated by nondeterminism and heterogeneous resource profiles (cost, latency, and energy). We present OPTI-Q, a database-inspired, cost-based optimizer that implements a plan-before-execute paradigm for multi-LLM orchestration. OPTI-Q models LLM invocations as physical operators in an execution DAG and, for each question, searches for plans that optimize answer quality (QoA) while trading off financial cost, latency, and energy under user-specified resource constraints. Plans can include sequential operators that pass intermediate answers as context and parallel/blend operators that run models concurrently and merge their outputs. To search this space without executing each candidate plan, OPTI-Q uses PERFDB, a statistics catalog populated and refreshed from benchmarks and execution traces, to estimate the QoA and resource costs of both individual operators and composed subplans. Using these estimates, OPTI-Q performs Pareto-frontier search and selects a final plan based on user preferences. On MMLU-Pro and SimpleQA under user-specified budgets, OPTI-Q improves average QoA by ~58% and ~41% over baselines at comparable cost, demonstrating that database-style planning yields better quality-resource trade-offs for multi-LLM QA.