# Prompt Engineering Through the Lens of Optimal Control

arXiv: https://arxiv.org/abs/2310.14201 · HTML: https://mlsanity.com/paper/2310.14201/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 48 references that are in the map.
- First posted on arXiv 22 Oct 2023.

## Builds on (most cited first, 30 of 33)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Out of One, Many: Using Language Models to Simulate Human Samples](https://mlsanity.com/paper/2209.06899/) (2022)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Complexity-Based Prompting for Multi-Step Reasoning](https://mlsanity.com/paper/2210.00720/) (2022)
- [RLPrompt: Optimizing Discrete Text Prompts with Reinforcement Learning](https://mlsanity.com/paper/2205.12548/) (2022)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [MINT: Evaluating LLMs in Multi-turn Interaction with Tools and Language Feedback](https://mlsanity.com/paper/2309.10691/) (2023)
- [Reasoning with Language Model Prompting: A Survey](https://mlsanity.com/paper/2212.09597/) (2022)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [Generated Knowledge Prompting for Commonsense Reasoning](https://mlsanity.com/paper/2110.08387/) (2021)
- [Improving Language Model Negotiation with Self-Play and In-Context Learning from AI Feedback](https://mlsanity.com/paper/2305.10142/) (2023)
- [Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers](https://mlsanity.com/paper/2212.10559/) (2022)
- [Maieutic Prompting: Logically Consistent Reasoning with Recursive Explanations](https://mlsanity.com/paper/2205.11822/) (2022)
- [Progressive-Hint Prompting Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2304.09797/) (2023)
- [Cutting Down on Prompts and Parameters: Simple Few-Shot Learning with Language Models](https://mlsanity.com/paper/2106.13353/) (2021)
- [AraGPT2: Pre-Trained Transformer for Arabic Language Generation](https://mlsanity.com/paper/2012.15520/) (2020)
- [What's the Magic Word? A Control Theory of LLM Prompting](https://mlsanity.com/paper/2310.04444/) (2023)
- [Growing Action Spaces](https://mlsanity.com/paper/1906.12266/) (2019)

## Built on by (most cited first, 16 of 16)

- [Aligning Large Language Models with Representation Editing: A Control Perspective](https://mlsanity.com/paper/2406.05954/) (2024)
- [LLM as Dataset Analyst: Subpopulation Structure Discovery with Large Language Model](https://mlsanity.com/paper/2405.02363/) (2024)
- [LiSeCo: Linear Semantic Control for Language Generation](https://mlsanity.com/paper/2405.15454/) (2024)
- [Activation Steering with a Feedback Controller](https://mlsanity.com/paper/2510.04309/) (2025)
- [Anchor function: a type of benchmark functions for studying language models](https://mlsanity.com/paper/2401.08309/) (2024)
- [Preemptive Detection and Steering of LLM Misalignment via Latent Reachability](https://mlsanity.com/paper/2509.21528/) (2025)
- [Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control](https://mlsanity.com/paper/2604.19018/) (2026)
- [A Sequential Optimal Learning Approach to Automated Prompt Engineering in Large Language Models](https://mlsanity.com/paper/2501.03508/) (2025)
- [Machine Unlearning Meets Adversarial Robustness via Constrained Interventions on LLMs](https://mlsanity.com/paper/2510.03567/) (2025)
- [A Unified Theory of Sparse Dictionary Learning in Mechanistic Interpretability: Piecewise Biconvexity and Spurious Minima](https://mlsanity.com/paper/2512.05534/) (2025)
- [CXR-LanIC: Language-Grounded Interpretable Classifier for Chest X-Ray Diagnosis](https://mlsanity.com/paper/2510.21464/) (2025)
- [Decentralized Multi-Agent Goal Assignment for Path Planning using Large Language Models](https://mlsanity.com/paper/2510.23824/) (2025)
- [Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equations](https://mlsanity.com/paper/2603.18331/) (2026)
- [When Language Overwrites Vision: Over-Alignment and Geometric Debiasing in Vision-Language Models](https://mlsanity.com/paper/2605.08245/) (2026)
- [Training-Free Universal Approximation by Prompting Random Transformers](https://mlsanity.com/paper/2608.09558/) (2026)
- [Dual Filter: A Transformer-like Inference Architecture for Hidden Markov Models](https://mlsanity.com/paper/2505.00818/) (2025)

## Abstract (arXiv)

Prompt Engineering (PE) has emerged as a critical technique for guiding Large Language Models (LLMs) in solving intricate tasks. Its importance is highlighted by its potential to significantly enhance the efficiency and effectiveness of human-machine interaction. As tasks grow increasingly complex, recent advanced PE methods have extended beyond the limitations of single-round interactions to embrace multi-round interactions, which allows for a deeper and more nuanced engagement with LLMs. In this paper, we propose an optimal control framework tailored for multi-round interactions with LLMs. This framework provides a unified mathematical structure that not only systematizes the existing PE methods but also sets the stage for rigorous analytical improvements. Furthermore, we extend this framework to include PE via ensemble methods and multi-agent collaboration, thereby enlarging the scope of applicability. By adopting an optimal control perspective, we offer fresh insights into existing PE methods and highlight theoretical challenges that warrant future research. Besides, our work lays a foundation for the development of more effective and interpretable PE methods.