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Align-Pro: A Principled Approach to Prompt Optimization for LLM Alignment

Prashant Trivedi, Souradip Chakraborty, Avinash Reddy, Vaneet Aggarwal, Amrit Singh Bedi, George K. Atia

TL;DR

This work formulates prompt optimization as an optimization problem and tries to provide theoretical insights into the optimality of such a framework and provides empirical validation through experiments, demonstrating that prompt optimization can effectively align LLMs, even when parameter fine-tuning is not feasible.

Abstract

The alignment of large language models (LLMs) with human values is critical as these models become increasingly integrated into various societal and decision-making processes. Traditional methods, such as reinforcement learning from human feedback (RLHF), achieve alignment by fine-tuning model parameters, but these approaches are often computationally expensive and impractical when models are frozen or inaccessible for parameter modification. In contrast, prompt optimization is a viable alternative to RLHF for LLM alignment. While the existing literature has shown empirical promise of prompt optimization, its theoretical underpinning remains under-explored. We address this gap by formulating prompt optimization as an optimization problem and try to provide theoretical insights into the optimality of such a framework. To analyze the performance of the prompt optimization, we study theoretical suboptimality bounds and provide insights in terms of how prompt optimization depends upon the given prompter and target model. We also provide empirical validation through experiments on various datasets, demonstrating that prompt optimization can effectively align LLMs, even when parameter fine-tuning is not feasible.

Align-Pro: A Principled Approach to Prompt Optimization for LLM Alignment

TL;DR

This work formulates prompt optimization as an optimization problem and tries to provide theoretical insights into the optimality of such a framework and provides empirical validation through experiments, demonstrating that prompt optimization can effectively align LLMs, even when parameter fine-tuning is not feasible.

Abstract

The alignment of large language models (LLMs) with human values is critical as these models become increasingly integrated into various societal and decision-making processes. Traditional methods, such as reinforcement learning from human feedback (RLHF), achieve alignment by fine-tuning model parameters, but these approaches are often computationally expensive and impractical when models are frozen or inaccessible for parameter modification. In contrast, prompt optimization is a viable alternative to RLHF for LLM alignment. While the existing literature has shown empirical promise of prompt optimization, its theoretical underpinning remains under-explored. We address this gap by formulating prompt optimization as an optimization problem and try to provide theoretical insights into the optimality of such a framework. To analyze the performance of the prompt optimization, we study theoretical suboptimality bounds and provide insights in terms of how prompt optimization depends upon the given prompter and target model. We also provide empirical validation through experiments on various datasets, demonstrating that prompt optimization can effectively align LLMs, even when parameter fine-tuning is not feasible.
Paper Structure (20 sections, 2 theorems, 38 equations, 3 figures, 1 table)

This paper contains 20 sections, 2 theorems, 38 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries and Background
  4. Prompt Optimization Framework for LLM Alignment
  5. Proposed Approach: Align-Pro
  6. Optimization Problem for Prompter
  7. Theoretical Insights w.r.t Fine-Tuning
  8. Experimental Evaluations
  9. Experimental Setup
  10. Results
  11. Conclusion, Limitations and Future Work
  12. Proof of Lemma \ref{['thm:opt-rho']}
  13. Proof of Theorem \ref{['thm:final-per-bound']}
  14. Some Additional Experimental Details
  15. Meta Prompt
  16. ...and 5 more sections

Key Result

Lemma 5.1

Let $R(x,x') := \mathbb{E}_{y \sim \pi_F(\cdot | x')} [r^*(x, y)] \:$, and $\lambda>0$ be the prompter tuning parameter. The optimal prompt distribution $\rho^*$ that maximizes the objective function of the optimization problem eqn:op-rho is given by: where $Z(x)$ is the log partition function given by

Figures (3)

  • Figure 1: A basic overview of the prompt optimization framework. A prompter modifies the prompt before passing it through the target frozen LLM.
  • Figure 2: Reward mean comparisons. Figure shows the reward mean across the chosen datasets. Align-Pro shows an improvement over the no fine-tuning approach. We employ two prompters P1 (Phi-3.5-Instruct) and P2 (Qwen-2.5-1.5B-Instruct), along with two frozen LLMs, denoted as F1 (Llama-3.1-8B-Instruct) and F2 (Llama-3.1-8B-Instruct). The oracle is fine-tuned LLM via RLHF.
  • Figure 3: Reward variance comparisons. Align-Pro has the least variance compared to Oracle and no fine-tuning approach. Due to the prompter's precise guidance, the frozen LLM generates almost similar responses in terms of helpfulness and coherence, which results in less diverse responses. We use the following terminologies for the prompters and the frozen models: P1 (Phi-3.5-Instruct), P2 (Qwen-2.5-1.5B-Instruct), F1 (Llama-3.1-8B-Instruct), and F2 (Llama-3.1-8B-Instruct), respectively.

Theorems & Definitions (5)

  • Lemma 5.1
  • Theorem 6.1
  • Remark 7.1
  • proof
  • proof