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Direct Preference Optimization (DPO) 简介与流程解析

Direct Preference Optimization (DPO) 是一种基于人类偏好的强化学习优化方法，用于训练语言模型，使其更好地满足用户需求或偏好。本文将详细介绍 DPO 的核心思想、优化流程，并结合代码示例分析其具体实现方式。

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1. 什么是 DPO？

DPO 是一种优化策略，它通过最小化损失函数来直接学习人类偏好数据，而无需依赖复杂的强化学习框架，如 Proximal Policy Optimization (PPO)。

DPO 的关键思想：

1. 使用人类偏好数据集来构建训练样本，包含“偏好”和“非偏好”对比项。
2. 通过直接优化偏好损失函数，引导策略模型学习偏好分布，同时控制 KL 散度，避免模型过度偏离参考分布。

DPO 的优势：

• 不依赖环境交互： DPO 在离线数据上训练，无需与环境实时交互，降低了训练复杂度。
• 直接利用人类偏好： 简化了强化学习的步骤，将人类偏好直接应用于优化过程。
• 更稳定的训练过程： 通过 KL 散度约束保持策略分布平稳，减少训练不稳定性。

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2. DPO 的主要流程

Step 1: 数据集准备

假设我们有一个人类偏好标注的数据集 ($D$)：

$$D=\{(x_i,y_w^i,y_l^i){\}}_{i=1}^N$$

其中：

• ($x_i$)：提示（prompt）或输入样本。
• ($y_w^i$)：偏好的输出（preferred completion）。
• ($y_l^i$)：不偏好的输出（less preferred completion）。

示例数据：

Prompt	Preferred Output (($y_w$))	Less Preferred Output (($y_l$))
“Summarize this text.”	“Key points are…”	“The main topic is…”
“Translate to French.”	“Bonjour tout le monde.”	“Salut à tous.”

Step 2: 初始化参考模型 ((${\pi }_{ref}$))

1. 如果已有监督微调模型 ((${\pi }_{SFT}$))，则直接使用它作为参考模型：

$${\pi }_{ref}={\pi }_{SFT}$$

2. 如果没有 (${\pi }_{SFT}$)，则通过最大似然估计 (MLE) 预训练一个参考模型：

$${\pi }_{ref}=\arg \underset{\pi }{\max }{\mathbb{E}}_{(x,y_w)\sim D}[\log \pi (y_w|x)]$$

解释：
参考模型用于提供基准分布，帮助控制训练过程中的分布偏移，确保策略模型不会偏离参考分布太远。

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Step 3: 损失函数定义与优化

DPO 的损失函数旨在优化策略模型 (${\pi }_{\theta }$) 相对于参考模型 (${\pi }_{ref}$) 的表现，同时引入 KL 散度惩罚项控制更新幅度：

损失函数公式：

$$L_{DPO}(\theta )=-\log \sigma \left(\beta \left[\log \frac{{\pi }_{\theta }(y_w|x)}{{\pi }_{\theta }(y_l|x)}-\log \frac{{\pi }_{ref}(y_w|x)}{{\pi }_{ref}(y_l|x)}\right]\right)$$

其中：

• ($\beta$)：控制 KL 散度强度的超参数。
• ($\sigma (\cdot )$)：Sigmoid 函数，用于平滑处理。
• (${\pi }_{\theta }$)：当前策略模型的输出概率。
• (${\pi }_{ref}$)：参考模型的输出概率。

直观解释：

• 比较策略模型与参考模型在偏好和非偏好输出上的概率比率，优化模型使得偏好输出的概率更大，同时限制变化幅度。

代码实现：

摘录自原paper: https://arxiv.org/pdf/2305.18290

import torch.nn.functional as Fdef dpo_loss(pi_logps, ref_logps, yw_idxs, yl_idxs, beta):"""计算 DPO 损失函数Args:pi_logps: 策略模型的对数概率, shape (B,)ref_logps: 参考模型的对数概率, shape (B,)yw_idxs: 偏好输出的索引, shape (T,)yl_idxs: 不偏好输出的索引, shape (T,)beta: KL 惩罚项超参数Returns:losses: 损失值rewards: 奖励信号"""# 取出偏好与非偏好对应的对数概率pi_yw_logps, pi_yl_logps = pi_logps[yw_idxs], pi_logps[yl_idxs]ref_yw_logps, ref_yl_logps = ref_logps[yw_idxs], ref_logps[yl_idxs]# 计算策略与参考模型的概率比率pi_logratios = pi_yw_logps - pi_yl_logpsref_logratios = ref_yw_logps - ref_yl_logps# 损失函数losses = -F.logsigmoid(beta * (pi_logratios - ref_logratios))# 奖励信号rewards = beta * (pi_logps - ref_logps).detach()return losses, rewards

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Step 4: 模型训练设置

摘录自原paper: https://arxiv.org/pdf/2305.18290

1. 优化器与超参数设置：

   • 使用 RMSprop 优化器。
   • 学习率：($1\times 10^{-6}$)。
   • 批量大小：64。
   • 学习率线性预热 150 步，从 0 增加到 ($1\times 10^{-6}$)。

2. 特定任务调整：

   • 摘要任务：将 ($\beta =0.5$)。

3. 训练过程：

   • 从参考模型加载初始参数。
   • 根据数据集批量计算损失和奖励。
   • 逐步更新策略模型，平衡偏好学习和 KL 散度控制。

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3. DPO 的实际应用与优势分析

应用场景：

1. 对话生成：
   • 使用人类反馈优化对话质量，使模型更符合用户期望。
2. 摘要生成：
   • 根据偏好数据训练模型生成更简洁或更详细的摘要。
3. 翻译任务：
   • 微调翻译模型使其符合语言习惯和文化背景。

与传统方法对比：

方法	特点	优势
PPO	在线交互式优化，依赖环境反馈	强鲁棒性，但实现复杂，训练成本高
DPO	离线偏好优化，无需环境交互，直接优化损失函数	简单易实现，训练更稳定，适合大规模预训练模型微调

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4. 总结

DPO 提供了一种高效稳定的方式，将人类偏好直接融入语言模型训练过程。通过对比参考模型与策略模型的输出概率，并结合 KL 散度控制，DPO 避免了传统强化学习中的不稳定性，尤其适合大规模预训练模型的偏好微调任务。

关键点回顾：

1. 准备偏好数据集，标注“偏好”和“非偏好”输出。
2. 初始化参考模型，确保稳定的分布基础。
3. 计算损失函数，通过 KL 散度控制更新幅度。
4. 利用超参数调优，平衡偏好优化与探索能力。

DPO 简化了强化学习流程，为语言模型的微调提供了一种高效且实用的解决方案。

Introduction to Direct Preference Optimization (DPO): Process and Implementation

Direct Preference Optimization (DPO) is a reinforcement learning-based optimization method that trains language models to better align with user preferences. This blog provides a detailed explanation of DPO’s core concepts, step-by-step pipeline, and practical implementation using code examples.

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1. What is DPO?

DPO is an optimization strategy that directly learns from human preference data by minimizing a preference-based loss function, eliminating the need for complex reinforcement learning frameworks like Proximal Policy Optimization (PPO).

Key Ideas of DPO:

1. Utilize human preference datasets containing pairs of “preferred” and “less preferred” completions.
2. Optimize a preference-based loss function to guide the policy model while controlling KL divergence to prevent distributional shifts.

Advantages of DPO:

• No Environment Interaction Required: DPO trains offline, reducing complexity compared to traditional reinforcement learning.
• Direct Use of Human Preferences: Simplifies optimization by directly leveraging preference data.
• Stable Training Process: KL divergence constraints ensure smooth updates and prevent instability.

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2. Main Workflow of DPO

Step 1: Prepare the Dataset

Assume we have a human-annotated preference dataset ($D$):

$$D=\{(x_i,y_w^i,y_l^i){\}}_{i=1}^N$$

Where:

• ($x_i$): Prompt or input example.
• ($y_w^i$): Preferred output (completion).
• ($y_l^i$): Less preferred output.

Sample Data:

Prompt	Preferred Output (($y_w$))	Less Preferred Output (($y_l$))
“Summarize this text.”	“Key points are…”	“The main topic is…”
“Translate to French.”	“Bonjour tout le monde.”	“Salut à tous.”

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Step 2: Initialize Reference Model ((${\pi }_{ref}$))

1. If a supervised fine-tuned model ((${\pi }_{SFT}$)) is available, use it as the reference model:

$${\pi }_{ref}={\pi }_{SFT}$$

2. If (${\pi }_{SFT}$) is not available, pre-train a reference model via Maximum Likelihood Estimation (MLE):

$${\pi }_{ref}=\arg \underset{\pi }{\max }{\mathbb{E}}_{(x,y_w)\sim D}[\log \pi (y_w|x)]$$

Explanation:
The reference model provides a baseline distribution that prevents distributional shifts during training, ensuring stability.

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Step 3: Define and Optimize the Loss Function

DPO’s loss function is designed to optimize the policy model (${\pi }_{\theta }$) relative to the reference model (${\pi }_{ref}$) while introducing a KL-divergence penalty to constrain updates.

Loss Function Formula:

$$L_{DPO}(\theta )=-\log \sigma \left(\beta \left[\log \frac{{\pi }_{\theta }(y_w|x)}{{\pi }_{\theta }(y_l|x)}-\log \frac{{\pi }_{ref}(y_w|x)}{{\pi }_{ref}(y_l|x)}\right]\right)$$

Where:

• ($\beta$): Temperature parameter controlling KL penalty strength.
• ($\sigma (\cdot )$): Sigmoid function for smoothing.
• (${\pi }_{\theta }$): Current policy model probabilities.
• (${\pi }_{ref}$): Reference model probabilities.

Intuitive Explanation:

• Compare the probability ratios between preferred and less preferred outputs.
• Optimize the model to increase probabilities for preferred outputs while limiting deviation from the reference model.

Code Implementation:

import torch.nn.functional as Fdef dpo_loss(pi_logps, ref_logps, yw_idxs, yl_idxs, beta):"""Compute DPO loss.Args:pi_logps: Log-probabilities from the policy model, shape (B,)ref_logps: Log-probabilities from the reference model, shape (B,)yw_idxs: Indices of preferred completions, shape (T,)yl_idxs: Indices of less preferred completions, shape (T,)beta: KL penalty strengthReturns:losses: Loss valuesrewards: Reward signals"""# Extract log-probs for preferred and less preferred completionspi_yw_logps, pi_yl_logps = pi_logps[yw_idxs], pi_logps[yl_idxs]ref_yw_logps, ref_yl_logps = ref_logps[yw_idxs], ref_logps[yl_idxs]# Compute log-ratiospi_logratios = pi_yw_logps - pi_yl_logpsref_logratios = ref_yw_logps - ref_yl_logps# Compute losslosses = -F.logsigmoid(beta * (pi_logratios - ref_logratios))# Compute rewardsrewards = beta * (pi_logps - ref_logps).detach()return losses, rewards

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Step 4: Model Training Settings

1. Optimizer and Hyperparameters:

   • Optimizer: RMSprop.
   • Learning Rate: ($1\times 10^{-6}$).
   • Batch Size: 64.
   • Linear warmup: Gradually increase learning rate from 0 to ($1\times 10^{-6}$) over 150 steps.

2. Task-Specific Adjustments:

   • For summarization: Set ($\beta =0.5$).

3. Training Process:

   • Load initial parameters from the reference model.
   • Compute losses and rewards in batches using the preference dataset.
   • Update the policy model step-by-step, balancing preference optimization and KL divergence constraints.

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3. Applications and Advantages

Use Cases:

1. Dialogue Generation:
   • Optimize conversational quality to better match user expectations.
2. Summarization Tasks:
   • Train models to generate concise or detailed summaries based on preferences.
3. Translation Models:
   • Fine-tune translations to match linguistic and cultural nuances.

Comparison with Traditional Methods:

Method	Features	Advantages
PPO	Online optimization, requires environment feedback	Robust but complex implementation and expensive
DPO	Offline preference optimization, no interaction needed	Simple implementation, more stable training

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4. Conclusion

DPO provides an efficient and stable method for integrating human preferences into language model training. By comparing probabilities between preferred and less preferred outputs and applying KL-divergence constraints, DPO avoids instability often seen in traditional reinforcement learning, making it ideal for fine-tuning large language models.

Key Takeaways:

1. Prepare a preference dataset labeled with “preferred” and “less preferred” outputs.
2. Initialize a reference model for stable training.
3. Optimize the preference loss function while controlling distribution shifts.
4. Tune hyperparameters to balance preference learning and exploration.

DPO simplifies reinforcement learning and offers a practical solution for preference-based fine-tuning of pre-trained language models.

参考

[1] DPO（Direct Preference Optimization）算法解释：中英双语

后记

2024年12月26日21点19分于上海，在GPT4o大模型辅助下完成。