本篇解读DPOTrainer，这是TRL源码系列的最后一篇了，虽然还有好些trainer没有解读，例如：KTO, online DPO等，但都可以看作是PPO或者DPO的变种。最开始我以为本篇就一个DPO算法，但是后面发现自己太naive了，作者在源码里集成了太多的变种，想把所有变种都搞清楚但是时间不允许，因此变种部分仅做简要介绍。

1.DPO基础

（1）理论简介

DPO算法严格来说已经不是一种RL算法了，它可以直接根据preference data pair进行微调。但它确确实实又用到了RL的思想，它是利用Bradley-Terry模型和PPO目标函数推导出来的（推导过程见原论文附录Direct Preference Optimization:Your Language Model is Secretly a Reward Model），其中包含了隐式奖励函数。所以才会有论文的标题，说你的语言模型是一个隐藏的奖励模型。

Bradley-Terry模型

PPO目标函数

由Bradley-Terry模型和PPO目标函数推导得到隐式奖励函数和DPO目标函数。

隐式奖励函数

DPO目标函数

不得不说该算法十分精妙，从数学角度证明了，从奖励函数到最优策略的解析映射，省去了传统强化学习方法的复杂操作。

（2）数据输入

因为是直接从偏好数据进行学习，不同于PPO系列里的输入为prompt, DPO的输入与reward model类似，都是prompt+chosen response和prompt+rejected response。

DPO数据输入格式

（3）超参数介绍

https://github.com/huggingface/trl/blob/main/trl/trainer/dpo_config.py是DPOTrainer的超参数配置。

learning_rate: float = 1e-6
beta: float = 0.1
label_smoothing: float = 0.0
loss_type: Literal[
    "sigmoid",
    "hinge",
    "ipo",
    "exo_pair",
    "nca_pair",
    "robust",
    "bco_pair",
    "sppo_hard",
    "aot",
    "aot_pair",
    "apo_zero",
    "apo_down",
] = "sigmoid"
use_weighting: bool = False
label_pad_token_id: int = -100
padding_value: Optional[int] = None
truncation_mode: str = "keep_end"
max_length: Optional[int] = None
max_prompt_length: Optional[int] = None
max_target_length: Optional[int] = None  # deprecated in favor of max_completion_length
max_completion_length: Optional[int] = None
is_encoder_decoder: Optional[bool] = None
disable_dropout: bool = True
generate_during_eval: bool = False
precompute_ref_log_probs: bool = False
dataset_num_proc: Optional[int] = None
model_init_kwargs: Optional[Dict[str, Any]] = None
ref_model_init_kwargs: Optional[Dict[str, Any]] = None
model_adapter_name: Optional[str] = None
ref_adapter_name: Optional[str] = None
reference_free: bool = False
force_use_ref_model: bool = False
f_divergence_type: FDivergenceType = FDivergenceType.REVERSE_KL
f_alpha_divergence_coef: float = 1.0
sync_ref_model: bool = False
ref_model_mixup_alpha: float = 0.9
ref_model_sync_steps: int = 64
rpo_alpha: Optional[float] = None

超参数实在太多了，我只解释比较难理解的，其他简单的可以直接看源码的说明：

• beta: DPO 损失的温度，通常在 0.1 到 0.5 之间。它控制了我们对参考模型的关注程度，beta 越小，我们就越忽略参考模型（不理解的话，可以回到PPO目标函数公式看）。但因为loss_type有很多种，有的也背离了beta原来的意思；

• label_smoothing: label的噪音比例，介于0.0-0.5之间；

• loss_type: 不同损失函数的类型（后面会具体介绍），默认的是sigmoid；

• use_weighting: 是否使用加权的DPO损失WPO;

• label_pad_token_id: 用于pad label的token id, pad掉的token不计入损失，一般会把prompt的label pad掉；

• precompute_ref_log_probs: 是否提前计算ref_log，如果提前计算可以在训练阶段减少GPU内存的使用

• reference_free: 如果为TRUE，则忽略ref_model， ref_log的每一项默认均等分概率；

• force_use_ref_model: 是否强制使用ref_model，当传递PEFT model的时候，可以替代单独的ref_model，如果强制使用则还是使用ref_model。

• f_divergence_type: f散度类型，用于计算policy和reference模型输出的散度

• f_alpha_divergence_coef: 当f_divergence_type是α散度时的α系数

• sync_ref_model: TR-DPO的内容，DPOTrainer未使用

• ref_model_mixup_alpha: TR-DPO的内容，DPOTrainer未使用

• ref_model_sync_steps: TR-DPO的内容，DPOTrainer未使用

• rpo_alpha: RPO的系数

2.DPO loss

（1）散度的计算

默认散度是KL散度 log(u)，相当于代码里的chosen_logratios和rejected_logratios，注意u是不带log的policy/reference概率之比， 只有搞懂了这个，代码里α散度计算和JS散度计算的推导才能说得通。

如果reference_free为True，代表忽略reference model，ref_logratios是0，因为ref_chosen_logps 和 ref_rejected_logps是相同的等分概率，二者之差为0。

另外，根据DPO目标函数的计算公式可知道，logits = logratios - ref_logratios和logits = chosen_logratios - rejected_logratios是等价的。

# Get the log ratios for the chosen and rejected responses
chosen_logratios = chosen_logps.to(device) - (not self.reference_free) * ref_chosen_logps.to(device)
rejected_logratios = rejected_logps.to(device) - (not self.reference_free) * ref_rejected_logps.to(device)

if self.f_divergence_type == FDivergenceType.ALPHA_DIVERGENCE.value:
    # The alpha-divergence formula: (1 - u^-alpha) / alpha
    # The divergence difference between the chosen and rejected sample is:
    #     (1 - u[w]^-alpha) / alpha - (1 - u[l]^-alpha) / alpha
    #        = (u[l]^-alpha - u[w]^-alpha) / alpha
    # where u[w] and u[l] are the policy/reference probability ratios
    # for the chosen and rejected samples, respectively.
    alpha_coef = FDivergenceConstants.ALPHA_DIVERGENCE_COEF_DEFAULT
    if self.f_divergence_params and FDivergenceConstants.ALPHA_DIVERGENCE_COEF_KEY in self.f_divergence_params:
        alpha_coef = float(self.f_divergence_params[FDivergenceConstants.ALPHA_DIVERGENCE_COEF_KEY])
    logits = (cap_exp(rejected_logratios * -alpha_coef) - cap_exp(chosen_logratios * -alpha_coef)) / alpha_coef
else:
    logratios = chosen_logps - rejected_logps
    if self.reference_free:
        ref_logratios = torch.tensor([0], dtype=logratios.dtype, device=logratios.device)
    else:
        ref_logratios = ref_chosen_logps - ref_rejected_logps

    logratios = logratios.to(self.accelerator.device)
    ref_logratios = ref_logratios.to(self.accelerator.device)
    logits = logratios - ref_logratios

    if self.f_divergence_type == FDivergenceType.JS_DIVERGENCE.value:
        # The js-divergence formula: log(2 * u / (1 + u))
        # The divergence difference between the chosen and rejected sample is:
        #     log(2 * u[w] / (1 + u[w])) - log(2 * u[l] / (1 + u[l]))
        #       = log(u[w]) - log(u[l]) - (log(1 + u[w]) - log(1 + u[l]))
        # where u[w] and u[l] are the policy/reference probability ratios
        # for the chosen and rejected samples, respectively.
        logits -= F.softplus(chosen_logratios) - F.softplus(rejected_logratios)

（2）不同的loss

1）sigmoid
这是DPO的原始的损失函数logsigmoid, beta的作用在超参数里面已经说了，label_smoothing的作用主要是对label的不确定性进行一个trade-off，防止有脏标签。

保守的DPO目标函数

其中ϵ是标签中噪声的比例（一般很小），就是代码里的label_smoothing

if self.loss_type == "sigmoid":
    losses = (
            -F.logsigmoid(self.beta * logits) * (1 - self.label_smoothing)
            - F.logsigmoid(-self.beta * logits) * self.label_smoothing
    )

2）robust
这是一个针对有噪声标签的专门损失函数 Robust DPO, 用于提升学习的鲁棒性。
Provably Robust DPO: Aligning Language Models with Noisy Feedback

Robust DPO Loss

elif self.loss_type == "robust":
    losses = (
                     -F.logsigmoid(self.beta * logits) * (1 - self.label_smoothing)
                     + F.logsigmoid(-self.beta * logits) * self.label_smoothing
             ) / (1 - 2 * self.label_smoothing)

3）exo_pair
EXO提出了一种高效精确优化的损失函数，旨在解决DPO收敛难的问题。
Towards Efficient Exact Optimization of Language Model Alignment

elif self.loss_type == "exo_pair":
    # eqn (16) of the EXO paper: https://huggingface.co/papers/2402.00856
    import math

    if self.label_smoothing == 0:
        self.label_smoothing = 1e-3
    losses = (self.beta * logits).sigmoid() * (
            F.logsigmoid(self.beta * logits) - math.log(1 - self.label_smoothing)
    ) + (-self.beta * logits).sigmoid() * (F.logsigmoid(-self.beta * logits) - math.log(self.label_smoothing))

后面的loss太多了，不作介绍了，感兴趣的自己去看论文吧
4）hinge

elif self.loss_type == "hinge":
    losses = torch.relu(1 - self.beta * logits)

5） ipo

elif self.loss_type == "ipo":
    # eqn (17) of the paper where beta is the regularization parameter for the IPO loss, denoted by tau in the paper.
    losses = (logits - 1 / (2 * self.beta)) ** 2

6）bco_pair

elif self.loss_type == "bco_pair":
    chosen_logratios = chosen_logps - ref_chosen_logps
    rejected_logratios = rejected_logps - ref_rejected_logps
    chosen_rewards = self.beta * chosen_logratios
    rejected_rewards = self.beta * rejected_logratios
    rewards = torch.cat((chosen_rewards, rejected_rewards), 0).mean().detach()
    self.running.update(rewards)
    delta = self.running.mean
    losses = -F.logsigmoid((self.beta * chosen_logratios) - delta) - F.logsigmoid(
        -(self.beta * rejected_logratios - delta)
    )

7）sppo_hard

elif self.loss_type == "sppo_hard":
    # In the paper (https://huggingface.co/papers/2405.00675), SPPO employs a soft probability approach,
    # estimated using the PairRM score. The probability calculation is conducted outside of the trainer class.
    # The version described here is the hard probability version, where P in Equation (4.7) of Algorithm 1 is
    # set to 1 for the winner and 0 for the loser.
    a = chosen_logps - ref_chosen_logps
    b = rejected_logps - ref_rejected_logps
    losses = (a - 0.5 / self.beta) ** 2 + (b + 0.5 / self.beta) ** 2

8）nca_pair

elif self.loss_type == "nca_pair":
    chosen_rewards = (chosen_logps - ref_chosen_logps) * self.beta
    rejected_rewards = (rejected_logps - ref_rejected_logps) * self.beta
    losses = (
            -F.logsigmoid(chosen_rewards)
            - 0.5 * F.logsigmoid(-chosen_rewards)
            - 0.5 * F.logsigmoid(-rejected_rewards)
    )

9）aot_pair

elif self.loss_type == "aot_pair":
    chosen_logratios = chosen_logps - ref_chosen_logps
    rejected_logratios = rejected_logps - ref_rejected_logps
    chosen_logratios_sorted, _ = torch.sort(chosen_logratios, dim=0)
    rejected_logratios_sorted, _ = torch.sort(rejected_logratios, dim=0)
    delta = chosen_logratios_sorted - rejected_logratios_sorted
    losses = (
            -F.logsigmoid(self.beta * delta) * (1 - self.label_smoothing)
            - F.logsigmoid(-self.beta * delta) * self.label_smoothing
    )

10）aot

elif self.loss_type == "aot":
    logratios = chosen_logps - rejected_logps
    ref_logratios = ref_chosen_logps - ref_rejected_logps
    logratios_sorted, _ = torch.sort(logratios, dim=0)
    ref_logratios_sorted, _ = torch.sort(ref_logratios, dim=0)
    delta = logratios_sorted - ref_logratios_sorted
    losses = (
            -F.logsigmoid(self.beta * delta) * (1 - self.label_smoothing)
            - F.logsigmoid(-self.beta * delta) * self.label_smoothing
    )

11）apo_zero

elif self.loss_type == "apo_zero":
    # Eqn (7) of the APO paper (https://huggingface.co/papers/2408.06266)
    # Use this loss when you believe the chosen outputs are better than your model's default output
    losses_chosen = 1 - F.sigmoid(self.beta * chosen_logratios)  # Increase chosen likelihood
    losses_rejected = F.sigmoid(self.beta * rejected_logratios)  # Decrease rejected likelihood
    losses = losses_chosen + losses_rejected

12）apo_down

elif self.loss_type == "apo_down":
    # Eqn (8) of the APO paper (https://huggingface.co/papers/2408.06266)
    # Use this loss when you believe the chosen outputs are worse than your model's default output.
    # Decrease chosen likelihood and decrease rejected likelihood more
    losses_chosen = F.sigmoid(self.beta * chosen_logratios)
    losses_rejected = 1 - F.sigmoid(self.beta * (chosen_logratios - rejected_logratios))
    losses = losses_chosen + losses_rejected

3.Loss的后处理

在函数get_batch_loss_metrics里面有几个可选的后续处理，根据配置相关，做个简要介绍。

（1）增加NLL loss——RPO

Iterative Reasoning Preference Optimization

RPO损失计算公式

if self.args.rpo_alpha is not None:
    losses = losses + self.args.rpo_alpha * model_output["nll_loss"]  # RPO loss from V3 of the paper

个人理解其中NLL loss相当于sft了chosen数据一次

if self.args.rpo_alpha is not None:
   # Only use the chosen logits for the RPO loss
   chosen_logits = logits[:num_examples]
   chosen_labels = labels[:num_examples]

   # Compute the log probabilities of the labels
   output["nll_loss"] = F.cross_entropy(
       torch.flatten(chosen_logits, end_dim=1), torch.flatten(chosen_labels, end_dim=1), ignore_index=0
   )

（2）加权的DPO——WPO

WPO: Enhancing RLHF with Weighted Preference Optimization

WPO损失函数

if self.use_weighting:
    losses = losses * model_output["policy_weights"]

其中权重公式计算如下：

policy_weights计算公式

if self.use_weighting:
    with torch.no_grad():
        # Eq (2) of the WPO paper: https://huggingface.co/papers/2406.11827
        logprobs = F.log_softmax(logits, dim=-1)
        weights_adjustment_factor = torch.logsumexp(2 * logprobs, dim=-1)  # same as sum(probs**2) in log space
        per_token_logps_adjusted = per_token_logps - weights_adjustment_factor
        all_weights = (per_token_logps_adjusted * loss_mask).sum(-1) / loss_mask.sum(-1)
        chosen_weights = all_weights[:num_examples]
        rejected_weights = all_weights[num_examples:]
        output["policy_weights"] = torch.clamp(torch.exp(chosen_weights + rejected_weights), max=1)

（3）添加辅助损失(Auxiliary Loss)

这是模型自带路由器辅助损失，跟RL无关，这里不作介绍。

if self.aux_loss_enabled:
    losses = losses + self.aux_loss_coef * model_output["aux_loss"]