PPO GRPO GSPO DAPO的Loss计算与代码实现

首先看一下KL的基础公式

KL

KL1:

大模型的KL一般是反向的：

[KL(pi_theta||pi_{ref}) = E_{xsimpi_theta(cdot|o_{<t})}logfrac{pi_theta(x|o_{<t})}{pi_{ref}(x|o_{<t})} ]

(xsimpi_theta(cdot|o_{<t})) 代表 当前模型根据前t-1个token采样得到第t个token x

KL3(GRPO使用的无偏，低方差KL1估计) http://joschu.net/blog/kl-approx.html：

[KL(pi_theta||pi_{ref}) = mathbb{E}_{xsimpi_theta(cdot|o_{<t})}frac{pi_{ref}}{pi_{theta}} - log(frac{pi_{ref}}{pi_{theta}})-1 ]

• 正向KL：倾向于使模型分布 Q 覆盖目标分布 P 的所有支持点，适合于需要模型分布更广泛覆盖的情况。
• 反向KL：倾向于使模型分布 Q 集中在目标分布 P 的高概率区域，适合于生成任务，能够提高生成样本的质量和稳定性。

因此，在大语言模型和生成任务中，反向KL通常更受青睐。

不同RL算法 loss的计算

对于q的第(i)个sample的第(t)个token的loss: (loss_{i,t}=pg_loss_{i,t}+entropy_loss_{i, t}+kl_loss_{i,t})

再对一个batch中所有的token loss (loss_{i,t})做聚合agg，得到这个batch的整体loss，可用于后续的反向传播和模型更新。

每个token的loss	(pg_loss_{i,t})	(kl_loss_{i,t})	loss agg mode
PPO	(max(IS_{i,t}*-A_{i,t},clip(IS_{i,t})*-A_{i,t}))	(r_t=-mathbb{D1}_{KL}(pi_{old}||pi_{ref})+r_t)	(frac{1}{G}sum_{i=1}^Gfrac{1}{|o_i|}sum_{t=1}^{|o_i|}loss_{i,t}) seq-mean-token-mean
Dual-clip PPO	for A<0, (min(max(IS_{i,t}*-A_{i,t},clip(IS_{i,t})*-A), clip_c*-A))	(r_t=-mathbb{D1}_{KL}(pi_{old}||pi_{ref})+r_t)	(frac{1}{G}sum_{i=1}^Gfrac{1}{|o_i|}sum_{t=1}^{|o_i|}loss_{i,t}) seq-mean-token-mean
GRPO	(max(IS_{i,t}*-A_{i,t},clip(IS_{i,t})*-A_{i,t}))	(beta*mathbb{D3}_{KL}(pi_{theta}||pi_{ref}))	(frac{1}{G}sum_{i=1}^Gfrac{1}{|o_i|}sum_{t=1}^{|o_i|}loss_{i,t}) seq-mean-token-mean
GSPO	(IS_{i,t} = sg[frac{pi_{theta}(o_i|q)}{pi_{old}(o_i|q)}]*frac{pi_theta(o_{i,t}|q,o_{i,<t})}{sg[pi_{theta}(o_{i,t}|q,o_{i,<t})]}) (max(IS_{i,t}*-A_{i,t},clip(IS_{i,t})*-A_{i,t}))	(beta*mathbb{D3}_{KL}(pi_{theta}||pi_{ref}))	(frac{1}{G}sum_{i=1}^Gfrac{1}{|o_i|}sum_{t=1}^{|o_i|}loss_{i,t}) seq-mean-token-mean
DAPO	(max(IS_{i,t}*-A_{i,t},clip(IS_{i,t})*-A_{i,t}))	(beta*mathbb{D3}_{KL}(pi_{theta}||pi_{ref}))	(frac{1}{sum_{i=1}^G|o_i|}sum_{i=1}^Gsum_{t=1}^{|o_i|}loss_{i,t}) token-mean

PPO

优化目标：

[J = mathbb{E}_{osimpi_{old}}frac{1}{|o|}sum_{i=1}^{|o|} [min(frac{pi_{theta}(o_i|o_{<i}, q)}{pi_{old}(o_i|o_{<i}, q)}A_i, clip(frac{pi_{theta}(o_i|o_{<i}, q)}{pi_{old}(o_i|o_{<i}, q)}, 1-epsilon, 1+epsilon)A_i] ]

优势： GAE
递推公式，t步的累积优势=t步的优势+ t+1步的累积优势=t步及之后 每一步的优势=t步及之后所有的奖励-第t步的预计奖励

[begin{aligned} A_t &= (r_t+gamma V_{t+1}-V_t)+gamma A_{t+1}\ A_t &= sum_{i=t}^T gamma ^{i-t}(r_t+gamma V_{t+1}-V_t)\ A_t &= r_t+gamma r_{t+1}+gamma^2 r_{t+2}+...+gamma^{T-t}r_T-V_t\ end{aligned} ]

奖励：

[r_t=begin{cases}-KL(pi_{old}||pi_{ref}), &tneq T \ -KL(pi_{old}||pi_{ref})+RM(q,o_i), &t=T end{cases} ]

verl/trainer/ppo/ray_trainer.py verl ｜ 如何在奖励中添加KL惩罚项？

################################################### # 将KL惩罚loss应用到reward中。原始的reward是[0, 0, 0, ..., RM(q,o_i)] # return KL(pi_old||pi_{ref}) + reward ################################################### def apply_kl_penalty(data: DataProto, kl_ctrl: core_algos.AdaptiveKLController, kl_penalty="kl"):     """Apply KL penalty to the token-level rewards.      This function computes the KL divergence between the reference policy and current policy,     then applies a penalty to the token-level rewards based on this divergence.      Args:         data (DataProto): The data containing batched model outputs and inputs.         kl_ctrl (core_algos.AdaptiveKLController): Controller for adaptive KL penalty.         kl_penalty (str, optional): Type of KL penalty to apply. Defaults to "kl".      Returns:         tuple: A tuple containing:             - The updated data with token-level rewards adjusted by KL penalty             - A dictionary of metrics related to the KL penalty     """     response_mask = data.batch["response_mask"]     token_level_scores = data.batch["token_level_scores"]     batch_size = data.batch.batch_size[0]      # compute kl between ref_policy and current policy     # When apply_kl_penalty, algorithm.use_kl_in_reward=True, so the reference model has been enabled.     kld = core_algos.kl_penalty(         data.batch["old_log_probs"], data.batch["ref_log_prob"], kl_penalty=kl_penalty     )  # (batch_size, response_length)     kld = kld * response_mask     beta = kl_ctrl.value      token_level_rewards = token_level_scores - beta * kld 

KL

[KL(pi_{old}||pi_{ref}) = log(frac{pi_{old}(o_t|q, o_{<t})}{pi_{ref}(o_t|q, o_{<t})}) ]

PPO的KL散度是old到ref的

PPO的代码实现详见下面的Dual-clip PPO（PPO的改进版）

Dual-clip PPO

https://arxiv.org/pdf/1912.09729：对A<0的token的重要性采样IS做clip

论文发现当A<0时，重要性采样的比值*A可以是负无穷，这会导致训练不稳定（梯度爆炸）的现象，因此在ppo的clip上，对于A<0又进一步添加了新的clip (clip_ratio_c)。

[mathrm{per token objection} = begin{cases} min(IS*A, clip(IS, 1-epsilon, 1+epsilon)*A), &Ageq0\ max(min(IS*A, clip(IS, 1-epsilon, 1+epsilon)*A), clip_ratio_c*A), &A<0\ end{cases} ]

代码：

整体的ppo_loss是由pg_loss + kl_loss + entropy_loss构成，不同的RL方法pg_loss, kl_loss的计算方法是不同的。

• pg_loss：具体于verl/trainer/ppo/core_algos.py（我将在dual-clip ppo和gspo部分介绍对应的pg_loss代码）。
• kl_loss：同样位于verl/trainer/ppo/core_algos.py（我将会在grpo部分介绍具体的low_var_kl代码）。

verl/verl/workers/roles/utils/losses.py: ppo_loss的计算

###################################################### # 此函数用于计算整体的actor loss ###################################################### def ppo_loss(config: ActorConfig, model_output, data: TensorDict, dp_group=None):     log_prob = model_output["log_probs"]     entropy = model_output.get("entropy", None)      log_prob = no_padding_2_padding(log_prob, data)  # (bsz, response_length)     if entropy is not None:         entropy = no_padding_2_padding(entropy, data)  # (bsz, response_length)      metrics = {}      response_mask = data["response_mask"].to(bool)     # compute policy loss     old_log_prob = data["old_log_probs"]     advantages = data["advantages"]      loss_agg_mode = config.loss_agg_mode      loss_mode = config.policy_loss.get("loss_mode", "vanilla")      policy_loss_fn = get_policy_loss_fn(loss_mode)     # 调用下面的计算pg_loss的代码框     pg_loss, pg_clipfrac, ppo_kl, pg_clipfrac_lower = policy_loss_fn(         old_log_prob=old_log_prob,         log_prob=log_prob,         advantages=advantages,         response_mask=response_mask,         loss_agg_mode=loss_agg_mode,         config=config,     )      metrics.update(         {             "pg_loss": pg_loss.detach().item(),             "pg_clipfrac": pg_clipfrac.detach().item(),             "ppo_kl": ppo_kl.detach().item(),             "pg_clipfrac_lower": pg_clipfrac_lower.detach().item(),         }     )     policy_loss = pg_loss      # 是否使用entropy loss     # add entropy loss     if entropy is not None:         entropy_loss = agg_loss(loss_mat=entropy, loss_mask=response_mask, loss_agg_mode=loss_agg_mode)         entropy_coeff = config.entropy_coeff         # token的entropy越大越好，而loss是越小越好，因此是 减去 entropy         policy_loss -= entropy_coeff * entropy_loss      # 是否使用KL loss（grpo/gspo使用，ppo/dapo不使用）     # add kl loss     if config.use_kl_loss:         ref_log_prob = data["ref_log_prob"]         # compute kl loss         kld = kl_penalty(logprob=log_prob, ref_logprob=ref_log_prob, kl_penalty=config.kl_loss_type)         kl_loss = agg_loss(loss_mat=kld, loss_mask=response_mask, loss_agg_mode=config.loss_agg_mode)          policy_loss += kl_loss * config.kl_loss_coef         metrics["kl_loss"] = kl_loss.detach().item()         metrics["kl_coef"] = config.kl_loss_coef      return policy_loss, metrics 

verl/trainer/ppo/core_algos.py不同的RL方法计算pg_loss是不同的，这里的是ppo的pg_loss，后面还会介绍gspo的pg_loss的实现。

###################################################### # 此函数用于计算pg_loss，并不计算KL惩罚项 ###################################################### @register_policy_loss("vanilla")  # type: ignore[arg-type] def compute_policy_loss_vanilla(     old_log_prob: torch.Tensor,     log_prob: torch.Tensor,     advantages: torch.Tensor,     response_mask: torch.Tensor,     loss_agg_mode: str = "token-mean",     config: Optional[DictConfig | AlgoConfig] = None,     rollout_is_weights: torch.Tensor | None = None, ) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:     """     Compute the clipped policy objective and related metrics for PPO.      Adapted from     https://github.com/huggingface/trl/blob/main/trl/trainer/ppo_trainer.py#L1122      Args:         old_log_prob (torch.Tensor):             Log-probabilities of actions under the old policy, shape (batch_size, response_length).         log_prob (torch.Tensor):             Log-probabilities of actions under the current policy, shape (batch_size, response_length).         advantages (torch.Tensor):             Advantage estimates for each action, shape (batch_size, response_length).         response_mask (torch.Tensor):             Mask indicating which tokens to include in the loss, shape (batch_size, response_length).         loss_agg_mode (str, optional):             Aggregation mode for `agg_loss`. Defaults to "token-mean".         config: `(verl.trainer.config.ActorConfig)`:             config for the actor.         rollout_log_probs: `(torch.Tensor)`:             log probabilities of actions under the rollout policy, shape (batch_size, response_length).     """      assert config is not None     assert not isinstance(config, AlgoConfig)     clip_ratio = config.clip_ratio  # Clipping parameter ε for standard PPO. See https://arxiv.org/abs/1707.06347.     clip_ratio_low = config.clip_ratio_low if config.clip_ratio_low is not None else clip_ratio     clip_ratio_high = config.clip_ratio_high if config.clip_ratio_high is not None else clip_ratio     clip_ratio_c = config.get(  # Lower bound of the ratio for dual-clip PPO. See https://arxiv.org/pdf/1912.09729.         "clip_ratio_c", 3.0     )      cliprange = clip_ratio     cliprange_low = clip_ratio_low     cliprange_high = clip_ratio_high      assert clip_ratio_c > 1.0, (         "The lower bound of the clip_ratio_c for dual-clip PPO should be greater than 1.0,"         + f" but get the value: {clip_ratio_c}."     )      # 计算每一个token的重要性采样的比值的log     # log(pi_{theta}(o_{i,t}|q,o_{i,<t}))-log(pi_{old}(o_{i,t}|q,o_{i<t}))     negative_approx_kl = log_prob - old_log_prob     # 对IS的log做clip，避免过大或过小     # Clamp negative_approx_kl for stability     negative_approx_kl = torch.clamp(negative_approx_kl, min=-20.0, max=20.0)     # 这里ratio是真正的IS 重要性采样     ratio = torch.exp(negative_approx_kl)     # 计算出-IS在token-level上的均值     ppo_kl = verl_F.masked_mean(-negative_approx_kl, response_mask)      ######################################################     # 下面开始计算pg_loss=     #A>0, max(ratio*-A, clip(ratio, 1-epsilon_low, 1+epsilon_high)*-A)     #A<0, min(max(ratio*-A, clip(ratio, 1-epsilon_low, 1+epsilon_high)*-A), clip_ratio_c*-A)     ######################################################     pg_losses1 = -advantages * ratio     if cliprange_low is None:         cliprange_low = cliprange     if cliprange_high is None:         cliprange_high = cliprange     # clip后的loss     pg_losses2 = -advantages * torch.clamp(         ratio, 1 - cliprange_low, 1 + cliprange_high     )  # - clip(ratio, 1-cliprange, 1+cliprange) * A     # ppo per token loss     clip_pg_losses1 = torch.maximum(         pg_losses1, pg_losses2     )  # max(-ratio * A, -clip(ratio, 1-cliprange, 1+cliprange) * A)     # 计算被才剪掉的token在 这个batch的所有未mask的token的比例（axis=None）【常数】     pg_clipfrac = verl_F.masked_mean(torch.gt(pg_losses2, pg_losses1).float(), response_mask)      # 这里是dual-clip PPO提出，使用clip_ratio_c限制A<0的token的loss     pg_losses3 = -advantages * clip_ratio_c     # min(max(ratio*-A, clip(ratio, 1-epsilon_low, 1+epsilon_high)*-A), clip_ratio_c*-A)     clip_pg_losses2 = torch.min(pg_losses3, clip_pg_losses1)     # 记录在传统ppo下，进一步裁减的A<0的IS大于clip_ratio_c的token在 这个batch的所有未mask的token的比例【常数】     pg_clipfrac_lower = verl_F.masked_mean(         torch.gt(clip_pg_losses1, pg_losses3) * (advantages < 0).float(), response_mask     )      # pg_losses是分段函数(记录每个token的loss)，A<0时用clip_pg_losses2, A>=0时用clip_pg_losses1     pg_losses = torch.where(advantages < 0, clip_pg_losses2, clip_pg_losses1)     # pg_losses: (bsz, response_length)     # 如何计算一整个batch的所有token的整体loss。这有多种方式，主要看配置的loss_agg_mode     pg_loss = agg_loss(loss_mat=pg_losses, loss_mask=response_mask, loss_agg_mode=loss_agg_mode)      return pg_loss, pg_clipfrac, ppo_kl, pg_clipfrac_lower  

咱们继续看几种token loss的agg mode。不同RL方法，loss agg mode也是不同的

verl/trainer/ppo/core_algos.py

def agg_loss(loss_mat: torch.Tensor, loss_mask: torch.Tensor, loss_agg_mode: str):     """     Aggregate the loss matrix into a scalar.      Args:         loss_mat: `(torch.Tensor)`:             shape: (bs, response_length)         loss_mask: `(torch.Tensor)`:             shape: (bs, response_length)         loss_agg_mode: (str) choices:             method to aggregate the loss matrix into a scalar.     Returns:         loss: `a scalar torch.Tensor`             aggregated loss     """     if loss_agg_mode == "token-mean":         loss = verl_F.masked_mean(loss_mat, loss_mask)     elif loss_agg_mode == "seq-mean-token-sum":         seq_losses = torch.sum(loss_mat * loss_mask, dim=-1)  # token-sum         loss = torch.mean(seq_losses)  # seq-mean     elif loss_agg_mode == "seq-mean-token-mean":         seq_losses = torch.sum(loss_mat * loss_mask, dim=-1) / torch.sum(loss_mask, dim=-1)  # token-mean         loss = torch.mean(seq_losses)  # seq-mean     elif loss_agg_mode == "seq-mean-token-sum-norm":         seq_losses = torch.sum(loss_mat * loss_mask, dim=-1)         loss = torch.sum(seq_losses) / loss_mask.shape[-1]  # The divisor         # (loss_mask.shape[-1]) should ideally be constant         # throughout training to well-replicate the DrGRPO paper.         # TODO: Perhaps add user-defined normalizer argument to         # agg_loss to ensure divisor stays constant throughout.     else:         raise ValueError(f"Invalid loss_agg_mode: {loss_agg_mode}")      return loss 

GRPO

优化目标：

[J= mathbb{E}_{{o_i}_{i=1}^Gsimpi_{old}(cdot|q)} frac{1}{|G|} sum_{i=1}^{|G|}frac{1}{|o|}sum_{t=1}^{|o_i|}{min[frac{pi_{theta}(o_{i,t}|q, o_{i,<t})}{pi_{old}(o_{i,t}|q, o_{i, <t})}A_{i, t}, clip(frac{pi_{theta}(o_{i,t}|q, o_{i,<t})}{pi_{old}(o_{i,t}|q, o_{i, <t})}, 1-epsilon, 1+epsilon)A_{i,t}]-beta mathbb{D}_{KL}(pi_{theta}||pi_{ref})} ]

优势：

[A_{i,t} = frac{r_i-mean(r)}{std(r)} ]

KL3

[mathbb{D}_{KL}(pi_{theta}||pi_{ref}) =frac{pi_{ref}(o_{i, t}|q,o_{i,<t})}{pi_{theta}(o_{i,t}|q, o_{i, <t})} -log(frac{pi_{ref}(o_{i, t}|q,o_{i,<t})}{pi_{theta}(o_{i,t}|q, o_{i, <t})})-1 ]

KL3的方差比KL1小，且是KL1的无偏估计

证明

[begin{aligned} mathbb{D3}_{KL}(P||Q) &= sum_{xsim_{P}}P(x) [frac{Q(x)}{P(x)} - log(frac{P(x)}{Q(x)})-1]\ &= sum_{xsim P}Q(x)+P(x)log(frac{P(x)}{Q(x)})-P(x)\ &=sum_{xsim P}Q(x) -sum_{xsim P}P(x)+mathbb{D1}_{KL}(P||Q) \ &=mathbb{D1}_{KL}(P||Q)+sum_{xsim P}Q(x)-1 当P所有采样在Q中的概率和为1时（vocab一样的话）\ &=mathbb{D_1}_{KL}(P||Q) end{aligned} ]

verl/trainer/ppo/core_algos.py 下面是verl对kl_loss的实现：

def kl_penalty_forward(logprob: torch.FloatTensor, ref_logprob: torch.FloatTensor, kl_penalty) -> torch.FloatTensor:     """Compute KL divergence given logprob and ref_logprob.     Copied from https://github.com/huggingface/trl/blob/main/trl/trainer/ppo_trainer.py#L1104     See more description in http://joschu.net/blog/kl-approx.html      Args:         logprob:         ref_logprob:      Returns:         kl_estimate     """     if kl_penalty in ("kl", "k1"):         return logprob - ref_logprob      if kl_penalty == "abs":         return (logprob - ref_logprob).abs()      if kl_penalty in ("mse", "k2"):         return 0.5 * (logprob - ref_logprob).square()      ##############################################################     # 这里的low_var_kl与上述的grpo的KL计算公式相同     ##############################################################     # J. Schulman. Approximating kl divergence, 2020.     # # URL http://joschu.net/blog/kl-approx.html.     if kl_penalty in ("low_var_kl", "k3"):         kl = ref_logprob - logprob         # For numerical stability         kl = torch.clamp(kl, min=-20, max=20)         ratio = torch.exp(kl)         kld = (ratio - kl - 1).contiguous()         return torch.clamp(kld, min=-10, max=10)      if kl_penalty == "full":         # so, here logprob and ref_logprob should contain the logits for every token in vocabulary         raise NotImplementedError      raise NotImplementedError 

GSPO

seq-level 优化目标：

[J= mathbb{E}_{{o_i}_{i=1}^Gsimpi_{old}(cdot|q)} frac{1}{|G|} sum_{i=1}^{|G|}min[(frac{pi_{theta}(o_{i}|q)}{pi_{old}(o_{i}|q)})^{frac{1}{|o_i|}}A_{i}, clip((frac{pi_{theta}(o_{i}|q)}{pi_{old}(o_{i}|q)})^{frac{1}{|o_i|}}, 1-epsilon, 1+epsilon)A_{i}] ]

[frac{pi_{theta}(o_i|q)}{pi_{old}(o_i|q)} = frac{Pi_{t=1}^{|o_i|} pi_{theta}(o_{i,t}|q, o_{i,<t})}{Pi_{t=1}^{|o_i|} pi_{old}(o_{i,t}|q, o_{i,<t})} ]

token-level 优化目标：

[J = mathbb{E}_{{o_i}_{i=1}^Gsim pi_{old}(cdot|q)}frac{1}{G}sum_{i=1}^Gfrac{1}{|o_i|}sum_{t=1}^{|o_i|} min(s_{i,t}A_{i,t}, clip(s_{i,t}, 1-epsilon,1+epsilon)A_{i,t})\ hat{s}_{i,t} = sg[(frac{pi_{theta}(o_i|q)}{pi_{old}(o_i|q)})^{frac{1}{|o_i|}}]* frac{pi_{theta}(o_{i,t}|q,o_{i,<t})}{sg[pi_{theta}(o_{i,t}|q,o_{i,<t})]} ]

可以发现的是 (sg[s_{i,t}]=sg[s_{i}],s_{i}=(frac{pi_{theta}(o_i|q)}{pi_{old}(o_i|q)})^{frac{1}{|o_i|}})，但是在方向上不同

通过证明，可以发现，当(A_{i,t}=A_i)时，seq-level和token-level在前向传播和反向传播上是一样的
token-level 可以更好地扩展 同sample不同token的A的灵活度（每个token的A可以不相同）

verl/trainer/ppo/core_algos.py

########################################################## # 计算gspo的pg_loss,重点关注IS的计算 ########################################################## @register_policy_loss("gspo") def compute_policy_loss_gspo(     old_log_prob: torch.Tensor,     log_prob: torch.Tensor,     advantages: torch.Tensor,     response_mask: torch.Tensor,     loss_agg_mode: str = "seq-mean-token-mean",     config: Optional[DictConfig | ActorConfig] = None,     rollout_is_weights: torch.Tensor | None = None, ) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:     """     Compute the clipped policy objective and related metrics for GSPO.      See https://arxiv.org/pdf/2507.18071 for more details.      Args:         old_log_prob (torch.Tensor):             Log-probabilities of actions under the old policy, shape (batch_size, response_length).         log_prob (torch.Tensor):             Log-probabilities of actions under the current policy, shape (batch_size, response_length).         advantages (torch.Tensor):             Advantage estimates for each action, shape (batch_size, response_length).         response_mask (torch.Tensor):             Mask indicating which tokens to include in the loss, shape (batch_size, response_length).         loss_agg_mode (str, optional):             Aggregation mode for `agg_loss`. For GSPO, it is recommended to use "seq-mean-token-mean".     """      assert config is not None     assert isinstance(config, ActorConfig)     clip_ratio_low = config.clip_ratio_low if config.clip_ratio_low is not None else config.clip_ratio     clip_ratio_high = config.clip_ratio_high if config.clip_ratio_high is not None else config.clip_ratio      negative_approx_kl = log_prob - old_log_prob      # compute sequence-level importance ratio:     # si(θ) = (π_θ(yi|x)/π_θold(yi|x))^(1/|yi|) =     # exp [(1/|y_i|) * Σ_t log(π_θ(y_i,t|x,y_i,<t)/π_θold(y_i,t|x,y_i,<t))]     seq_lengths = torch.sum(response_mask, dim=-1).clamp(min=1)     negative_approx_kl_seq = torch.sum(negative_approx_kl * response_mask, dim=-1) / seq_lengths      # Combined ratio at token level:     # s_i,t(θ) = sg[s_i(θ)] · π_θ(y_i,t|x, y_i,<t) / sg[π_θ(y_i,t|x, y_i,<t)]     # In log space: log(s_i,t(θ)) = sg[log(s_i(θ))] + log_prob - sg[log_prob]     log_seq_importance_ratio = log_prob - log_prob.detach() + negative_approx_kl_seq.detach().unsqueeze(-1)     log_seq_importance_ratio = torch.clamp(log_seq_importance_ratio, max=10.0)  # clamp for numerical stability      # finaly exp() to remove log     seq_importance_ratio = torch.exp(log_seq_importance_ratio)      pg_losses1 = -advantages * seq_importance_ratio     pg_losses2 = -advantages * torch.clamp(seq_importance_ratio, 1 - clip_ratio_low, 1 + clip_ratio_high)     pg_losses = torch.maximum(pg_losses1, pg_losses2)      # Apply rollout importance sampling weights if provided     if rollout_is_weights is not None:         pg_losses = pg_losses * rollout_is_weights      # for GSPO, we need to aggregate the loss at the sequence level (seq-mean-token-mean)     pg_loss = agg_loss(loss_mat=pg_losses, loss_mask=response_mask, loss_agg_mode="seq-mean-token-mean")      # For compatibility, return zero for pg_clipfrac_lower (not used in standard GSPO)     pg_clipfrac = verl_F.masked_mean(torch.gt(pg_losses2, pg_losses1).float(), response_mask)     pg_clipfrac_lower = torch.tensor(0.0, device=pg_loss.device)      ppo_kl = verl_F.masked_mean(-negative_approx_kl, response_mask)      return pg_loss, pg_clipfrac, ppo_kl, pg_clipfrac_lower  

DAPO

优化目标：

[mathcal{J} = mathbb{E}_{(q,a)sim mathcal{D}, {o_i}_{i=1}^Gsim pi_{old}(cdot|q)} [frac{1}{sum_{i=1}^G|o_i|}sum_{i=1}^Gsum_{t=1}^{|o_i|}min(r_{i,t}(theta)A_{i, t}, clip(r_{i,t}(theta),1-epsilon_{low}, 1+epsilon_{high})A_{i,t})]\ s.t. 0<|{o_i|is_equivalent(o_i,a)}|<G ]

其中

[r_{i,t}(theta)=frac{pi_{theta}(o_{i,t}|q,o_{i,<t})}{pi_{old}(o_{i,t}|q,o_{i,<t})}, A_{i,t} = frac{R_i-mean({R_i}_{i=1}^G)}{std({R_i}_{i=1}^G)} ]

其loss agg mode是token-mean。