PPO 策略梯度损失推导

PPO（Proximal Policy Optimization）: 近端策略优化
PG: Policy Gradient

推导过程

PPO 是在 PG 基础上增加了对 $r^t$ 的裁剪，限制策略更新幅度，遵循 “保守更新” 原则。

标准PPO的问题

• $A^t$ < 0, 原始$r^t$(θ) > 1+ϵ时，$r^t$​(θ)$A^t$​ < (1+ϵ)$A^t​$, 此时min操作会选择更小的原始乘积$r^t$​(θ)$A^t$​，裁剪完全不起作用
  • 例子：$A^t$ ​= −10，离策略下$r^t$​(θ) = 100（极易出现的极端值）：
    • 原始乘积：100×(−10)=−1000
    • 裁剪后乘积：1.2×(−10)=−12
    • min (-1000, -12) = -1000，裁剪完全失效，损失项直接取极端负值
• 无界性：离策略场景下，$r^t$​(θ)可以无限大（当前策略对该动作的概率远高于历史采样策略），$A^t$​也可以出现极端负值，因此$r^t$​(θ)$A^t$​可以无限趋近于负无穷，完全没有任何下界约束

Dual-Clip PPO

Dual-Clip PPO没有修改概率比的裁剪逻辑，而是直接对损失项的最终结果增加了硬下界约束，从根源上解决无界问题：

$L^{DUAL−CLIP}$(θ) = $E^t$​[max(min($r^t$​(θ)$A^t$​, clip($r^t​$(θ),1−ϵ,1+ϵ)$A^t​$), c⋅A^t​)]

其中c>1是超参数（原论文设为3），当$A^t$​<0时，c⋅$A^t$​就是损失项的硬下界 —— 无论$r^t$​(θ)多大、$A^t$​多负，损失项都不会小于c⋅$A^t$​，彻底解决了标准 PPO 在离策略场景下的无界方差和收敛性问题。

Dual-Clip PPO算法的策略梯度损失计算逻辑:

def compute_policy_loss(
    old_log_prob,
    log_prob,
    advantages,
    response_mask,
    cliprange=None,
    cliprange_low=None,
    cliprange_high=None,
    clip_ratio_c=3.0,
    loss_agg_mode="token-mean",
):
    """Adapted from https://github.com/huggingface/trl/blob/main/trl/trainer/ppo_trainer.py#L1122
    Args:
        old_log_prob: `(torch.Tensor)`
            shape: (bs, response_length)
        log_prob: `(torch.Tensor)`
            shape: (bs, response_length)
        advantages: `(torch.Tensor)`
            shape: (bs, response_length)
        response_mask: `(torch.Tensor)`
            shape: (bs, response_length)
        cliprange: (float)
            The clip range used in PPO. See https://arxiv.org/abs/1707.06347
        cliprange_low: (float)
            The lower clip range used in PPO.
        cliprange_high: (float)
            The higher clip range used in PPO.
        clip_ratio_c: (float) default: 3.0
            The lower bound of the ratio for dual-clip PPO, See https://arxiv.org/pdf/1912.09729
        loss_agg_mode: (str) choices: "token-mean" /
                                      "seq-mean-token-sum" /
                                      "seq-mean-token-mean" /
                                      "seq-mean-token-sum-norm" /
            "token-mean" is the default behavior

    Returns:
        pg_loss: `a scalar torch.Tensor`
            policy gradient loss computed via PPO
        pg_clipfrac: (float)
            the fraction of policy gradient loss being clipped
        ppo_kl: (float)
            the estimated KL divergence between the latest updating policy and the old sampling policy
        pg_clipfrac_lower: (float)
            the fraction of policy gradient loss being clipped when the advantage is negative
    """
    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}."

    negative_approx_kl = log_prob - old_log_prob
    max_negative_approx_kl = torch.max(negative_approx_kl).cpu().item()
    negative_approx_kl_clipped = torch.clamp(negative_approx_kl, min=-10.0, max=10.0)
    ratio = torch.exp(negative_approx_kl_clipped)
    ppo_kl = verl_F.masked_mean(-negative_approx_kl_clipped, response_mask)

    pg_losses1 = -advantages * ratio
    if cliprange_low is None:
        cliprange_low = cliprange
    if cliprange_high is None:
        cliprange_high = cliprange
    pg_losses2 = -advantages * torch.clamp(ratio, 1 - cliprange_low, 1 + cliprange_high)
    clip_pg_losses1 = torch.maximum(pg_losses1, pg_losses2)
    pg_clipfrac = verl_F.masked_mean(torch.gt(pg_losses2, pg_losses1).float(), response_mask)

    pg_losses3 = -advantages * clip_ratio_c
    clip_pg_losses2 = torch.min(pg_losses3, clip_pg_losses1)
    pg_clipfrac_lower = verl_F.masked_mean(torch.gt(clip_pg_losses1, pg_losses3) * (advantages < 0).float(), response_mask)

    pg_losses = torch.where(advantages < 0, clip_pg_losses2, clip_pg_losses1)
    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