PPO clipped surrogate loss

Problem

PPO trains a policy for several epochs on one batch of samples. The importance ratio compares the new policy with the policy that collected the samples. PPO clips this ratio, so that one update cannot move the policy too far. The same clipped loss is the core of many RLHF pipelines.

Task

Write three functions. Each takes the new log probabilities, the old log probabilities and the advantages of N samples, and the clip size eps.

1. ppo_clip_loss(logp_new, logp_old, advantages, eps=0.2) returns the loss to minimize.
2. clip_fraction(logp_new, logp_old, advantages, eps=0.2) returns the fraction of clipped samples.
3. ppo_clip_grad(logp_new, logp_old, advantages, eps=0.2) returns the gradient of the loss with respect to logp_new.

The ratio of sample t is r_t = \exp(\log\pi_{new,t} - \log\pi_{old,t}). The loss is:

Sample t is clipped when A_t > 0 and r_t > 1 + \epsilon, or when A_t < 0 and r_t < 1 - \epsilon. Both comparisons are strict. A sample with A_t = 0 is not clipped.

The gradient of a clipped sample is 0. The gradient of any other sample is -r_t A_t / N.

Input and output

• ppo_clip_loss returns a float.
• clip_fraction returns a float from 0 to 1.
• ppo_clip_grad returns a float array of shape (N,).

Constraints

• 1 <= N <= 4096.
• Log probabilities are from -1000 to 0.
• Do not normalize the advantages.
• Do not change the input arrays.
• Use numpy only.

Examples

pythonCopylogp_old = np.log(np.array([0.5, 0.5, 0.5, 0.5]))
logp_new = np.log(np.array([0.7, 0.55, 0.3, 0.45]))
advantages = np.array([1.0, 2.0, -1.0, -0.5])
ppo_clip_loss(logp_new, logp_old, advantages)
clip_fraction(logp_new, logp_old, advantages)
ppo_clip_grad(logp_new, logp_old, advantages)

textCopy-0.5375000000000001
0.5
[ 0.     -0.55    0.      0.1125]

The ratios are [1.4, 1.1, 0.6, 0.9]. Sample 0 has A > 0 and r > 1.2. Sample 2 has A < 0 and r < 0.8. These two samples are clipped.