code: def pugail_loss(
      positive_class_prior: float,
      entropy_coefficient: float,
      pugail_beta: Optional[float] = None,
  ) -> Loss:
      """Computes the PUGAIL loss (https://arxiv.org/pdf/1911.00459.pdf)."""
  
      def loss_fn(
          discriminator_fn: DiscriminatorFn,
          discriminator_state: State,
          demo_transitions: types.Transition,
          rb_transitions: types.Transition,
          rng_key: networks_lib.PRNGKey,
      ) -> LossOutput:
          del rng_key
  
          demo_logits, discriminator_state = discriminator_fn(
              discriminator_state, demo_transitions
          )
          rb_logits, discriminator_state = discriminator_fn(
              discriminator_state, rb_transitions
          )
  
          # Quick Maths:
          # output = logit(D) = ln(D) - ln(1-D)
          # -softplus(-output) = ln(D)
          # softplus(output) = -ln(1-D)
  
          # prior * -ln(D(expert))
          positive_loss = positive_class_prior * -jax.nn.log_sigmoid(
              demo_logits
          )
          # -ln(1 - D(policy)) - prior * -ln(1 - D(expert))
          negative_loss = jax.nn.softplus(
              rb_logits
          ) - positive_class_prior * jax.nn.softplus(demo_logits)
          if pugail_beta is not None:
              negative_loss = jnp.clip(
                  negative_loss, a_min=-1.0 * pugail_beta
              )
  
          classification_loss = jnp.mean(positive_loss + negative_loss)
  
          entropy = jnp.mean(
              _logit_bernoulli_entropy(
                  jnp.concatenate([demo_logits, rb_logits])
              )
          )
          entropy_loss = -entropy_coefficient * entropy
  
          total_loss = classification_loss + entropy_loss
  
          metrics = {
              "total_loss": total_loss,
              "positive_loss": jnp.mean(positive_loss),
              "negative_loss": jnp.mean(negative_loss),
              "demo_logits": jnp.mean(demo_logits),
              "rb_logits": jnp.mean(rb_logits),
              "entropy_loss": entropy_loss,
              "classification_loss": classification_loss,
          }
          return total_loss, (
              metrics,
              discriminator_state,
          )  # pytype: disable=bad-return-type  # jnp-type
  
      return loss_fn
  
file_path: acme/acme/agents/jax/ail/losses.py
imports: import functools
  from typing import Callable, Dict, Optional, Tuple
  from acme import types
  from acme.jax import networks
  import jax
  import jax.numpy
  import tensorflow_probability
  import tree
label_desc: Use image node_id 6 for calling a global function with example usage: pugail_loss(positive_class_prior, entropy_coefficient, pugail_beta) and returns: loss_fn, total_loss,  metrics,  discriminator_state