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name: policy_gradient_outer_update description: Apply the score-function outer update for probabilistic bilevel coreset selection without implicit differentiation.

Policy Gradient Outer Update

Use this skill when a sampled coreset has been trained in an inner loop and an outer validation loss is available. It implements the paper's policy-gradient estimator and then delegates feasibility to capped-simplex projection.

Do not use this skill for backpropagating through the inner optimizer, Hessian inverse approximations, or greedy subset addition. Its contract is specifically the forward-loss score-function update from Equation (6).

Inputs

• Current probabilities s.
• Sampled binary mask m from the same probabilities.
• Scalar validation or outer loss.
• Learning rate eta.
• Coreset budget K.

Outputs

• Feasible updated probabilities.
• Raw pre-projection values.
• Score-function gradient diagnostics.

Workflow

1. Import or otherwise use the mask-relaxation score gradient.
2. Multiply the score gradient by the observed outer loss.
3. Take a descent step on probabilities.
4. Project the result with the capped-simplex projection.
5. Log diagnostics so recovery can prove the generated skills were exercised.

Validation

Run python tests/test_policy_update.py or validate the skill tree with tests enabled. The tests confirm finite gradients, probability movement, and post-update feasibility.

Limitations

The update quality depends on the caller's inner-training and validation-loss computation. This skill intentionally does not own model training.