Entropy Regularization

Entropy Regularization is a technique that adds the entropy of the model's output distribution to the training objective — encouraging higher entropy (more exploration, less certainty) or lower entropy (more decisive predictions) depending on the application.

Entropy Regularization Forms

• Maximum Entropy: Add $+\beta H(p)$ to reward higher entropy — prevents premature convergence to deterministic policies.
• Minimum Entropy: Add $-\beta H(p)$ to penalize high entropy — encourages decisive, low-entropy predictions.
• Semi-Supervised: Use entropy minimization on unlabeled data — push unlabeled predictions toward confident (low-entropy) decisions.
• Conditional Entropy: Regularize the conditional entropy $H(Y|X)$ — controls per-input prediction sharpness.

Why It Matters

• RL Exploration: Maximum entropy RL (SAC) prevents premature policy collapse — maintains exploration.
• Semi-Supervised: Entropy minimization is a key component of semi-supervised learning.
• Calibration: Entropy regularization helps produce well-calibrated probability predictions.

Entropy Regularization is controlling the model's decisiveness — using entropy to balance between confident predictions and exploratory uncertainty.