entropyregularized

Entropyregularized refers to the practice of augmenting an optimization objective with an entropy term to promote higher-entropy, more diverse solutions. The approach is used across machine learning, reinforcement learning, and optimization to encourage exploration, avoid premature convergence, and yield robust, stable policies or models. The core idea is that, by penalizing low-entropy (overly deterministic) distributions, the solution remains flexible and less prone to overfitting.

Mathematically, entropy regularization typically adds a term proportional to the entropy of a probability distribution to the objective. For a discrete distribution p over actions or outcomes, the entropy is H(p) = - sum p(a) log p(a). An entropy-regularized objective might take the form maximize f(p) + lambda H(p), where lambda > 0 controls the strength of the regularization. In continuous settings, differential entropy is used. Entropy regularization is closely related to maximum entropy principles and to regularization with Kullback–Leibler divergence, such as encouraging a policy p to stay close to a prior q via lambda KL(p || q).

Common applications include entropy-regularized reinforcement learning, where the policy is optimized to maximize expected return plus an entropy term to encourage exploration; and entropy-regularized optimal transport, where the transport plan is stabilized by a entropy term, enabling efficient computation with algorithms like Sinkhorn iterations. In variational inference and probabilistic modeling, entropy regularization helps prevent overconfident posteriors and supports smoother, more robust distributions.

Choosing the regularization strength lambda is a practical concern, balancing exploration and convergence speed. If lambda is too large, solutions may become overly diffuse; if too small, the benefits of exploration may be limited.