**Gumbel-Softmax** is a continuous distribution that has the property that it can be smoothly annealed into a categorical distribution, and whose parameter gradients can be easily computed via the reparameterization trick.

**Mirror Descent Policy Optimization (MDPO)** is a policy gradient algorithm based on the idea of iteratively solving a trust-region problem that minimizes a sum of two terms: a linearization of the standard RL objective function and a proximity term that restricts two consecutive updates to be close to each other. It is based on Mirror Descent, which is a general trust region method that
attempts to keep consecutive iterates close to each other.

MDPO

Mirror Descent Policy Optimization

Gumbel Softmax

Categorical Reparameterization with Gumbel-Softmax

**Local Prior Matching** is a semi-supervised objective for speech recognition that distills knowledge from a strong prior (e.g. a language model) to provide learning signal to a discriminative model trained on unlabeled speech. The LPM objective minimizes the cross entropy between the local prior and the model distribution, and is minimized when $q\_{y\mid{x}} = \bar{p}\_{y\mid{x}}$. Intuitively, LPM encourages the ASR model to assign posterior probabilities proportional to the linguistic probabilities of the proposed hypotheses.

Source	Categorical Reparameterization with Gumbel-Softmax
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com