If we estimate the gradient of $f(x)$ using the likelihood ratio/score function, i.e. $$\nabla f = f^*\dfrac{\partial \log p(x)}{\partial \theta}$$ is there any agreed upon terminology to call "$f^*$"? Specifically I'm thinking of the case where you may use some sort of baseline/control variate or a critic, so $f^*$ is not $f$.

I've seen $f^*$ called the learning signal or the cost. In reinforcement learning, you would call $f^*$ the advantage, but I think that terminology is only specific for RL. What is a general way to call $f^*$ that is not specific to RL?



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