# A Better Privacy Analysis of the Exponential Mechanism

A basic and frequent task in data analysis is *selection* – given a set of options \(\mathcal{Y}\), output the (approximately) best one, where “best” is defined by some loss function \(\ell : \mathcal{Y} \times \mathcal{X}^n \to \mathbb{R}\) and a dataset \(x \in \mathcal{X}^n\). That is, we want to output some \(y \in \mathcal{Y}\) that approximately minimizes \(\ell(y,x)\). Naturally, we are interested in *private selection* – i.e., the output should be differentially private in terms of the dataset \(x\).
This post discusses algorithms for private selection – in particular, we give an improved privacy analysis of the popular exponential mechanism.