Optimal Bounds between $f$-Divergences and Integral Probability Metrics

Understand

The families of $f$-divergences (e.g.

• the Kullback-Leibler divergence) and Integral Probability Metrics (e.g.
• total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability distributions.
• In this work, we systematically study the relationship between these two families from the perspective of convex duality.