Title: Equilibrium-finding via exploitability descent with learned best-response functions. Abstract: There has been great progress on equilibrium-finding research over the last 20 years. Most of that work has focused on games with finite, discrete action spaces. However, many games involving space, time, money, etc. have continuous action spaces. We study the problem of computing approximate Nash equilibria of games with continuous strategy sets. The main measure of closeness to Nash equilibrium is exploitability, which measures how much players can benefit from unilaterally changing their strategy. We propose a new method that minimizes an approximation of  exploitability with respect to the strategy profile. This approximation is computed using learned best-response functions, which take the current strategy profile as input and return learned best responses. The strategy profile and best-response functions are trained simultaneously, with the former trying to minimize exploitability while the latter try to maximize it. We evaluate our method on various continuous games, showing that it outperforms prior methods.