Smooth markets: A basic mechanism for organizing gradient-based learners

With the success of modern machine learning, it is becoming increasingly important to understand and control how learning algorithms interact. Unfortunately, negative results from game theory show there is little hope of understanding or controlling general n-player games. We therefore introduce smooth markets (SM-games), a class of n-player games with pairwise zero sum interactions. SM-games codify a common design pattern in machine learning that includes (some) GANs, adversarial training, and other recent algorithms. We show that SM-games are amenable to analysis and optimization using first-order methods. "I began to see legibility as a central problem in modern statecraft. The premodern state was, in many respects, partially blind [. . .] It lacked anything like a detailed 'map' of its terrain and its people. It lacked, for the most part, a measure, a metric that would allow it to 'translate' what it knew into a common standard necessary for a synoptic view. As a result, its interventions were often crude and self-defeating." -from Seeing like a State by Scott (1999)