Rethinking generative adversarial networks with applications towards robust machine learning systems
Abstract
The existing theoretical understanding of generative adversarial networks (GANs) pales when compared to their tremendous popularity in practice. While promising to hold the state-of-the-art role in many unsupervised machine learning problems, including data generation, compression, domain transfer, and recognition, the GAN results stagnate due to their difficulty in training, which cannot be addressed with the current over-reliance on heuristics and trial-and-error. The basic GAN optimization problem is a non-convex, robust machine learning (ML) problem that has even applications in other ML domains, including reinforcement learning, robust decision making under combinatorial constraints, and adversarial robustness for neural networks. As a result, we develop a new non-convex optimization algebra with broad implications. We not only question how the GAN learning formulations are formed, but also increase their utility in making neural networks more robust via developing provable algorithms with rates. We integrate a tightly inter-related four research thrusts: Thrust I: Mixed Nash Equilibria of GANs. This thrust will build mathematically principled research avenues for GANs that address not only how we set up and optimize GANs, but also provide solutions that will attain the so-called mixed Nash Equilibrium for the chosen formulations. In stark contrast to the literature, we seek to establish a global strategy for training GANs as opposed to relying on local stability. Thrust II: Equilibria of GANs beyond Nash and Alternating Algorithms. This thrust will import powerful frameworks from the theory of differential games and study equilibria notions that are beyond Nash. The major incentive is to bridge the gap between the theoretically-motivated simultaneous updates and the practically-preferred alternating steps in current approach. We will also algorithmic solve novel equilibria, in particular leading to the first alternating methods that possess rigorous guarantees. Thrust III: Equilibria of GANs via smoothing. This thrust takes on a homotopy-based optimization approach to attain local stationary points with rates. We avoid a neural discriminator network in the cost function so as to remove fragile stationary points due to the so-called dual updates. Instead, we show how to smooth the GAN cost function (e.g., minimizing Wasserstein distance) in a gradual fashion that approximates the stationary point of the original GAN problem with rates without a primal-dual reformulation. Thrust IV: GANs as Prior. This thrust initiates a novel approach in making neural networks robust against adversarial attacks by using GAN models. To achieve the desiderata, we develop a new non-convex optimization framework that can handle non-linear constraints rigorously with rate guarantees. We also develop generalization bounds for such an algorithmic framework and further seek its applications to key scientific problems such as solving semidefinite programs as well as reinforcement learning. The non-convexity arising in GANs remains poorly understood to date, and necessarily restricts the scope of optimization-based frameworks to local theory. Our mixed NE perspective can be considered as a first affirmative step towards a global theory of training GANs, under the practically-supported premise that sampling for a single neural net succeeds. There are several broader impacts in robust machine learning, which we further discuss in the proposal, from semidefinite programming to reinforcement learning.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 19, 2019
- Source ID
- W911NF1910404
Entities
People
- Volkan Cevher
Organizations
- Army Contracting Command
- ETH Zurich
- United States Army