We present Theseus, an efficient application-agnostic open source library for differentiable nonlinear least squares (DNLS) optimization built on PyTorch, providing a common framework for end-to-end structured learning in robotics and vision. Existing DNLS implementations are application specific and do not always incorporate many ingredients important for efficiency. Theseus is application-agnostic, as we illustrate with several example applications that are built using the same underlying differentiable components, such as second-order optimizers, standard costs functions, and Lie groups. For efficiency, Theseus incorporates support for sparse solvers, automatic vectorization, batching, GPU acceleration, and gradient computation with implicit differentiation and direct loss minimization. We do extensive performance evaluation in a set of applications, demonstrating significant efficiency gains and better scalability when these features are incorporated.

Fixed-point iterations are at the heart of numerical computing and are often a computational bottleneck in real-time applications that typically need a fast solution of moderate accuracy. We present neural fixed-point acceleration which combines ideas from meta-learning and classical acceleration methods to automatically learn to accelerate fixed-point problems that are drawn from a distribution. We apply our framework to SCS, the state-of-the-art solver for convex cone programming, and design models and loss functions to overcome the challenges of learning over unrolled optimization and acceleration instabilities. Our work brings neural acceleration into any optimization problem expressible with CVXPY.

We formulate and address the problem of discovering dynamic malicious regions on the Internet. We model this problem as one of adaptively pruning a known decision tree, but with additional challenges: (1) severe space requirements, since the underlying decision tree has over 4 billion leaves, and (2) a changing target function, since malicious activity on the Internet is dynamic. We present a novel algorithm that addresses this problem, by putting together a number of different ``experts algorithms and online paging algorithms. We prove guarantees on our algorithms performance as a function of the best possible pruning of a similar size, and our experiments show that our algorithm achieves high accuracy on large real-world data sets, with significant improvements over existing approaches.