相关论文: Understanding Riemannian Acceleration via a Proxim…

Estimating and reacting to external disturbances is of fundamental importance for robust control of quadrotors. Existing estimators typically require significant tuning or training with a large amount of data, including the ground truth, to…

We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed on the product space of the mode-2 unfolding matrices of the core tensors in tensor ring…

We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…

We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hull of a finite number of points, in the case when the number…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

In this paper we introduce a theoretical framework for semi-discrete optimization using ideas from optimal transport. Our primary motivation is in the field of deep learning, and specifically in the task of neural architecture search. With…

Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…

Precision matrix estimation is a fundamental topic in multivariate statistics and modern machine learning. This paper proposes an adversarially perturbed precision matrix estimation framework, motivated by recent developments in adversarial…

We consider a class of (possibly strongly) geodesically convex optimization problems on Hadamard manifolds, where the objective function splits into the sum of a smooth and a possibly nonsmooth function. We introduce an intrinsic convex…

Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…

For solving strongly convex optimization problems, we propose and study the global convergence of variants of the A-HPE and large-step A-HPE algorithms of Monteiro and Svaiter. We prove linear and the superlinear…

We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This…

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…

Accelerated gradient methods play a central role in optimization, achieving optimal rates in many settings. While many generalizations and extensions of Nesterov's original acceleration method have been proposed, it is not yet clear what is…

We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and…

Optimization problems with access to only zeroth-order information of the objective function on Riemannian manifolds arise in various applications, spanning from statistical learning to robot learning. While various zeroth-order algorithms…

A Hessian based optimal control method is presented in Liouville space to mitigate previously undesirable polynomial scaling of computation time. This new method, an improvement to the state-of-the-art Newton-Raphson GRAPE method, is…

We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…

Neighbour embeddings (NE) allow the representation of high dimensional datasets into lower dimensional spaces and are often used in data visualisation. In practice, accelerated approximations are employed to handle very large datasets.…

Meta-learning problem is usually formulated as a bi-level optimization in which the task-specific and the meta-parameters are updated in the inner and outer loops of optimization, respectively. However, performing the optimization in the…