Related papers: Introducing memory to a family of multi-step multi…

In ultrahigh dimensional setting, independence screening has been both theoretically and empirically proved a useful variable selection framework with low computation cost. In this work, we propose a two-step framework by using marginal…

In this paper we consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a…

We present a family of multistep integrators based on the Adams-Bashforth methods. These schemes can be constructed for arbitrary convergence order with arbitrary step size variation. The step size can differ between different subdomains of…

In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT…

This work focuses on the construction of a new class of fourth-order accurate methods for multirate time evolution of systems of ordinary differential equations. We base our work on the Recursive Flux Splitting Multirate (RFSMR) version of…

Whereas the ability of deep networks to produce useful predictions has been amply demonstrated, estimating the reliability of these predictions remains challenging. Sampling approaches such as MC-Dropout and Deep Ensembles have emerged as…

Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, in practice, organizations are not able to be fully flexible, as decisions…

In order to approximate solutions of stochastic partial differential equations (SPDEs) that do not possess commutative noise, one has to simulate the involved iterated stochastic integrals. Recently, two approximation methods for iterated…

This work addresses flexibility in deep learning by means of transductive reasoning. For adaptation to new data and tasks, e.g., in continual learning, existing methods typically involve tuning learnable parameters or complete re-training…

Differential Dynamic Programming (DDP) is a popular technique used to generate motion for dynamic-legged robots in the recent past. However, in most cases, only the first-order partial derivatives of the underlying dynamics are used,…

Gradient-based bilevel optimisation is a powerful technique with applications in hyperparameter optimisation, task adaptation, algorithm discovery, meta-learning more broadly, and beyond. It often requires differentiating through the…

In this paper, we consider Markov Decision Processes (MDPs) with error states. Error states are those states entering which is undesirable or dangerous. We define the risk with respect to a policy as the probability of entering such a state…

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the…

We investigate a family of approximate multi-step proximal point methods, accelerated by implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…

In this paper, a two-step inertial Tseng extragradient method involving self-adaptive and Armijo-like step sizes is introduced for solving variational inequalities with a quasimonotone cost function in the setting of a real Hilbert space.…

This work proposes neural training as a \emph{process tensor}: a multi-time map that takes a sequence of controllable instruments (batch choices, augmentations, optimizer micro-steps) and returns an observable of the trained model. Building…

Multi-step forceful manipulation tasks, such as opening a push-and-twist childproof bottle, require a robot to make various planning choices that are substantially impacted by the requirement to exert force during the task. The robot must…

We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics, both in time and space, which include the relaxation schemes by S. Jin and Z. Xin. These methods can use CFL number larger…

In continual learning, where task data arrives in a sequence, fine-tuning on later tasks will often lead to performance degradation on earlier tasks. This is especially pronounced when these tasks come from diverse domains. In this setting,…