Related papers: Practical Perspectives on Symplectic Accelerated O…

Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…

We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…

We present a practical algorithm based on symplectic splitting methods to integrate numerically in time the Schr\"odinger equation. When discretized in space, the Schr\"odinger equation can be recast as a classical Hamiltonian system…

It is well-known that proper scaling can increase the efficiency of computational problems. In this paper we define and show that a balancing technique can substantially improve the computational efficiency of optimal control algorithms. We…

Machine learning frameworks adopt iterative optimizers to train neural networks. Conventional eager execution separates the updating of trainable parameters from forward and backward computations. However, this approach introduces…

Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…

Numerical Simulation is an essential part of the design and optimisation of astronomical adaptive optics systems. Simulations of adaptive optics are computationally expensive and the problem scales rapidly with telescope aperture size, as…

Machine learning methods are widely used in the natural sciences to model and predict physical systems from observation data. Yet, they are often used as poorly understood "black boxes," disregarding existing mathematical structure and…

We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…

The Rodeo Algorithm is a quantum computing method for computing the energy spectrum of a Hamiltonian and preparing its energy eigenstates. We discuss how to improve the performance of the rodeo algorithm for each of these two applications.…

This paper presents a generic technique for improving hybrid algorithms through the discovery of and tuning of meta-heuristics. The idea is to represent a family of push/pull heuristics that are based upon inserting and removing tasks in a…

In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…

We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…

We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…

Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…

In this paper, we present a concurrent and scalable trajectory optimization method to improve the quality of robot-assisted manufacturing. Our method simultaneously optimizes tool orientations, kinematic redundancy, and waypoint timing on…

Learning-based methods have shown promising performance for accelerating motion planning, but mostly in the setting of static environments. For the more challenging problem of planning in dynamic environments, such as multi-arm assembly…

Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…

This paper proposes a hybrid learning and optimization framework for mobile manipulators for complex and physically interactive tasks. The framework exploits an admittance-type physical interface to obtain intuitive and simplified human…