Related papers: Tensor Train for Global Optimization Problems in R…
The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a…
Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize…
We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
A new technique of global optimization and its applications in particular to neural networks are presented. The algorithm is also compared to other global optimization algorithms such as Gradient descent (GD), Monte Carlo (MC), Genetic…
In this article we consider min-min type of problems or minimization by two groups of variables. Min-min problems may occur in case if some groups of variables in convex optimization have different dimensions or if these groups have…
The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple…
We present a tensor train (TT) based algorithm designed for sampling from a target distribution and employ TT approximation to capture the high-dimensional probability density evolution of overdamped Langevin dynamics. This involves…
Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
In robotics, ergodic control extends the tracking principle by specifying a probability distribution over an area to cover instead of a trajectory to track. The original problem is formulated as a spectral multiscale coverage problem,…
In recent years, Generative Adversarial Networks (GANs) have drawn a lot of attentions for learning the underlying distribution of data in various applications. Despite their wide applicability, training GANs is notoriously difficult. This…
Since traditional tokenizers are isolated from a downstream task and model, they cannot output an appropriate tokenization depending on the task and model, although recent studies imply that the appropriate tokenization improves the…
We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183--204, 2017], which is a gradient-free optimization method for general…
Differential drive robots are widely used in various scenarios thanks to their straightforward principle, from household service robots to disaster response field robots. There are several types of driving mechanisms for real-world…
Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
First-order methods with momentum such as Nesterov's fast gradient method are very useful for convex optimization problems, but can exhibit undesirable oscillations yielding slow convergence rates for some applications. An adaptive…