Related papers: Learning algorithms for mean field optimal control
We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to…
This work puts forward a novel numerical approach for solving the stochastic optimal control problem (SOCP) and the mean field control (MFC) problem using projection algorithm inspired by the stochastic maximum principle (SMP) which is also…
We describe a new algorithm for computing the ideal class group, the regulator and a system of fundamental units in number fields under the generalized Riemann hypothesis. We use sieving techniques adapted from the number field sieve…
In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its optimal solution. This infinite dimensional, function space,…
We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is to the problem of mean-field variational inference, which…
We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…
We propose a novel reformulation of the stochastic optimal control problem as an approximate inference problem, demonstrating, that such a interpretation leads to new practical methods for the original problem. In particular we characterise…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
We show how machine-learning techniques, particularly neural networks, offer a very effective and highly efficient solution to the approximate model-checking problem for continuous and hybrid systems, a solution where the general-purpose…
We study control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…
In this article we propose a shooting algorithm for optimal control problems governed by systems that are affine in one part of the control variable. Finitely many equality constraints on the initial and final state are considered. We…
We study an optimal intervention problem on the linear threshold model (LTM) in which a social planner aims to design minimal-cost interventions that modify the agents' thresholds, under the constraint that at least a predefined fraction of…
Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…
We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…
Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge…
Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been…