4 citations · 4 across the 1 of their papers we have counts for
6 papers
Solving path dependent PDEs with LSTM networks and path signatures
Marc Sabate-Vidales, David Šiška, Lukasz Szpruch
Using a combination of recurrent neural networks and signature methods from the rough paths theory we design efficient algorithms for solving parametric families of path dependent…
A modified MSA for stochastic control problems
Bekzhan Kerimkulov, David Šiška, Łukasz Szpruch
The classical Method of Successive Approximations (MSA) is an iterative method for solving stochastic control problems and is derived from Pontryagin's optimality principle. It is…
Mean-Field Neural ODEs via Relaxed Optimal Control
Jean-François Jabir, David Šiška, Łukasz Szpruch
We develop a framework for the analysis of deep neural networks and neural ODE models that are trained with stochastic gradient algorithms. We do that by identifying the connection…
Weak Existence and Uniqueness for McKean-Vlasov SDEs with Common Noise
William R. P. Hammersley, David Šiška, Łukasz Szpruch
This paper concerns the McKean-Vlasov stochastic differential equation (SDE) with common noise. An appropriate definition of a weak solution to such an equation is developed. The i…
Exponential Convergence and stability of Howards's Policy Improvement Algorithm for Controlled Diffusions
B. Kerimkulov, D. Šiška, Ł. Szpruch
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howa…
McKean-Vlasov SDEs under Measure Dependent Lyapunov Conditions
William Hammersley, David Šiška, Lukasz Szpruch
We prove the existence of weak solutions to McKean-Vlasov SDEs defined on a domain with continuous and unbounded coefficients that satisfy Lyapunov type…