Title

Convergence of the modified MSA and its natural gradient flows

Abstract

The method of successive approximation is an iterative algorithm for solving (stochastic) control problems based on the Pontryagin optimality principle. We show how regularised version can be shown to converge in Euclidean and Wasserstein setting. In fact the MSA can be seen as discretisation of an appropriate gradient flow. We will show that under appropriate conditions a) the gradient flow converges and b) regularised MSA converges to the gradient flow as the intensity of the regularisation is increased. This is joint work with Bekzhan Kerimkulov and Lukasz Szpruch.

Speaker Biography

David Siska is a reader at the School of Mathematics, University of Edinburgh, where he received his PhD in 2007. His main research interests are in stochastic control theory, reinforcement learning and applications in industry. He has spent his career more-or-less evenly split between academia and industry, most recently helping develop software for Vega protocol: a decentralised derivatives exchange.

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