(Oxford University)

Regularization of linear least squares problems is necessary in a variety of contexts. However, the optimal regularization parameter is usually unknown a priori and is often to be determined in an ad hoc manner, which may involve solving the problem for multiple regularization parameters. In this talk, we will discuss three randomized algorithms, building on the sketch-and-precondition framework in randomized numerical linear algebra (RNLA), to efficiently solve this set of problems. In particular, we consider preconditioners for a set of Tikhonov regularization problems to be solved iteratively. The first algorithm is a Cholesky-based algorithm employing a single sketch for multiple parameters; the second algorithm is SVD-based and improves the computational complexity by requiring a single decomposition of the sketch for multiple parameters. Finally, we introduce an algorithm capable of exploiting low-rank structure (specifically, low statistical dimension), requiring a single sketch and a single decomposition to compute multiple preconditioners with low-rank structure. This algorithm avoids the Gram matrix, resulting in improved stability as compared to related work.

Time-optimal control can be used to improve driving efficiency for autonomous
vehicles and it enables us explore vehicle and driver behaviour in extreme
situations. Due to the computational cost and limited scope of classical
optimal control methods we have seen new interest in applying reinforcement
learning algorithms to autonomous driving tasks.
In this talk we present methods for translating time-optimal vehicle control
problems into reinforcement learning environments. For this translation we
construct a sequence of environments, starting from the closest representation
of our optimisation problem, and gradually improve the environments reward
signal and feature quality. The trained agents we obtain are able to generalise
across different race tracks and obtain near optimal solutions, which can then
be used to speed up the solution of classical time-optimal control problems.

Many problems in engineering can be understood as controlling the bifurcation structure of a given device. For example, one may wish to delay the onset of instability, or bring forward a bifurcation to enable rapid switching between states. In this talk, we will describe a numerical technique for controlling the bifurcation diagram of a nonlinear partial differential equation by varying the shape of the domain or a parameter in the equation. Our aim is to delay or advance a given branch point to a target parameter value. The algorithm consists of solving an optimization problem constrained by an augmented system of equations that characterize the location of the branch points. The flexibility and robustness of the method also allow us to advance or delay a Hopf bifurcation to a target value of the bifurcation parameter, as well as controlling the oscillation frequency. We will apply this technique on systems arising from biology, fluid dynamics, and engineering, such as the FitzHugh-Nagumo model, Navier-Stokes, and hyperelasticity equations.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome