Title: Optimisation with occasionally accurate data
Speaker: Coralia Cartis
Affiliation: Mathematical Institute – Oxford and Balliol College
Location: Huxley building
Time: 2:00pm (1 hour)
Abstract. We present global rates of convergence for a general class of methods for nonconvex smooth optimization that include linesearch, trust-region and regularisation strategies, but that allow inaccurate problem information. Namely, we assume the local (first- or second-order) models of our function are only sufficiently accurate with a certain probability, and they can be arbitrarily poor otherwise. This framework subsumes certain stochastic gradient analyses and derivative-free techniques based on random sampling of function values. It can also be viewed as a robustness assessment of deterministic methods and their resilience to inaccurate derivative computation such as due to processor failure in a distribute framework. We show that in terms of the order of the accuracy, the evaluation complexity of such methods is the same as their counterparts that use deterministic accurate models; the use of probabilistic models only increases the complexity by a constant, which depends on the probability of the models being good. Time permitting, we also discuss the case of inaccurate, probabilistic function value information, that arises in stochastic optimization. This work is joint with Katya Scheinberg (Lehigh University, USA).
About the speaker. Coralia Cartis (BSc Mathematics, Babesh-Bolyai University, Romania; PhD Mathematics, University of Cambridge (2005)) has joined the Mathematical Institute at Oxford and Balliol College in 2013 as Associate Professor in Numerical Optimization. Previously, she worked as a research scientist at Rutherford Appleton Laboratory and as a postdoctoral researcher at Oxford University. Between 2007-2013, she was a (permanent) lecturer and senior lecturer in the School of Mathematics, University of Edinburgh. Her research interests address the development, analysis and implementation of algorithms for linear and nonlinear non-convex optimization problems, suitable for large-scale problems. A particular focus of her recent research has been the complexity analysis/global rates of convergence of nonconvex optimization algorithms. Some of her methods have been included in GALAHAD optimization software library. She has also worked on applications of optimization in compressed sensing, signal processing and for parameter estimation in climate modelling.