Gradient-based stochastic optimization under chance constraints

Speaker: Felisa Vazquez-Abad (City University New York) Title: Gradient-based stochastic optimization under chance constraints Summary: Optimization under probability (or chance) constraints is known to be a challenging problem. Generalizing our preliminary results for one-dimensional problems, we study here the general model where the constraints may depend on a stochastic process parametrized by the control variable of the optimization problem. The distribution of the underlying process is not known and only samples of it are available, so the optimization algorithm must be built for streaming data. Instead of formulating the constraints as probability constraints, we use the alternative form in terms of quantile constraints, which is known to yield more efficient gradient-based algorithms. Common methods for solving such problems make use of advanced statistical functional estimation of the distribution function directly, using approximations that are provably convergent. Instead, we propose to build statistical estimators for both the quantile and its derivative, in order to drive the optimization procedure. We discuss the computational challenges: because quantiles are commonly estimated using the complete history of samples obtained, they require an undesirable super-linear running time and unbounded memory. We discuss various approaches to overcome this difficulty. Biography: Felisa Vázquez-Abad is Professor of Computer Science at City University New York (CUNY). She is interested in stochastic optimization and computer simulation of complex systems under uncertainty, primarily to build efficient self-regulated learning systems. She has applied novel techniques for simulation and optimization in telecommunications, transportation, medical and biological models, finance and insurance, and has a particular interest in real life problems. Felisa co-authored a US patent for an optical network switch and was research consultant to the Melbourne Airport. With over 100 research papers published, she is also the author of the upcoming textbook “Optimization and Learning via Stochastic Gradient Search”, being published by Princeton University Press in 2025. Felisa is committed to actively participating in events and programs that encourage women and minority students to succeed in Computer Sciences.