Session: Robustness in learning from data
Chair: Jun-ya Gotoh
Cluster: Optimization For Data Science
Talk 1: The exploration-exploitation-robustness tradeoff for multi-period data driven problems with learning
Speaker: Andrew Lim
Abstract: We study the tradeoff between exploration, exploration and robustness in the setting of a robust optimal stopping problem with learning. We show that a decision maker (DM) concerned about model uncertainty explores less, even though additional data reduces model uncertainty, because the “learning shock” when it is collected increases the sensitivity of the expected reward to worst-case deviations from the nominal model. We also show that this “conservatism” can be fixed by introducing hedging instruments that offset the learning shocks. (With Thaisiri Watewai (Chulalongkorn University) and Anas Abdelhakmi (National University of Singapore)).
Talk 2: Biased Mean Quadrangle and Applications
Speaker: Anton Malandii
Abstract: The \emph{Risk Quadrangle} (RQ) is a framework that bridges risk management, optimization, and statistical estimation. Each RQ consists of four stochastic functionals—error, regret, risk, and deviation—linked together by a statistic. This paper introduces a new quadrangle, the \emph{biased mean quadrangle}, and studies its mathematical properties. In this quadrangle, the risk can be applied for risk management, while the error, referred to as the \emph{superexpectation error}, can be used for regression analysis. The statistic in this quadrangle is the mean value, adjusted by a real-valued parameter known as bias. Consequently, the linear regression within this quadrangle can be used to estimate the conditional biased mean. We demonstrate the extended regularity of this quadrangle and establish its connection to the quantile quadrangle. In particular, we prove the equivalence between biased mean and quantile regressions. Notably, when the bias is set to zero, the linear biased mean regression becomes equivalent to ordinary least squares (OLS) regression under standard statistical assumptions. Furthermore, the minimization of the superexpectation error reduces to a linear programming (LP) problem, allowing OLS to be reformulated as an LP. We provide numerical experiments that support these theoretical findings.
Talk 3: Convex vs. Nonconvex Regularization Terms---A Comparative Study of Regression B-Splines with Knot and Spline Selection
Speaker: Jun-ya Gotoh
Abstract: Robustness is important in learning from data. From the perspective of mathematical optimization, there are two contrasting approaches: robust optimization, which emphasizes worst-case samples, and robust regression, which reduces/ignores the contribution of unfavorable samples. The former tends to be realized by convex regularization, and the latter by non-convex regularization. On the other hand, l1 regularization, which is popular because it often leads to sparsity of the solution or associated quantities, is somewhere in between, but is closer to robust optimization in that it preserves convexity. In this presentation, we will compare convex and non-convex regularizations using knot selection and spline selection in multivariate B-spline regression as an example and discuss the choice between the two regularization methods from a practical per
