17 research outputs found
Online Regularization for High-Dimensional Dynamic Pricing Algorithms
We propose a novel \textit{online regularization} scheme for
revenue-maximization in high-dimensional dynamic pricing algorithms. The online
regularization scheme equips the proposed optimistic online regularized maximum
likelihood pricing (\texttt{OORMLP}) algorithm with three major advantages:
encode market noise knowledge into pricing process optimism; empower online
statistical learning with always-validity over all decision points; envelop
prediction error process with time-uniform non-asymptotic oracle inequalities.
This type of non-asymptotic inference results allows us to design safer and
more robust dynamic pricing algorithms in practice. In theory, the proposed
\texttt{OORMLP} algorithm exploits the sparsity structure of high-dimensional
models and obtains a logarithmic regret in a decision horizon. These
theoretical advances are made possible by proposing an optimistic online LASSO
procedure that resolves dynamic pricing problems at the \textit{process} level,
based on a novel use of non-asymptotic martingale concentration. In
experiments, we evaluate \texttt{OORMLP} in different synthetic pricing problem
settings and observe that \texttt{OORMLP} performs better than \texttt{RMLP}
proposed in \cite{javanmard2019dynamic}
A Survey of Tuning Parameter Selection for High-dimensional Regression
Penalized (or regularized) regression, as represented by Lasso and its
variants, has become a standard technique for analyzing high-dimensional data
when the number of variables substantially exceeds the sample size. The
performance of penalized regression relies crucially on the choice of the
tuning parameter, which determines the amount of regularization and hence the
sparsity level of the fitted model. The optimal choice of tuning parameter
depends on both the structure of the design matrix and the unknown random error
distribution (variance, tail behavior, etc). This article reviews the current
literature of tuning parameter selection for high-dimensional regression from
both theoretical and practical perspectives. We discuss various strategies that
choose the tuning parameter to achieve prediction accuracy or support recovery.
We also review several recently proposed methods for tuning-free
high-dimensional regression.Comment: 28 pages, 2 figure