4 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}