  Devising dynamic pricing policy with always valid online statistical learning
procedure is an important and as yet unresolved problem. Most existing dynamic
pricing policy, which focus on the faithfulness of adopted customer choice
models, exhibit a limited capability for adapting the online uncertainty of
learned statistical model during pricing process. In this paper, we propose a
novel approach for designing dynamic pricing policy based regularized online
statistical learning with theoretical guarantees. The new approach overcomes
the challenge of continuous monitoring of online Lasso procedure and possesses
several appealing properties. In particular, we make the decisive observation
that the always-validity of pricing decisions builds and thrives on the online
regularization scheme. Our proposed online regularization scheme equips the
proposed optimistic online regularized maximum likelihood pricing (OORMLP)
pricing policy 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 more sample-efficient and robust dynamic
pricing algorithms in practice. In theory, the proposed OORMLP algorithm
exploits the sparsity structure of high-dimensional models and secures 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 process level, based on a novel use of
non-asymptotic martingale concentration. In experiments, we evaluate OORMLP in
different synthetic and real pricing problem settings, and demonstrate that
OORMLP advances the state-of-the-art methods.
