  In contextual dynamic pricing, a seller sequentially prices goods based on
contextual information. Buyers will purchase products only if the prices are
below their valuations. The goal of the seller is to design a pricing strategy
that collects as much revenue as possible. We focus on two different valuation
models. The first assumes that valuations linearly depend on the context and
are further distorted by noise. Under minor regularity assumptions, our
algorithm achieves an optimal regret bound of $\tilde{\mathcal{O}}(T^{2/3})$,
improving the existing results. The second model removes the linearity
assumption, requiring only that the expected buyer valuation is
$\beta$-H\"older in the context. For this model, our algorithm obtains a regret
$\tilde{\mathcal{O}}(T^{d+2\beta/d+3\beta})$, where $d$ is the dimension of the
context space.
