  In feature-based dynamic pricing, a seller sets appropriate prices for a
sequence of products (described by feature vectors) on the fly by learning from
the binary outcomes of previous sales sessions ("Sold" if valuation $\geq$
price, and "Not Sold" otherwise). Existing works either assume noiseless linear
valuation or precisely-known noise distribution, which limits the applicability
of those algorithms in practice when these assumptions are hard to verify. In
this work, we study two more agnostic models: (a) a "linear policy" problem
where we aim at competing with the best linear pricing policy while making no
assumptions on the data, and (b) a "linear noisy valuation" problem where the
random valuation is linear plus an unknown and assumption-free noise. For the
former model, we show a $\tilde{\Theta}(d^{\frac13}T^{\frac23})$ minimax regret
up to logarithmic factors. For the latter model, we present an algorithm that
achieves an $\tilde{O}(T^{\frac34})$ regret, and improve the best-known lower
bound from $\Omega(T^{\frac35})$ to $\tilde{\Omega}(T^{\frac23})$. These
results demonstrate that no-regret learning is possible for feature-based
dynamic pricing under weak assumptions, but also reveal a disappointing fact
that the seemingly richer pricing feedback is not significantly more useful
than the bandit-feedback in regret reduction.
