We consider a firm that sells products over $T$ periods without knowing the
demand function. The firm sequentially sets prices to earn revenue and to learn
the underlying demand function simultaneously. A natural heuristic for this
problem, commonly used in practice, is greedy iterative least squares (GILS).
At each time period, GILS estimates the demand as a linear function of the
price by applying least squares to the set of prior prices and realized
demands. Then a price that maximizes the revenue, given the estimated demand
function, is used for the next time period. The performance is measured by the
regret, which is the expected revenue loss from the optimal (oracle) pricing
policy when the demand function is known. Recently, den Boer and Zwart (2014)
and Keskin and Zeevi (2014) demonstrated that GILS is sub-optimal. They
introduced algorithms which integrate forced price dispersion with GILS and
achieve asymptotically optimal performance.
In this paper, we consider this dynamic pricing problem in a data-rich
environment. In particular, we assume that the firm knows the expected demand
under a particular price from historical data, and in each period, before
setting the price, the firm has access to extra information (demand covariates)
which may be predictive of the demand. We prove that in this setting GILS
achieves asymptotically optimal regret of order $\log(T)$. We also show the
following surprising result: in the original dynamic pricing problem of den
Boer and Zwart (2014) and Keskin and Zeevi (2014), inclusion of any set of
covariates in GILS as potential demand covariates (even though they could carry
no information) would make GILS asymptotically optimal. We validate our results
via extensive numerical simulations on synthetic and real data sets.

研究了带有需求协变量的动态定价问题，证明了 GILS 取得了渐进最优表现，即使将没有信息的任何一组协变量包含在 GILS 中也能使其渐进最优。