We consider a novel dynamic pricing and learning setting where in addition to setting prices of products in sequential rounds, the seller also ex-ante commits to 'advertising schemes'. That is, in the beginning of each round the seller can decide what kind of signal they will provide to the buyer about the product's quality upon realization. Using the popular Bayesian persuasion framework to model the effect of these signals on the buyers' valuation and purchase responses, we formulate the problem of finding an optimal design of the advertising scheme along with a pricing scheme that maximizes the seller's expected revenue. Without any apriori knowledge of the buyers' demand function, our goal is to design an online algorithm that can use past purchase responses to adaptively learn the optimal pricing and advertising strategy. We study the regret of the algorithm when compared to the optimal clairvoyant price and advertising scheme. Our main result is a computationally efficient online algorithm that achieves an $O(T^{2/3}(m\log T)^{1/3})$ regret bound when the valuation function is linear in the product quality. Here $m$ is the cardinality of the discrete product quality domain and $T$ is the time horizon. This result requires some natural monotonicity and Lipschitz assumptions on the valuation function, but no Lipschitz or smoothness assumption on the buyers' demand function. For constant $m$, our result matches the regret lower bound for dynamic pricing within logarithmic factors, which is a special case of our problem. We also obtain several improved results for the widely considered special case of additive valuations, including an $\tilde{O}(T^{2/3})$ regret bound independent of $m$ when $m\le T^{1/3}$.

翻译：我们考虑一种新颖的动态定价与学习场景：卖家在序贯轮次中设定产品价格的同时，还需事前承诺“广告方案”。即每轮开始时，卖家可决定在产品质量实现后向买家提供何种类型的信号。利用流行的贝叶斯说服框架建模这些信号对买家估值及购买行为的影响，我们提出了一个联合优化广告方案设计与定价方案以最大化卖家期望收益的问题。在缺乏买家需求函数先验知识的情况下，我们的目标是设计一种能利用历史购买反馈自适应学习最优定价与广告策略的在线算法。我们研究了该算法与最优预知定价及广告方案相比的遗憾值。主要成果是：当估值函数关于产品质量线性时，我们提出了一种计算高效的在线算法，实现了$O(T^{2/3}(m\log T)^{1/3})$的遗憾界，其中$m$为离散产品质量域基数，$T$为时间范围。该结果要求估值函数满足自然的单调性和Lipschitz假设，但无需对买家需求函数施加Lipschitz或光滑性假设。当$m$为常数时，我们的结果在动态定价（本问题特例）的遗憾下界上仅差对数因子。针对广泛研究的加性估值特例，我们进一步获得了若干改进结果：当$m\le T^{1/3}$时，实现了与$m$无关的$\tilde{O}(T^{2/3})$遗憾界。