We consider the problem of multi-product dynamic pricing with demand learning and propose a nonparametric online learning algorithm based on the simultaneous perturbation stochastic approximation (SPSA) method. The algorithm uses only two price experimentations at each iteration, regardless of problem dimension, and could be especially efficient for solving high-dimensional problems. Under moderate conditions, we prove that the price estimates converge in mean-squared error (MSE) to the optimal price. Furthermore, we show that by suitably choosing input parameters, our algorithm achieves an expected cumulative regret of order over periods, which is the best possible growth rate in the literature. The exact constants in the rate can be identified explicitly. We investigate the extensions of the algorithm to application scenarios characterized by non-stationary demand and inventory constraints. Simulation experiments reveal that our algorithm is effective for a range of test problems and performs favorably compared with a recently proposed alternative method for high-dimensional problems.

中文翻译：

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通过同时价格扰动进行需求学习的非参数多产品动态定价


我们考虑了需求学习的多产品动态定价问题，并提出了一种基于同时扰动随机逼近（SPSA）方法的非参数在线学习算法。无论问题维度如何，该算法在每次迭代时仅使用两次价格实验，并且对于解决高维度问题特别有效。在温和条件下，我们证明价格估计的均方误差 (MSE) 收敛于最优价格。此外，我们表明，通过适当选择输入参数，我们的算法实现了一段时间内订单的预期累积遗憾，这是文献中可能的最佳增长率。可以明确地识别速率中的确切常数。我们研究了该算法对以非平稳需求和库存约束为特征的应用场景的扩展。仿真实验表明，我们的算法对于一系列测试问题都是有效的，并且与最近提出的高维问题替代方法相比，其性能更佳。