Dynamic Pricing with Adversarially-Censored Demands

We study an online dynamic pricing problem where the potential demand at each time period $t=1,2,\ldots, T$ is stochastic and dependent on the price. However, a perishable inventory is imposed at the beginning of each time $t$, censoring the potential demand if it exceeds the inventory level. To address this problem, we introduce a pricing algorithm based on the optimistic estimates of derivatives. We show that our algorithm achieves $\tilde{O}(\sqrt{T})$ optimal regret even with adversarial inventory series. Our findings advance the state-of-the-art in online decision-making problems with censored feedback, offering a theoretically optimal solution against adversarial observations.