In contextual dynamic pricing, a seller sequentially prices goods based on contextual information.

Since the provider's goal of maximizing revenue can only be achieved

In contextual dynamic pricing, a seller sequentially prices goods based on contextual information.

Since the provider's goal of maximizing revenue can only be achieved

Dynamic pricing, the practice of adjusting prices based on contextual factors, has gained significant attention due to its impact on revenue maximization. In this paper, we address the contextual dynamic pricing problem, which involves pricing decisions based on observable product features and customer characteristics. We propose a novel algorithm that achieves improved regret bounds while minimizing assumptions about the problem. Our algorithm discretizes the unknown noise distribution and combines the upper confidence bounds with a layered data partitioning technique to effectively regulate regret in each episode. These techniques effectively control the regret associated with pricing decisions, leading to the minimax optimality. Specifically, our algorithm achieves a regret upper bound of $\tilde{\mathcal{O}}(\rho_{\mathcal{V}}^{\frac{1}{3}}(\delta) T^{\frac{2}{3}})$, where $\rho_{\mathcal{V}}(\delta)$ represents the estimation error of the valuation function. Importantly, this bound matches the lower bound up to logarithmic terms, demonstrating the minimax optimality of our approach. Furthermore, our method extends beyond linear valuation models commonly used in dynamic pricing by considering general function spaces. We simplify the estimation process by reducing it to general offline regression oracles, making implementation more straightforward.

In contextual dynamic pricing, a seller sequentially prices goods based on contextual information. Buyers will purchase products only if the prices are below their valuations. The goal of the seller is to design a pricing strategy that collects as much revenue as possible. We focus on two different valuation models. The first assumes that valuations linearly depend on the context and are further distorted by noise. Under minor regularity assumptions, our algorithm achieves an optimal regret bound of $\tilde{\mathcal{O}}(T^{2/3})$, improving the existing results. The second model removes the linearity assumption, requiring only that the expected buyer valuation is $\beta$-H\"older in the context. For this model, our algorithm obtains a regret $\tilde{\mathcal{O}}(T^{d+2\beta/d+3\beta})$, where $d$ is the dimension of the context space.

Measuring the value of individual samples is critical for many data-driven tasks, e.g., the training of a deep learning model. Recent literature witnesses the substantial efforts in developing data valuation methods. The primary data valuation methodology is based on the Shapley value from game theory, and various methods are proposed along this path. {Even though Shapley value-based valuation has solid theoretical basis, it is entirely an experiment-based approach and no valuation model has been constructed so far.} In addition, current data valuation methods ignore the interpretability of the output values, despite an interptable data valuation method is of great helpful for applications such as data pricing. This study aims to answer an important question: is data valuation learnable and interpretable? A learned valuation model have several desirable merits such as fixed number of parameters and knowledge reusability. An intrepretable data valuation model can explain why a sample is valuable or invaluable. To this end, two new data value modeling frameworks are proposed, in which a multi-layer perception~(MLP) and a new regression tree are utilized as specific base models for model training and interpretability, respectively. Extensive experiments are conducted on benchmark datasets. {The experimental results provide a positive answer for the question.} Our study opens up a new technical path for the assessing of data values. Large data valuation models can be built across many different data-driven tasks, which can promote the widespread application of data valuation.

We study an online contextual dynamic pricing problem, where customers decide whether to purchase a product based on its features and price. We introduce a novel approach to modeling a customer's expected demand by incorporating feature-based price elasticity, which can be equivalently represented as a valuation with heteroscedastic noise. To solve the problem, we propose a computationally efficient algorithm called "Pricing with Perturbation (PwP)", which enjoys an $O(\sqrt{dT\log T})$ regret while allowing arbitrary adversarial input context sequences. We also prove a matching lower bound at $\Omega(\sqrt{dT})$ to show the optimality regarding $d$ and $T$ (up to $\log T$ factors). Our results shed light on the relationship between contextual elasticity and heteroscedastic valuation, providing insights for effective and practical pricing strategies.