Improved Algorithms for Contextual Dynamic Pricing
This work improves algorithms for sellers in e-commerce or online markets, though it is incremental as it builds on existing models with specific theoretical gains.
The paper tackles the problem of designing pricing strategies in contextual dynamic pricing to maximize revenue, achieving an optimal regret bound of \tilde{\mathcal{O}}(T^{2/3}) for a linear valuation model and \tilde{\mathcal{O}}(T^{d+2β/d+3β}) for a non-linear model.
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 $β$-Hölder in the context. For this model, our algorithm obtains a regret $\tilde{\mathcal{O}}(T^{d+2β/d+3β})$, where $d$ is the dimension of the context space.