Improved Algorithms for Contextual Dynamic Pricing
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929712221126656 |
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| author | Tullii, Matilde Gaucher, Solenne Merlis, Nadav Perchet, Vianney |
| author_facet | Tullii, Matilde Gaucher, Solenne Merlis, Nadav Perchet, Vianney |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved Algorithms for Contextual Dynamic Pricing Tullii, Matilde Gaucher, Solenne Merlis, Nadav Perchet, Vianney Machine Learning Data Structures and Algorithms Computer Science and Game Theory 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. |
| title | Improved Algorithms for Contextual Dynamic Pricing |
| topic | Machine Learning Data Structures and Algorithms Computer Science and Game Theory |
| url | https://arxiv.org/abs/2406.11316 |