Bandit Profit-maximization for Targeted Marketing
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arXiv
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| Format: | Preprint |
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2024
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| author | Huh, Joon Suk Vitercik, Ellen Kandasamy, Kirthevasan |
| author_facet | Huh, Joon Suk Vitercik, Ellen Kandasamy, Kirthevasan |
| contents | We study a sequential profit-maximization problem, optimizing for both price and ancillary variables like marketing expenditures. Specifically, we aim to maximize profit over an arbitrary sequence of multiple demand curves, each dependent on a distinct ancillary variable, but sharing the same price. A prototypical example is targeted marketing, where a firm (seller) wishes to sell a product over multiple markets. The firm may invest different marketing expenditures for different markets to optimize customer acquisition, but must maintain the same price across all markets. Moreover, markets may have heterogeneous demand curves, each responding to prices and marketing expenditures differently. The firm's objective is to maximize its gross profit, the total revenue minus marketing costs.
Our results are near-optimal algorithms for this class of problems in an adversarial bandit setting, where demand curves are arbitrary non-adaptive sequences, and the firm observes only noisy evaluations of chosen points on the demand curves. For $n$ demand curves (markets), we prove a regret upper bound of $\tilde{O}(nT^{3/4})$ and a lower bound of $Ω((nT)^{3/4})$ for monotonic demand curves, and a regret bound of $\tildeΘ(nT^{2/3})$ for demands curves that are monotonic in price and concave in the ancillary variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bandit Profit-maximization for Targeted Marketing Huh, Joon Suk Vitercik, Ellen Kandasamy, Kirthevasan Machine Learning Computer Science and Game Theory General Economics Economics General Finance We study a sequential profit-maximization problem, optimizing for both price and ancillary variables like marketing expenditures. Specifically, we aim to maximize profit over an arbitrary sequence of multiple demand curves, each dependent on a distinct ancillary variable, but sharing the same price. A prototypical example is targeted marketing, where a firm (seller) wishes to sell a product over multiple markets. The firm may invest different marketing expenditures for different markets to optimize customer acquisition, but must maintain the same price across all markets. Moreover, markets may have heterogeneous demand curves, each responding to prices and marketing expenditures differently. The firm's objective is to maximize its gross profit, the total revenue minus marketing costs. Our results are near-optimal algorithms for this class of problems in an adversarial bandit setting, where demand curves are arbitrary non-adaptive sequences, and the firm observes only noisy evaluations of chosen points on the demand curves. For $n$ demand curves (markets), we prove a regret upper bound of $\tilde{O}(nT^{3/4})$ and a lower bound of $Ω((nT)^{3/4})$ for monotonic demand curves, and a regret bound of $\tildeΘ(nT^{2/3})$ for demands curves that are monotonic in price and concave in the ancillary variables. |
| title | Bandit Profit-maximization for Targeted Marketing |
| topic | Machine Learning Computer Science and Game Theory General Economics Economics General Finance |
| url | https://arxiv.org/abs/2403.01361 |