Learning to Bid in Discriminatory Auctions with Budget Constraints
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Computer Science > Machine Learning
Title:Learning to Bid in Discriminatory Auctions with Budget Constraints
Abstract:We study repeated bidding in multi-unit discriminatory (pay-as-bid) auctions for a single bidder with per-round utility equal to value minus $\alpha$ times payment, where $\alpha\in[0,1]$ is a cost-of-capital parameter. The bidder aims to maximize cumulative utility over $T$ rounds subject to a total budget $B$. The problem is challenging even without budgets: the action space is exponential in $M$, the maximum demand of the bidder and the valuation vector (context) varies over time. Exploiting a decomposition of utility across units, we develop polynomial-time learning algorithms based on shortest paths in a directed acyclic graph, obtaining sublinear regret under both full-information and bandit feedback. In the bandit setting, the regret is independent of the number of contexts due to complete cross-learning: observing the utility of the chosen action under the realized context reveals the utility for the same action under all counterfactual contexts. With budget constraints, when the average normalized per-round budget $\rho=\frac{B}{MT}<1$, we design a coupled primal-dual algorithm in which the DAG-based procedure uses dual-adjusted edge weights for primal updates, while online gradient descent updates the dual variable, yielding $\rho$-approximate sublinear regret. Finally, we give implementations whose per-round time and space are independent of the number of contexts, enabling scalability to large or even infinite context spaces.
| Comments: | 54 pages, 1 figure. Appeared at AISTATS 2026 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2606.29252 [cs.LG] |
| (or arXiv:2606.29252v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.29252
arXiv-issued DOI via DataCite (pending registration)
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