Learning to Bid in Repeated Second-Price Auctions with Dynamic Values and Aggregated Feedback

2026-05-27

AI Summary

This work addresses the problem of learning optimal bidding strategies in repeated second-price auctions with dynamic valuations, where a bidder’s current value depends on the time elapsed since their last win and only aggregated feedback is observable. The authors propose a learning algorithm that integrates plug-in estimation with a differential equation characterizing the optimal bidding policy, effectively balancing immediate rewards against future value impacts without requiring explicit exploration or randomization. For the first time in this setting, the theoretical analysis establishes near-optimal regret bounds: $\widetilde{O}(\log N)$ for piecewise linear valuation functions and $\widetilde{O}(N^{1/3})$ for smooth valuations. Numerical experiments further demonstrate the algorithm’s strong empirical performance in dynamic environments.

Abstract

We study the problem of learning to bid when the bidder's value is dynamic, i.e., when the current value depends on past outcomes. Specifically, we consider a bidder participating in repeated second-price auctions whose value depends on the time elapsed since their last successful bid, with auctions arriving in continuous time and only aggregated feedback revealed at the end of the horizon. Such a bidder must (1) balance the immediate benefit of winning the current auction against its impact on future values and (2) learn unknown environmental parameters. We derive regret bounds for a class of learning methods that combine plug-in estimators with a differential-equation characterization of the optimal policy, and show that a specific confidence bound algorithm learns the optimal policy with a near optimal regret of $\widetilde{O}(\log N)$ for piecewise linear primitives, and $\widetilde{O}(N^{1/3})$ for general, smooth primitives, achieving these regrets without explicit randomization. These theoretical results are supported by numerical experiments.

Problem

• dynamic values
• second-price auctions
• aggregated feedback
• learning to bid
• repeated auctions

Innovation

• dynamic values
• aggregated feedback
• second-price auctions
• regret minimization
• confidence bound algorithm