Researchers have introduced a model for budgeted auctions where the spacing of wins over time is crucial, especially in settings like online retail, compute services, and advertising campaigns.
The model considers how the value of a win diminishes with time, leading to the importance of evenly spaced wins for a given number of total wins.
The research extends to cases where not all wins result in actual gains, and the conversion probability depends on context.
The objective is to optimize and evenly distribute conversions over time rather than just wins.
The study focuses on optimal strategies in second-price auctions and provides learning algorithms for bidders to minimize regret in a Bayesian online setting.
An online learning algorithm is introduced, achieving approximately square root regret in terms of time complexity.
The algorithm operates by learning a bidding policy based on the context and system state, such as the time elapsed since the last win or conversion.
State-independent strategies are found to incur linear regret even without uncertainty in conversions.
Certain state-independent strategies can achieve a near-optimal reward approximation despite still having linear regret.