Learning to Bid in Non-Stationary Repeated First-Price Auctions
This addresses the challenge for advertisers in digital markets like Google's first-price auctions, where non-stationary opponent behaviors make bidding complex, though it is incremental as it builds on prior dynamic regret frameworks.
The paper tackles the problem of learning optimal bidding strategies in non-stationary first-price auctions, where opponents' behaviors change over time, by introducing regularity metrics to quantify non-stationarity and developing an Optimistic Mirror Descent method that achieves minimax-optimal dynamic regret rates, with synthetic validation showing it outperforms existing methods.
First-price auctions have recently gained significant traction in digital advertising markets, exemplified by Google's transition from second-price to first-price auctions. Unlike in second-price auctions, where bidding one's private valuation is a dominant strategy, determining an optimal bidding strategy in first-price auctions is more complex. From a learning perspective, the learner (a specific bidder) can interact with the environment (other bidders, i.e., opponents) sequentially to infer their behaviors. Existing research often assumes specific environmental conditions and benchmarks performance against the best fixed policy (static benchmark). While this approach ensures strong learning guarantees, the static benchmark can deviate significantly from the optimal strategy in environments with even mild non-stationarity. To address such scenarios, a dynamic benchmark--representing the sum of the highest achievable rewards at each time step--offers a more suitable objective. However, achieving no-regret learning with respect to the dynamic benchmark requires additional constraints. By inspecting reward functions in online first-price auctions, we introduce two metrics to quantify the regularity of the sequence of opponents' highest bids, which serve as measures of non-stationarity. We provide a minimax-optimal characterization of the dynamic regret for the class of sequences of opponents' highest bids that satisfy either of these regularity constraints. Our main technical tool is the Optimistic Mirror Descent (OMD) framework with a novel optimism configuration, which is well-suited for achieving minimax-optimal dynamic regret rates in this context. We then use synthetic datasets to validate our theoretical guarantees and demonstrate that our methods outperform existing ones.