Online advertising has become one of the most successful business models of the internet era. Impression opportunities are typically allocated through real-time auctions, where advertisers bid to secure advertisement slots. Deciding the best bid for an impression opportunity is challenging, due to the stochastic nature of user behavior and the variability of advertisement traffic over time. In this work, we propose a framework for training auto-bidding agents in multi-slot second-price auctions to maximize acquisitions (e.g., clicks, conversions) while adhering to budget and cost-per-acquisition (CPA) constraints. We exploit the insight that, after an advertisement campaign concludes, determining the optimal bids for each impression opportunity can be framed as a multiple-choice knapsack problem (MCKP) with a nonlinear objective. We propose an "oracle" algorithm that identifies a near-optimal combination of impression opportunities and advertisement slots, considering both past and future advertisement traffic data. This oracle solution serves as a training target for a student network which bids having access only to real-time information, a method we term Oracle Imitation Learning (OIL). Through numerical experiments, we demonstrate that OIL achieves superior performance compared to both online and offline reinforcement learning algorithms, offering improved sample efficiency. Notably, OIL shifts the complexity of training auto-bidding agents from crafting sophisticated learning algorithms to solving a nonlinear constrained optimization problem efficiently.

In online advertising, auto-bidding has become an essential tool for advertisers to optimize their preferred ad performance metrics by simply expressing the high-level campaign objectives and constraints. Previous works consider the design of auto-bidding agents from the single-agent view without modeling the mutual influence between agents. In this paper, we instead consider this problem from the perspective of a distributed multi-agent system, and propose a general Multi-Agent reinforcement learning framework for Auto-Bidding, namely MAAB, to learn the auto-bidding strategies. First, we investigate the competition and cooperation relation among auto-bidding agents, and propose temperature-regularized credit assignment for establishing a mixed cooperative-competitive paradigm. By carefully making a competition and cooperation trade-off among the agents, we can reach an equilibrium state that guarantees not only individual advertiser's utility but also the system performance (social welfare). Second, due to the observed collusion behaviors of bidding low prices underlying the cooperation, we further propose bar agents to set a personalized bidding bar for each agent, and then to alleviate the degradation of revenue. Third, to deploy MAAB to the large-scale advertising system with millions of advertisers, we propose a mean-field approach. By grouping advertisers with the same objective as a mean auto-bidding agent, the interactions among advertisers are greatly simplified, making it practical to train MAAB efficiently. Extensive experiments on the offline industrial dataset and Alibaba advertising platform demonstrate that our approach outperforms several baseline methods in terms of social welfare and guarantees the ad platform's revenue.