Bidding optimization is one of the most important problems in online advertising. Auto-bidding tools are designed to address this problem and are offered by most advertising platforms for advertisers to allocate their budgets. In this work, we present a Knowledge Graph-enriched Multi-Agent Reinforcement Learning Advertising Framework (KRAF). It combines Knowledge Graph (KG) techniques with a Multi-Agent Reinforcement Learning (MARL) algorithm for bidding optimization with the goal of maximizing advertisers' return on ad spend (ROAS) and user-ad interactions, which correlates to the ad platform revenue. In addition, this proposal is flexible enough to support different levels of user privacy and the advent of new advertising markets with more heterogeneous data. In contrast to most of the current advertising platforms that are based on click-through rate models using a fixed input format and rely on user tracking, KRAF integrates the heterogeneous available data (e.g., contextual features, interest-based attributes, information about ads) as graph nodes to generate their dense representation (embeddings). Then, our MARL algorithm leverages the embeddings of the entities to learn efficient budget allocation strategies. To that end, we propose a novel coordination strategy based on a mean-field style to coordinate the learning agents and avoid the curse of dimensionality when the number of agents grows. Our proposal is evaluated on three real-world datasets to assess its performance and the contribution of each of its components, outperforming several baseline methods in terms of ROAS and number of ad clicks.

We investigate quantum circuits for graph representation learning, and propose equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured data. Conceptually, EQGCs serve as a unifying framework for quantum graph representation learning, allowing us to define several interesting subclasses which subsume existing proposals. In terms of the representation power, we prove that the studied subclasses of EQGCs are universal approximators for functions over the bounded graph domain. This theoretical perspective on quantum graph machine learning methods opens many directions for further work, and could lead to models with capabilities beyond those of classical approaches. We empirically verify the expressive power of EQGCs through a dedicated experiment on synthetic data, and additionally observe that the performance of EQGCs scales well with the depth of the model and does not suffer from barren plateu issues.