Scalable Neural Incentive Design with Parameterized Mean-Field Approximation

Designing incentives for a multi-agent system to induce a desirable Nash equilibrium is both a crucial and challenging problem appearing in many decision-making domains, especially for a large number of agents $N$. Under the exchangeability assumption, we formalize this incentive design (ID) problem as a parameterized mean-field game (PMFG), aiming to reduce complexity via an infinite-population limit. We first show that when dynamics and rewards are Lipschitz, the finite-$N$ ID objective is approximated by the PMFG at rate $\mathscr{O}(\frac{1}{\sqrt{N}})$. Moreover, beyond the Lipschitz-continuous setting, we prove the same $\mathscr{O}(\frac{1}{\sqrt{N}})$ decay for the important special case of sequential auctions, despite discontinuities in dynamics, through a tailored auction-specific analysis. Built on our novel approximation results, we further introduce our Adjoint Mean-Field Incentive Design (AMID) algorithm, which uses explicit differentiation of iterated equilibrium operators to compute gradients efficiently. By uniting approximation bounds with optimization guarantees, AMID delivers a powerful, scalable algorithmic tool for many-agent (large $N$) ID. Across diverse auction settings, the proposed AMID method substantially increases revenue over first-price formats and outperforms existing benchmark methods.

An LLM-based Recommender System Environment

Reinforcement learning (RL) has gained popularity in the realm of recommender systems due to its ability to optimize long-term rewards and guide users in discovering relevant content. However, the successful implementation of RL in recommender systems is challenging because of several factors, including the limited availability of online data for training on-policy methods. This scarcity requires expensive human interaction for online model training. Furthermore, the development of effective evaluation frameworks that accurately reflect the quality of models remains a fundamental challenge in recommender systems. To address these challenges, we propose a comprehensive framework for synthetic environments that simulate human behavior by harnessing the capabilities of large language models (LLMs). We complement our framework with in-depth ablation studies and demonstrate its effectiveness with experiments on movie and book recommendations. By utilizing LLMs as synthetic users, this work introduces a modular and novel framework for training RL-based recommender systems. The software, including the RL environment, is publicly available.