Zhijian Duan

Zhijian Duan, Yunxuan Ma, Xiaotie Deng

Recently, remarkable progress has been made by approximating Nash equilibrium (NE), correlated equilibrium (CE), and coarse correlated equilibrium (CCE) through function approximation that trains a neural network to predict equilibria from game representations. Furthermore, equivariant architectures are widely adopted in designing such equilibrium approximators in normal-form games. In this paper, we theoretically characterize benefits and limitations of equivariant equilibrium approximators. For the benefits, we show that they enjoy better generalizability than general ones and can achieve better approximations when the payoff distribution is permutation-invariant. For the limitations, we discuss their drawbacks in terms of equilibrium selection and social welfare. Together, our results help to understand the role of equivariance in equilibrium approximators.

Yunxuan Ma, Siqiang Wang, Zhijian Duan et al.

This paper introduces TEDI (Truthful, Expressive, and Dimension-Insensitive approach), a discretization-free algorithm to learn truthful and utility-maximizing mechanisms. Existing learning-based approaches often rely on discretization of outcome spaces to ensure truthfulness, which leads to inefficiency with increasing problem size. To address this limitation, we formalize the concept of pricing rules, defined as functions that map outcomes to prices. Based on this concept, we propose a novel menu mechanism, which can be equivalent to a truthful direct mechanism under specific conditions. The core idea of TEDI lies in its parameterization of pricing rules using Partial GroupMax Network, a new network architecture designed to universally approximate partial convex functions. To learn optimal pricing rules, we develop novel training techniques, including covariance trick and continuous sampling, to derive unbiased gradient estimators compatible with first-order optimization. Theoretical analysis establishes that TEDI guarantees truthfulness, full expressiveness, and dimension-insensitivity. Experimental evaluation in the studied auction setting demonstrates that TEDI achieves strong performance, competitive with or exceeding state-of-the-art methods. This work presents the first approaches to learn truthful mechanisms without outcome discretization, thereby enhancing algorithmic efficiency. The proposed concepts, network architecture, and learning techniques might offer potential value and provide new insights for automated mechanism design and differentiable economics.

Zhijian Duan, Haoran Sun, Yurong Chen et al.

Automated auction design aims to find empirically high-revenue mechanisms through machine learning. Existing works on multi item auction scenarios can be roughly divided into RegretNet-like and affine maximizer auctions (AMAs) approaches. However, the former cannot strictly ensure dominant strategy incentive compatibility (DSIC), while the latter faces scalability issue due to the large number of allocation candidates. To address these limitations, we propose AMenuNet, a scalable neural network that constructs the AMA parameters (even including the allocation menu) from bidder and item representations. AMenuNet is always DSIC and individually rational (IR) due to the properties of AMAs, and it enhances scalability by generating candidate allocations through a neural network. Additionally, AMenuNet is permutation equivariant, and its number of parameters is independent of auction scale. We conduct extensive experiments to demonstrate that AMenuNet outperforms strong baselines in both contextual and non-contextual multi-item auctions, scales well to larger auctions, generalizes well to different settings, and identifies useful deterministic allocations. Overall, our proposed approach offers an effective solution to automated DSIC auction design, with improved scalability and strong revenue performance in various settings.

Zhijian Duan, Jingwu Tang, Yutong Yin et al.

One of the central problems in auction design is developing an incentive-compatible mechanism that maximizes the auctioneer's expected revenue. While theoretical approaches have encountered bottlenecks in multi-item auctions, recently, there has been much progress on finding the optimal mechanism through deep learning. However, these works either focus on a fixed set of bidders and items, or restrict the auction to be symmetric. In this work, we overcome such limitations by factoring \emph{public} contextual information of bidders and items into the auction learning framework. We propose $\mathtt{CITransNet}$, a context-integrated transformer-based neural network for optimal auction design, which maintains permutation-equivariance over bids and contexts while being able to find asymmetric solutions. We show by extensive experiments that $\mathtt{CITransNet}$ can recover the known optimal solutions in single-item settings, outperform strong baselines in multi-item auctions, and generalize well to cases other than those in training.

Zhijian Duan, Wenhan Huang, Dinghuai Zhang et al.

In this paper, we investigate the learnability of the function approximator that approximates Nash equilibrium (NE) for games generated from a distribution. First, we offer a generalization bound using the Probably Approximately Correct (PAC) learning model. The bound describes the gap between the expected loss and empirical loss of the NE approximator. Afterward, we prove the agnostic PAC learnability of the Nash approximator. In addition to theoretical analysis, we demonstrate an application of NE approximator in experiments. The trained NE approximator can be used to warm-start and accelerate classical NE solvers. Together, our results show the practicability of approximating NE through function approximation.

Weiping Song, Zhijian Duan, Ziqing Yang et al.

This paper studies recommender systems with knowledge graphs, which can effectively address the problems of data sparsity and cold start. Recently, a variety of methods have been developed for this problem, which generally try to learn effective representations of users and items and then match items to users according to their representations. Though these methods have been shown quite effective, they lack good explanations, which are critical to recommender systems. In this paper, we take a different route and propose generating recommendations by finding meaningful paths from users to items. Specifically, we formulate the problem as a sequential decision process, where the target user is defined as the initial state, and the edges on the graphs are defined as actions. We shape the rewards according to existing state-of-the-art methods and then train a policy function with policy gradient methods. Experimental results on three real-world datasets show that our proposed method not only provides effective recommendations but also offers good explanations.