Yongjie Yang

Guozhen Rong, Xin Li, Yongjie Yang

Preference restrictions have played a significant role in computational social choice. This paper studies a framework that connects preference restrictions with classical graph search paradigms. We model candidates as vertices of a graph and interpret the preference ordering of each voter as the outcome of traversing the graph according to a graph search. We focus on six fundamental paradigms: breadth-first search (BFS), depth-first search (DFS), breadth-first search (LexBFS), lexicographic depth-first (LexDFS), maximum cardinality search (MCS), and maximal neighborhood search (MNS). Within this framework, we study the problem of determining whether a given preference profile admits a graph support subject to structural restrictions, that is, whether there exists a graph such that each preference ordering can be generated by traversing the graph under the chosen paradigm. For all considered paradigms, we show that this problem is NP-hard when the graph support is required to have at most $k$ edges, where $k$ is a given integer. We further extend these hardness results to the case where the graph support is required to have maximum degree $k$. For DFS, we prove that recognizing whether a preference profile admits a tree support can be solved in polynomial time. Moreover, existing results imply polynomial-time solvability of the problem for all remaining graph traversals, except BFS and LexBFS, for which the complexity remains open.

Yongjie Yang

Sequential voting rules have played a crucial role in shaping decisions within parliamentary and legislative frameworks. After observing that the existing sequential rules fail several fundamental axioms, Horan and Sprumont [2022] proposed a sequential rule named two-stage majoritarian rule (TSMR). This paper examines this rule by investigating the complexity of {\sc{Agenda Control}}, {\sc{Coalition Manipulation}}, {\sc{Possible Winner}}, {\sc{Necessary Winner}}, and eight standard election control problems. Our study offers a comprehensive insight into the complexity landscape of these problems.

Junbin Qiu, Zhengpeng Xie, Xiangda Yan et al.

Zeroth-Order Optimization (ZOO) provides powerful tools for optimizing functions where explicit gradients are unavailable or expensive to compute. However, the underlying mechanisms of popular ZOO methods, particularly those employing randomized finite differences, and their connection to other optimization paradigms like Reinforcement Learning (RL) are not fully elucidated. This paper establishes a fundamental and previously unrecognized connection: ZOO with finite differences is equivalent to a specific instance of single-step Policy Optimization (PO). We formally unveil that the implicitly smoothed objective function optimized by common ZOO algorithms is identical to a single-step PO objective. Furthermore, we show that widely used ZOO gradient estimators, are mathematically equivalent to the REINFORCE gradient estimator with a specific baseline function, revealing the variance-reducing mechanism in ZOO from a PO perspective.Built on this unified framework, we propose ZoAR (Zeroth-Order Optimization with Averaged Baseline and Query Reuse), a novel ZOO algorithm incorporating PO-inspired variance reduction techniques: an averaged baseline from recent evaluations and query reuse analogous to experience replay. Our theoretical analysis further substantiates these techniques reduce variance and enhance convergence. Extensive empirical studies validate our theory and demonstrate that ZoAR significantly outperforms other methods in terms of convergence speed and final performance. Overall, our work provides a new theoretical lens for understanding ZOO and offers practical algorithmic improvements derived from its connection to PO.