Yu Nie

Jiayang Li, Jing Yu, Qianni Wang et al.

In a Stackelberg congestion game (SCG), a leader aims to maximize their own gain by anticipating and manipulating the equilibrium state at which the followers settle by playing a congestion game. Often formulated as bilevel programs, large-scale SCGs are well known for their intractability and complexity. Here, we attempt to tackle this computational challenge by marrying traditional methodologies with the latest differentiable programming techniques in machine learning. The core idea centers on replacing the lower-level equilibrium problem with a smooth evolution trajectory defined by the imitative logit dynamic (ILD), which we prove converges to the equilibrium of the congestion game under mild conditions. Building upon this theoretical foundation, we propose two new local search algorithms for SCGs. The first is a gradient descent algorithm that obtains the derivatives by unrolling ILD via differentiable programming. Thanks to the smoothness of ILD, the algorithm promises both efficiency and scalability. The second algorithm adds a heuristic twist by cutting short the followers' evolution trajectory. Behaviorally, this means that, instead of anticipating the followers' best response at equilibrium, the leader seeks to approximate that response by only looking ahead a limited number of steps. Our numerical experiments are carried out over various instances of classic SCG applications, ranging from toy benchmarks to large-scale real-world examples. The results show the proposed algorithms are reliable and scalable local solvers that deliver high-quality solutions with greater regularity and significantly less computational effort compared to the many incumbents included in our study.

Wenhao Li, Yu Nie, Zhongyao Yang et al.

In this paper, the influence of fan-shaped buffer zone on the performance of the toll plaza is researched. A two-dimensional traffic flow model and a comprehensive evaluation model based on mechanical model and psychological field are established. The traffic flow model is simulated by creating coordinate system. We first establish queue theory model to analyze vehicles when entering toll plaza. Then, a two-dimensional steadily car-following model is established based on psychological field for the analysis of vehicles when leaving toll plaza. According to psychological field theory, we analyze the force condition of each vehicle. The force of each vehicle is contributed by the vehicles in its observation area and obstacles. By projecting these vehicles and obstacles via the equipotential line in the psychological field, the influence on the value and direction acceleration of following vehicles is obtained. Consequently, the changes of each vehicle's speed and position are obtained as well. Next, we establish simulation based on the states of vehicles and make the rules of vehicle state-changing. By simulating the system, we obtain the throughput of the toll plaza's input and output. Then we obtained the bearing pressure on the road by the max throughput and the demand of the roads. Using the number of cars in per unit area as the safety factor. Then a comprehensive evaluation model is established based on bearing pressure on the road, cost and safety factor.

Boyi Liu, Jiayang Li, Zhuoran Yang et al.

To regulate a social system comprised of self-interested agents, economic incentives are often required to induce a desirable outcome. This incentive design problem naturally possesses a bilevel structure, in which a designer modifies the rewards of the agents with incentives while anticipating the response of the agents, who play a non-cooperative game that converges to an equilibrium. The existing bilevel optimization algorithms raise a dilemma when applied to this problem: anticipating how incentives affect the agents at equilibrium requires solving the equilibrium problem repeatedly, which is computationally inefficient; bypassing the time-consuming step of equilibrium-finding can reduce the computational cost, but may lead the designer to a sub-optimal solution. To address such a dilemma, we propose a method that tackles the designer's and agents' problems simultaneously in a single loop. Specifically, at each iteration, both the designer and the agents only move one step. Nevertheless, we allow the designer to gradually learn the overall influence of the incentives on the agents, which guarantees optimality after convergence. The convergence rate of the proposed scheme is also established for a broad class of games.

Jiayang Li, Jing Yu, Yu Marco Nie et al.

In a social system, the self-interest of agents can be detrimental to the collective good, sometimes leading to social dilemmas. To resolve such a conflict, a central designer may intervene by either redesigning the system or incentivizing the agents to change their behaviors. To be effective, the designer must anticipate how the agents react to the intervention, which is dictated by their often unknown payoff functions. Therefore, learning about the agents is a prerequisite for intervention. In this paper, we provide a unified framework for learning and intervention in games. We cast the equilibria of games as individual layers and integrate them into an end-to-end optimization framework. To enable the backward propagation through the equilibria of games, we propose two approaches, respectively based on explicit and implicit differentiation. Specifically, we cast the equilibria as the solutions to variational inequalities (VIs). The explicit approach unrolls the projection method for solving VIs, while the implicit approach exploits the sensitivity of the solutions to VIs. At the core of both approaches is the differentiation through a projection operator. Moreover, we establish the correctness of both approaches and identify the conditions under which one approach is more desirable than the other. The analytical results are validated using several real-world problems.