Deep Learning Method for Stationary Distribution of Reflected Brownian Motion

The stationary distribution of reflected Brownian motion (RBM) plays an important role in the analysis of high-dimensional stochastic systems, yet closed-form solutions are known only for a few special cases. Computing important performance metrics, such as tail probabilities, is even more intractable, despite their practical relevance. In this paper, we develop a deep learning approach that accurately and efficiently learns the Laplace transform of high-dimensional RBMs based on the basic adjoint relationship (BAR). Our framework combines a careful design of the loss function, training data sampling procedure, and neural network architecture. We evaluate the proposed method on RBM instances with known ground-truth tail probabilities and demonstrate near-perfect prediction in high-dimensional settings, highlighting its potential as a general tool for analyzing stochastic systems beyond analytically tractable regimes. Our code can be found at https://github.com/zhangz73/NN4MGF.

Generative Market Equilibrium Models with Stable Adversarial Learning via Reinforcement

We present a general computational framework for solving continuous-time financial market equilibria under minimal modeling assumptions while incorporating realistic financial frictions, such as trading costs, and supporting multiple interacting agents. Inspired by generative adversarial networks (GANs), our approach employs a novel generative deep reinforcement learning framework with a decoupling feedback system embedded in the adversarial training loop, which we term as the \emph{reinforcement link}. This architecture stabilizes the training dynamics by incorporating feedback from the discriminator. Our theoretically guided feedback mechanism enables the decoupling of the equilibrium system, overcoming challenges that hinder conventional numerical algorithms. Experimentally, our algorithm not only learns but also provides testable predictions on how asset returns and volatilities emerge from the endogenous trading behavior of market participants, where traditional analytical methods fall short. The design of our model is further supported by an approximation guarantee.

Atomic Proximal Policy Optimization for Electric Robo-Taxi Dispatch and Charger Allocation

Pioneering companies such as Waymo have deployed robo-taxi services in several U.S. cities. These robo-taxis are electric vehicles, and their operations require the joint optimization of ride matching, vehicle repositioning, and charging scheduling in a stochastic environment. We model the operations of the ride-hailing system with robo-taxis as a discrete-time, average reward Markov Decision Process with infinite horizon. As the fleet size grows, the dispatching is challenging as the set of system state and the fleet dispatching action set grow exponentially with the number of vehicles. To address this, we introduce a scalable deep reinforcement learning algorithm, called Atomic Proximal Policy Optimization (Atomic-PPO), that reduces the action space using atomic action decomposition. We evaluate our algorithm using real-world NYC for-hire vehicle data and we measure the performance using the long-run average reward achieved by the dispatching policy relative to a fluid-based reward upper bound. Our experiments demonstrate the superior performance of our Atomic-PPO compared to benchmarks. Furthermore, we conduct extensive numerical experiments to analyze the efficient allocation of charging facilities and assess the impact of vehicle range and charger speed on fleet performance.

A Survey of Online Auction Mechanism Design Using Deep Learning Approaches

Online auction has been very widespread in the recent years. Platform administrators are working hard to refine their auction mechanisms that will generate high profits while maintaining a fair resource allocation. With the advancement of computing technology and the bottleneck in theoretical frameworks, researchers are shifting gears towards online auction designs using deep learning approaches. In this article, we summarized some common deep learning infrastructures adopted in auction mechanism designs and showed how these architectures are evolving. We also discussed how researchers are tackling with the constraints and concerns in the large and dynamic industrial settings. Finally, we pointed out several currently unresolved issues for future directions.