Kaiwen Liu

Xiao Li, Kaiwen Liu, H. Eric Tseng et al.

Understanding the intention of vehicles in the surrounding traffic is crucial for an autonomous vehicle to successfully accomplish its driving tasks in complex traffic scenarios such as highway forced merging. In this paper, we consider a behavioral model that incorporates both social behaviors and personal objectives of the interacting drivers. Leveraging this model, we develop a receding-horizon control-based decision-making strategy, that estimates online the other drivers' intentions using Bayesian filtering and incorporates predictions of nearby vehicles' behaviors under uncertain intentions. The effectiveness of the proposed decision-making strategy is demonstrated and evaluated based on simulation studies in comparison with a game theoretic controller and a real-world traffic dataset.

Xiao Li, Kaiwen Liu, H. Eric Tseng et al.

Autonomous vehicles need to accomplish their tasks while interacting with human drivers in traffic. It is thus crucial to equip autonomous vehicles with artificial reasoning to better comprehend the intentions of the surrounding traffic, thereby facilitating the accomplishments of the tasks. In this work, we propose a behavioral model that encodes drivers' interacting intentions into latent social-psychological parameters. Leveraging a Bayesian filter, we develop a receding-horizon optimization-based controller for autonomous vehicle decision-making which accounts for the uncertainties in the interacting drivers' intentions. For online deployment, we design a neural network architecture based on the attention mechanism which imitates the behavioral model with online estimated parameter priors. We also propose a decision tree search algorithm to solve the decision-making problem online. The proposed behavioral model is then evaluated in terms of its capabilities for real-world trajectory prediction. We further conduct extensive evaluations of the proposed decision-making module, in forced highway merging scenarios, using both simulated environments and real-world traffic datasets. The results demonstrate that our algorithms can complete the forced merging tasks in various traffic conditions while ensuring driving safety.

Sadegh Mahdavi, Muchen Li, Kaiwen Liu et al.

Advances in Large Language Models (LLMs) have sparked interest in their ability to solve Olympiad-level math problems. However, the training and evaluation of these models are constrained by the limited size and quality of available datasets, as creating large-scale data for such advanced problems requires extensive effort from human experts. In addition, current benchmarks are prone to contamination, leading to unreliable evaluations. In this paper, we present an automated pipeline that leverages the rich resources of the Art of Problem Solving (AoPS) forum, which predominantly features Olympiad-level problems and community-driven solutions. Using open-source LLMs, we develop a method to extract question-answer pairs from the forum, resulting in AoPS-Instruct, a dataset of more than 600,000 high-quality QA pairs. Our experiments demonstrate that fine-tuning LLMs on AoPS-Instruct improves their reasoning abilities across various benchmarks. Moreover, we build an automatic pipeline that introduces LiveAoPSBench, an evolving evaluation set with timestamps, derived from the latest forum data, providing a contamination-resistant benchmark for assessing LLM performance. Notably, we observe a significant decline in LLM performance over time, suggesting their success on older examples may stem from pre-training exposure rather than true reasoning ability. Our work presents a scalable approach to creating and maintaining large-scale, high-quality datasets for advanced math reasoning, offering valuable insights into the capabilities and limitations of LLMs in this domain. Our benchmark and code is available at https://github.com/DSL-Lab/aops

Kaiwen Liu, Nan Li, H. Eric Tseng et al.

Merging is, in general, a challenging task for both human drivers and autonomous vehicles, especially in dense traffic, because the merging vehicle typically needs to interact with other vehicles to identify or create a gap and safely merge into. In this paper, we consider the problem of autonomous vehicle control for forced merge scenarios. We propose a novel game-theoretic controller, called the Leader-Follower Game Controller (LFGC), in which the interactions between the autonomous ego vehicle and other vehicles with a priori uncertain driving intentions is modeled as a partially observable leader-follower game. The LFGC estimates the other vehicles' intentions online based on observed trajectories, and then predicts their future trajectories and plans the ego vehicle's own trajectory using Model Predictive Control (MPC) to simultaneously achieve probabilistically guaranteed safety and merging objectives. To verify the performance of LFGC, we test it in simulations and with the NGSIM data, where the LFGC demonstrates a high success rate of 97.5% in merging.

Kaiwen Liu, Nan Li, Ilya Kolmanovsky et al.

This paper proposes a learning reference governor (LRG) approach to enforce state and control constraints in systems for which an accurate model is unavailable, and this approach enables the reference governor to gradually improve command tracking performance through learning while enforcing the constraints during learning and after learning is completed. The learning can be performed either on a black-box type model of the system or directly on the hardware. After introducing the LRG algorithm and outlining its theoretical properties, this paper investigates LRG application to fuel truck (tank truck) rollover avoidance. Through simulations based on a fuel truck model that accounts for liquid fuel sloshing effects, we show that the proposed LRG can effectively protect fuel trucks from rollover accidents under various operating conditions.