Dimension-free Relaxation Times of Informed MCMC Samplers on Discrete Spaces

Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by building upon and refining some recent theoretical advancements in Bayesian model selection problems. We establish sufficient conditions for a class of informed Metropolis-Hastings algorithms to attain relaxation times that are independent of the problem dimension. These conditions are grounded in high-dimensional statistical theory and allow for possibly multimodal posterior distributions. We obtain our results through two independent techniques: the multicommodity flow method and single-element drift condition analysis; we find that the latter yields a tighter mixing time bound. Our results and proof techniques are readily applicable to a broad spectrum of statistical problems with discrete parameter spaces.

Towards an In-Depth Comprehension of Case Relevance for Better Legal Retrieval

Legal retrieval techniques play an important role in preserving the fairness and equality of the judicial system. As an annually well-known international competition, COLIEE aims to advance the development of state-of-the-art retrieval models for legal texts. This paper elaborates on the methodology employed by the TQM team in COLIEE2024.Specifically, we explored various lexical matching and semantic retrieval models, with a focus on enhancing the understanding of case relevance. Additionally, we endeavor to integrate various features using the learning-to-rank technique. Furthermore, fine heuristic pre-processing and post-processing methods have been proposed to mitigate irrelevant information. Consequently, our methodology achieved remarkable performance in COLIEE2024, securing first place in Task 1 and third place in Task 3. We anticipate that our proposed approach can contribute valuable insights to the advancement of legal retrieval technology.

Soft-constrained Schrodinger Bridge: a Stochastic Control Approach

Schr\"{o}dinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process with a pre-specified terminal distribution $\mu_T$. We propose to generalize this stochastic control problem by allowing the terminal distribution to differ from $\mu_T$ but penalizing the Kullback-Leibler divergence between the two distributions. We call this new control problem soft-constrained Schr\"{o}dinger bridge (SSB). The main contribution of this work is a theoretical derivation of the solution to SSB, which shows that the terminal distribution of the optimally controlled process is a geometric mixture of $\mu_T$ and some other distribution. This result is further extended to a time series setting. One application of SSB is the development of robust generative diffusion models. We propose a score matching-based algorithm for sampling from geometric mixtures and showcase its use via a numerical example for the MNIST data set.

Multi-Agent Reinforcement Learning for Connected and Automated Vehicles Control: Recent Advancements and Future Prospects

Connected and automated vehicles (CAVs) have emerged as a potential solution to the future challenges of developing safe, efficient, and eco-friendly transportation systems. However, CAV control presents significant challenges, given the complexity of interconnectivity and coordination required among the vehicles. To address this, multi-agent reinforcement learning (MARL), with its notable advancements in addressing complex problems in autonomous driving, robotics, and human-vehicle interaction, has emerged as a promising tool for enhancing the capabilities of CAVs. However, there is a notable absence of current reviews on the state-of-the-art MARL algorithms in the context of CAVs. Therefore, this paper delivers a comprehensive review of the application of MARL techniques within the field of CAV control. The paper begins by introducing MARL, followed by a detailed explanation of its unique advantages in addressing complex mobility and traffic scenarios that involve multiple agents. It then presents a comprehensive survey of MARL applications on the extent of control dimensions for CAVs, covering critical and typical scenarios such as platooning control, lane-changing, and unsignalized intersections. In addition, the paper provides a comprehensive review of the prominent simulation platforms used to create reliable environments for training in MARL. Lastly, the paper examines the current challenges associated with deploying MARL within CAV control and outlines potential solutions that can effectively overcome these issues. Through this review, the study highlights the tremendous potential of MARL to enhance the performance and collaboration of CAV control in terms of safety, travel efficiency, and economy.

Joint Problems in Learning Multiple Dynamical Systems

Clustering of time series is a well-studied problem, with applications ranging from quantitative, personalized models of metabolism obtained from metabolite concentrations to state discrimination in quantum information theory. We consider a variant, where given a set of trajectories and a number of parts, we jointly partition the set of trajectories and learn linear dynamical system (LDS) models for each part, so as to minimize the maximum error across all the models. We present globally convergent methods and EM heuristics, accompanied by promising computational results.

Group-blind optimal transport to group parity and its constrained variants

Fairness holds a pivotal role in the realm of machine learning, particularly when it comes to addressing groups categorised by sensitive attributes, e.g., gender, race. Prevailing algorithms in fair learning predominantly hinge on accessibility or estimations of these sensitive attributes, at least in the training process. We design a single group-blind projection map that aligns the feature distributions of both groups in the source data, achieving (demographic) group parity, without requiring values of the protected attribute for individual samples in the computation of the map, as well as its use. Instead, our approach utilises the feature distributions of the privileged and unprivileged groups in a boarder population and the essential assumption that the source data are unbiased representation of the population. We present numerical results on synthetic data and real data.

Recent Progress in Energy Management of Connected Hybrid Electric Vehicles Using Reinforcement Learning

The growing adoption of hybrid electric vehicles (HEVs) presents a transformative opportunity for revolutionizing transportation energy systems. The shift towards electrifying transportation aims to curb environmental concerns related to fossil fuel consumption. This necessitates efficient energy management systems (EMS) to optimize energy efficiency. The evolution of EMS from HEVs to connected hybrid electric vehicles (CHEVs) represent a pivotal shift. For HEVs, EMS now confronts the intricate energy cooperation requirements of CHEVs, necessitating advanced algorithms for route optimization, charging coordination, and load distribution. Challenges persist in both domains, including optimal energy utilization for HEVs, and cooperative eco-driving control (CED) for CHEVs across diverse vehicle types. Reinforcement learning (RL) stands out as a promising tool for addressing these challenges at hand. Specifically, within the realm of CHEVs, the application of multi-agent reinforcement learning (MARL) emerges as a powerful approach for effectively tackling the intricacies of CED control. Despite extensive research, few reviews span from individual vehicles to multi-vehicle scenarios. This review bridges the gap, highlighting challenges, advancements, and potential contributions of RL-based solutions for future sustainable transportation systems.

Study on the Impacts of Hazardous Behaviors on Autonomous Vehicle Collision Rates Based on Humanoid Scenario Generation in CARLA

Testing of function safety and Safety Of The Intended Functionality (SOTIF) is important for autonomous vehicles (AVs). It is hard to test the AV's hazard response in the real world because it would involve hazards to passengers and other road users. This paper studied on virtual testing of AV on the CARLA platform and proposed a Humanoid Scenario Generation (HSG) scheme to investigate the impacts of hazardous behaviors on AV collision rates. The HSG scheme breakthrough the current limitation on the rarity and reproducibility of real scenes. By accurately capturing five prominent human driver behaviors that directly contribute to vehicle collisions in the real world, the methodology significantly enhances the realism and diversity of the simulation, as evidenced by collision rate statistics across various traffic scenarios. Thus, the modular framework allows for customization, and its seamless integration within the CARLA platform ensures compatibility with existing tools. Ultimately, the comparison results demonstrate that all vehicles that exhibited hazardous behaviors followed the predefined random speed distribution and the effectiveness of the HSG was validated by the distinct characteristics displayed by these behaviors.

Importance is Important: A Guide to Informed Importance Tempering Methods

Informed importance tempering (IIT) is an easy-to-implement MCMC algorithm that can be seen as an extension of the familiar Metropolis-Hastings algorithm with the special feature that informed proposals are always accepted, and which was shown in Zhou and Smith (2022) to converge much more quickly in some common circumstances. This work develops a new, comprehensive guide to the use of IIT in many situations. First, we propose two IIT schemes that run faster than existing informed MCMC methods on discrete spaces by not requiring the posterior evaluation of all neighboring states. Second, we integrate IIT with other MCMC techniques, including simulated tempering, pseudo-marginal and multiple-try methods (on general state spaces), which have been conventionally implemented as Metropolis-Hastings schemes and can suffer from low acceptance rates. The use of IIT allows us to always accept proposals and brings about new opportunities for optimizing the sampler which are not possible under the Metropolis-Hastings framework. Numerical examples illustrating our findings are provided for each proposed algorithm, and a general theory on the complexity of IIT methods is developed.

Energy Management of Multi-mode Plug-in Hybrid Electric Vehicle using Multi-agent Deep Reinforcement Learning

The recently emerging multi-mode plug-in hybrid electric vehicle (PHEV) technology is one of the pathways making contributions to decarbonization, and its energy management requires multiple-input and multiple-output (MIMO) control. At the present, the existing methods usually decouple the MIMO control into single-output (MISO) control and can only achieve its local optimal performance. To optimize the multi-mode vehicle globally, this paper studies a MIMO control method for energy management of the multi-mode PHEV based on multi-agent deep reinforcement learning (MADRL). By introducing a relevance ratio, a hand-shaking strategy is proposed to enable two learning agents to work collaboratively under the MADRL framework using the deep deterministic policy gradient (DDPG) algorithm. Unified settings for the DDPG agents are obtained through a sensitivity analysis of the influencing factors to the learning performance. The optimal working mode for the hand-shaking strategy is attained through a parametric study on the relevance ratio. The advantage of the proposed energy management method is demonstrated on a software-in-the-loop testing platform. The result of the study indiates that learning rate of the DDPG agents is the greatest factor in learning performance. Using the unified DDPG settings and a relevance ratio of 0.2, the proposed MADRL method can save up to 4% energy compared to the single-agent method.