Asymptotic Dynamics of Alternating Minimization for Non-Convex Optimization

This study investigates the asymptotic dynamics of alternating minimization applied to optimize a bilinear non-convex function with normally distributed covariates. We employ the replica method from statistical physics in a multi-step approach to precisely trace the algorithm's evolution. Our findings indicate that the dynamics can be described effectively by a two--dimensional discrete stochastic process, where each step depends on all previous time steps, revealing a memory dependency in the procedure. The theoretical framework developed in this work is broadly applicable for the analysis of various iterative algorithms, extending beyond the scope of alternating minimization.

Domain Adaptation for Time series Transformers using One-step fine-tuning

The recent breakthrough of Transformers in deep learning has drawn significant attention of the time series community due to their ability to capture long-range dependencies. However, like other deep learning models, Transformers face limitations in time series prediction, including insufficient temporal understanding, generalization challenges, and data shift issues for the domains with limited data. Additionally, addressing the issue of catastrophic forgetting, where models forget previously learned information when exposed to new data, is another critical aspect that requires attention in enhancing the robustness of Transformers for time series tasks. To address these limitations, in this paper, we pre-train the time series Transformer model on a source domain with sufficient data and fine-tune it on the target domain with limited data. We introduce the \emph{One-step fine-tuning} approach, adding some percentage of source domain data to the target domains, providing the model with diverse time series instances. We then fine-tune the pre-trained model using a gradual unfreezing technique. This helps enhance the model's performance in time series prediction for domains with limited data. Extensive experimental results on two real-world datasets show that our approach improves over the state-of-the-art baselines by 4.35% and 11.54% for indoor temperature and wind power prediction, respectively.

Stable Autonomous Flow Matching

In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective Lyapunov function. Despite this, connections between control theory and generative models in the literature are sparse, even though there are several machine learning applications with physically stable data points. In this paper, we focus on such data and a recent class of deep generative models called flow matching. We apply tools of stochastic stability for time-independent systems to flow matching models. In doing so, we characterize the space of flow matching models that are amenable to this treatment, as well as draw connections to other control theory principles. We demonstrate our theoretical results on two examples.

Neural Graphics Primitives-based Deformable Image Registration for On-the-fly Motion Extraction

Intra-fraction motion in radiotherapy is commonly modeled using deformable image registration (DIR). However, existing methods often struggle to balance speed and accuracy, limiting their applicability in clinical scenarios. This study introduces a novel approach that harnesses Neural Graphics Primitives (NGP) to optimize the displacement vector field (DVF). Our method leverages learned primitives, processed as splats, and interpolates within space using a shallow neural network. Uniquely, it enables self-supervised optimization at an ultra-fast speed, negating the need for pre-training on extensive datasets and allowing seamless adaptation to new cases. We validated this approach on the 4D-CT lung dataset DIR-lab, achieving a target registration error (TRE) of 1.15\pm1.15 mm within a remarkable time of 1.77 seconds. Notably, our method also addresses the sliding boundary problem, a common challenge in conventional DIR methods.

Stochastic COLREGs Evaluation for Safe Navigation under Uncertainty

The encounter situation between marine vessels determines how they should navigate to obey COLREGs, but time-varying and stochastic uncertainty in estimation of angles of encounter, and of closest point of approach, easily give rise to different assessment of situation at two approaching vessels. This may lead to high-risk conditions and could cause collision. This article considers decision making under uncertainty and suggests a novel method for probabilistic interpretation of vessel encounters that is explainable and provides a measure of uncertainty in the evaluation. The method is equally useful for decision support on a manned bridge as on Marine Autonomous Surface Ships (MASS) where it provides input for automated navigation. The method makes formal safety assessment and validation feasible. We obtain a resilient algorithm for machine interpretation of COLREGs under uncertainty and show its efficacy by simulations.

Feedback Loops With Language Models Drive In-Context Reward Hacking

Language models influence the external world: they query APIs that read and write to web pages, generate content that shapes human behavior, and run system commands as autonomous agents. These interactions form feedback loops: LLM outputs affect the world, which in turn affect subsequent LLM outputs. In this work, we show that feedback loops can cause in-context reward hacking (ICRH), where the LLM at test-time optimizes a (potentially implicit) objective but creates negative side effects in the process. For example, consider an LLM agent deployed to increase Twitter engagement; the LLM may retrieve its previous tweets into the context window and make them more controversial, increasing engagement but also toxicity. We identify and study two processes that lead to ICRH: output-refinement and policy-refinement. For these processes, evaluations on static datasets are insufficient -- they miss the feedback effects and thus cannot capture the most harmful behavior. In response, we provide three recommendations for evaluation to capture more instances of ICRH. As AI development accelerates, the effects of feedback loops will proliferate, increasing the need to understand their role in shaping LLM behavior.

Solving Complex Multi-UAV Mission Planning Problems using Multi-objective Genetic Algorithms

Due to recent booming of UAVs technologies, these are being used in many fields involving complex tasks. Some of them involve a high risk to the vehicle driver, such as fire monitoring and rescue tasks, which make UAVs excellent for avoiding human risks. Mission Planning for UAVs is the process of planning the locations and actions (loading/dropping a load, taking videos/pictures, acquiring information) for the vehicles, typically over a time period. These vehicles are controlled from Ground Control Stations (GCSs) where human operators use rudimentary systems. This paper presents a new Multi-Objective Genetic Algorithm for solving complex Mission Planning Problems (MPP) involving a team of UAVs and a set of GCSs. A hybrid fitness function has been designed using a Constraint Satisfaction Problem (CSP) to check if solutions are valid and Pareto-based measures to look for optimal solutions. The algorithm has been tested on several datasets optimizing different variables of the mission, such as the makespan, the fuel consumption, distance, etc. Experimental results show that the new algorithm is able to obtain good solutions, however as the problem becomes more complex, the optimal solutions also become harder to find.

CityFlowER: An Efficient and Realistic Traffic Simulator with Embedded Machine Learning Models

Traffic simulation is an essential tool for transportation infrastructure planning, intelligent traffic control policy learning, and traffic flow analysis. Its effectiveness relies heavily on the realism of the simulators used. Traditional traffic simulators, such as SUMO and CityFlow, are often limited by their reliance on rule-based models with hyperparameters that oversimplify driving behaviors, resulting in unrealistic simulations. To enhance realism, some simulators have provided Application Programming Interfaces (APIs) to interact with Machine Learning (ML) models, which learn from observed data and offer more sophisticated driving behavior models. However, this approach faces challenges in scalability and time efficiency as vehicle numbers increase. Addressing these limitations, we introduce CityFlowER, an advancement over the existing CityFlow simulator, designed for efficient and realistic city-wide traffic simulation. CityFlowER innovatively pre-embeds ML models within the simulator, eliminating the need for external API interactions and enabling faster data computation. This approach allows for a blend of rule-based and ML behavior models for individual vehicles, offering unparalleled flexibility and efficiency, particularly in large-scale simulations. We provide detailed comparisons with existing simulators, implementation insights, and comprehensive experiments to demonstrate CityFlowER's superiority in terms of realism, efficiency, and adaptability.

Ginger: An Efficient Curvature Approximation with Linear Complexity for General Neural Networks

Second-order optimization approaches like the generalized Gauss-Newton method are considered more powerful as they utilize the curvature information of the objective function with preconditioning matrices. Albeit offering tempting theoretical benefits, they are not easily applicable to modern deep learning. The major reason is due to the quadratic memory and cubic time complexity to compute the inverse of the matrix. These requirements are infeasible even with state-of-the-art hardware. In this work, we propose Ginger, an eigendecomposition for the inverse of the generalized Gauss-Newton matrix. Our method enjoys efficient linear memory and time complexity for each iteration. Instead of approximating the conditioning matrix, we directly maintain its inverse to make the approximation more accurate. We provide the convergence result of Ginger for non-convex objectives. Our experiments on different tasks with different model architectures verify the effectiveness of our method. Our code is publicly available.

A Reinforcement Learning Approach for Dynamic Rebalancing in Bike-Sharing System

Bike-Sharing Systems provide eco-friendly urban mobility, contributing to the alleviation of traffic congestion and to healthier lifestyles. Efficiently operating such systems and maintaining high customer satisfaction is challenging due to the stochastic nature of trip demand, leading to full or empty stations. Devising effective rebalancing strategies using vehicles to redistribute bikes among stations is therefore of uttermost importance for operators. As a promising alternative to classical mathematical optimization, reinforcement learning is gaining ground to solve sequential decision-making problems. This paper introduces a spatio-temporal reinforcement learning algorithm for the dynamic rebalancing problem with multiple vehicles. We first formulate the problem as a Multi-agent Markov Decision Process in a continuous time framework. This allows for independent and cooperative vehicle rebalancing, eliminating the impractical restriction of time-discretized models where vehicle departures are synchronized. A comprehensive simulator under the first-arrive-first-serve rule is then developed to facilitate the learning process by computing immediate rewards under diverse demand scenarios. To estimate the value function and learn the rebalancing policy, various Deep Q-Network configurations are tested, minimizing the lost demand. Experiments are carried out on various datasets generated from historical data, affected by both temporal and weather factors. The proposed algorithms outperform benchmarks, including a multi-period Mixed-Integer Programming model, in terms of lost demand. Once trained, it yields immediate decisions, making it suitable for real-time applications. Our work offers practical insights for operators and enriches the integration of reinforcement learning into dynamic rebalancing problems, paving the way for more intelligent and robust urban mobility solutions.