In this paper, we present a new approach for lifted MAP inference in Markov logic networks (MLNs). The key idea in our approach is to compactly encode the MAP inference problem as an Integer Polynomial Program (IPP) by schematically applying three lifted inference steps to the MLN: lifted decomposition, lifted conditioning, and partial grounding. Our IPP encoding is lifted in the sense that an integer assignment to a variable in the IPP may represent a truth-assignment to multiple indistinguishable ground atoms in the MLN. We show how to solve the IPP by first converting it to an Integer Linear Program (ILP) and then solving the latter using state-of-the-art ILP techniques. Experiments on several benchmark MLNs show that our new algorithm is substantially superior to ground inference and existing methods in terms of computational efficiency and solution quality.

We show that the usual score function for conditional Markov networks can be written as the expectation over the scores of their spanning trees. We also show that a small random sample of these output trees can attain a significant fraction of the margin obtained by the complete graph and we provide conditions under which we can perform tractable inference. The experimental results confirm that practical learning is scalable to realistic datasets using this approach.

The Markov property serves as a foundational assumption in most existing work on vehicle driving behavior, positing that future states depend solely on the current state, not the series of preceding states. This study validates the Markov properties of vehicle trajectories for both Autonomous Vehicles (AVs) and Human-driven Vehicles (HVs). A statistical method used to test whether time series data exhibits Markov properties is applied to examine whether the trajectory data possesses Markov characteristics. t test and F test are additionally introduced to characterize the differences in Markov properties between AVs and HVs. Based on two public trajectory datasets, we investigate the presence and order of the Markov property of different types of vehicles through rigorous statistical tests. Our findings reveal that AV trajectories generally exhibit stronger Markov properties compared to HV trajectories, with a higher percentage conforming to the Markov property and lower Markov orders. In contrast, HV trajectories display greater variability and heterogeneity in decision-making processes, reflecting the complex perception and information processing involved in human driving. These results have significant implications for the development of driving behavior models, AV controllers, and traffic simulation systems. Our study also demonstrates the feasibility of using statistical methods to test the presence of Markov properties in driving trajectory data.

Activity schedules, which represent the activities and associated travel behaviours of individuals, are a core component of many applied models in the transport, energy and epidemiology domains. Our data driven approach learns human preferences and scheduling logic without the need for complex interacting combinations of sub-models and custom-rules, this makes our approach significantly faster and simpler to operate that existing approaches. We find activity schedule data combines aspects of both continuous image data and also discrete text data, requiring novel approaches. We additionally contribute a novel schedule representation and comprehensive evaluation framework for generated schedules. Evaluation shows our approach is able to rapidly generate large, diverse and realistic synthetic samples of activity schedules.

LLM test-time compute (or LLM inference) via search has emerged as a promising research area with rapid developments. However, current frameworks often adopt distinct perspectives on three key aspects (task definition, LLM profiling, and search procedures), making direct comparisons challenging. Moreover, the search algorithms employed often diverge from standard implementations, and their specific characteristics are not thoroughly specified. In this survey, we provide a comprehensive technical review that unifies task definitions and provides modular definitions of LLM profiling and search procedures. The definitions enable precise comparisons of various LLM inference frameworks while highlighting their departures from conventional search algorithms. We also discuss the applicability, performance, and efficiency of these methods. For further details and ongoing updates, please refer to our GitHub repository: https://github.com/xinzhel/LLM-Agent-Survey/blob/main/search.md

Learning robust and generalizable world models is crucial for enabling efficient and scalable robotic control in real-world environments. In this work, we introduce a novel framework for learning world models that accurately capture complex, partially observable, and stochastic dynamics. The proposed method employs a dual-autoregressive mechanism and self-supervised training to achieve reliable long-horizon predictions without relying on domain-specific inductive biases, ensuring adaptability across diverse robotic tasks. We further propose a policy optimization framework that leverages world models for efficient training in imagined environments and seamless deployment in real-world systems. Through extensive experiments, our approach consistently outperforms state-of-the-art methods, demonstrating superior autoregressive prediction accuracy, robustness to noise, and generalization across manipulation and locomotion tasks. Notably, policies trained with our method are successfully deployed on ANYmal D hardware in a zero-shot transfer, achieving robust performance with minimal sim-to-real performance loss. This work advances model-based reinforcement learning by addressing the challenges of long-horizon prediction, error accumulation, and sim-to-real transfer. By providing a scalable and robust framework, the introduced methods pave the way for adaptive and efficient robotic systems in real-world applications.

Autonomous agents' interactions with humans are increasingly focused on adapting to their changing preferences in order to improve assistance in real-world tasks. Effective agents must learn to accurately infer human goals, which are often hidden, to collaborate well. However, existing Multi-Agent Reinforcement Learning (MARL) environments lack the necessary attributes required to rigorously evaluate these agents' learning capabilities. To this end, we introduce ColorGrid, a novel MARL environment with customizable non-stationarity, asymmetry, and reward structure. We investigate the performance of Independent Proximal Policy Optimization (IPPO), a state-of-the-art (SOTA) MARL algorithm, in ColorGrid and find through extensive ablations that, particularly with simultaneous non-stationary and asymmetric goals between a ``leader'' agent representing a human and a ``follower'' assistant agent, ColorGrid is unsolved by IPPO. To support benchmarking future MARL algorithms, we release our environment code, model checkpoints, and trajectory visualizations at https://github.com/andreyrisukhin/ColorGrid.

We study the problem of learning optimal policies in finite-horizon Markov Decision Processes (MDPs) using low-rank reinforcement learning (RL) methods. In finite-horizon MDPs, the policies, and therefore the value functions (VFs) are not stationary. This aggravates the challenges of high-dimensional MDPs, as they suffer from the curse of dimensionality and high sample complexity. To address these issues, we propose modeling the VFs of finite-horizon MDPs as low-rank tensors, enabling a scalable representation that renders the problem of learning optimal policies tractable. We introduce an optimization-based framework for solving the Bellman equations with low-rank constraints, along with block-coordinate descent (BCD) and block-coordinate gradient descent (BCGD) algorithms, both with theoretical convergence guarantees. For scenarios where the system dynamics are unknown, we adapt the proposed BCGD method to estimate the VFs using sampled trajectories. Numerical experiments further demonstrate that the proposed framework reduces computational demands in controlled synthetic scenarios and more realistic resource allocation problems.

The vast majority of work in self-supervised learning have focused on assessing recovered features by a chosen set of downstream tasks. While there are several commonly used benchmark datasets, this lens of feature learning requires assumptions on the downstream tasks which are not inherent to the data distribution itself. In this paper, we present an alternative lens, one of parameter identifiability: assuming data comes from a parametric probabilistic model, we train a self-supervised learning predictor with a suitable parametric form, and ask whether the parameters of the optimal predictor can be used to extract the parameters of the ground truth generative model.Specifically, we focus on latent-variable models capturing sequential structures, namely Hidden Markov Models with both discrete and conditionally Gaussian observations. We focus on masked prediction as the self-supervised learning task and study the optimal masked predictor. We show that parameter identifiability is governed by the task difficulty, which is determined by the choice of data model and the amount of tokens to predict.

Physical contacts are at the base of each embodied interaction. As for living beings, also robots continuously establish diverse contacts to fulfill their tasks. Over the last decades, one of the bold goals of robotics research has been to provide artificial agents with dexterity and adaptability - typical of biological systems - while interacting with their surroundings. Despite the huge work and the excellent outputs in this field, such capabilities still require hard refinements and studies to be fully delivered on our robots. The scientific contribution to this objective builds upon three pillars: the design of an appropriate embodiment - concerning its morphology, actuation strategy, and sensing technology; feature extraction algorithms from tactile signals to build a perception model of the experience; closed-loop robot control strategies that drive robot decisions according to either raw tactile feedback or perceptual representations.