We investigate the complexity of covariance matrix estimation for Gibbs distributions based on dependent samples from a Markov chain. We show that when $\pi$ satisfies a Poincar\'e inequality and the chain possesses a spectral gap, we can achieve similar sample complexity using MCMC as compared to an estimator constructed using i.i.d. samples, with potentially much better query complexity. As an application of our methods, we show improvements for the query complexity in both constrained and unconstrained settings for concrete instances of MCMC. In particular, we provide guarantees regarding isotropic rounding procedures for sampling uniformly on convex bodies.

Variational Autoencoders (VAE) are popular generative models used to sample from complex data distributions. Despite their empirical success in various machine learning tasks, significant gaps remain in understanding their theoretical properties, particularly regarding convergence guarantees. This paper aims to bridge that gap by providing non-asymptotic convergence guarantees for VAE trained using both Stochastic Gradient Descent and Adam algorithms.We derive a convergence rate of $\mathcal{O}(\log n / \sqrt{n})$, where $n$ is the number of iterations of the optimization algorithm, with explicit dependencies on the batch size, the number of variational samples, and other key hyperparameters. Our theoretical analysis applies to both Linear VAE and Deep Gaussian VAE, as well as several VAE variants, including $\beta$-VAE and IWAE. Additionally, we empirically illustrate the impact of hyperparameters on convergence, offering new insights into the theoretical understanding of VAE training.

General-purpose navigation in challenging environments remains a significant problem in robotics, with current state-of-the-art approaches facing myriad limitations. Classical approaches struggle with cluttered settings and require extensive tuning, while learning-based methods face difficulties generalizing to out-of-distribution environments. This paper introduces X-Mobility, an end-to-end generalizable navigation model that overcomes existing challenges by leveraging three key ideas. First, X-Mobility employs an auto-regressive world modeling architecture with a latent state space to capture world dynamics. Second, a diverse set of multi-head decoders enables the model to learn a rich state representation that correlates strongly with effective navigation skills. Third, by decoupling world modeling from action policy, our architecture can train effectively on a variety of data sources, both with and without expert policies: off-policy data allows the model to learn world dynamics, while on-policy data with supervisory control enables optimal action policy learning. Through extensive experiments, we demonstrate that X-Mobility not only generalizes effectively but also surpasses current state-of-the-art navigation approaches. Additionally, X-Mobility also achieves zero-shot Sim2Real transferability and shows strong potential for cross-embodiment generalization.

Understanding cognitive processes in multi-agent interactions is a primary goal in cognitive science. It can guide the direction of artificial intelligence (AI) research toward social decision-making in multi-agent systems, which includes uncertainty from character heterogeneity. In this paper, we introduce an episodic future thinking (EFT) mechanism for a reinforcement learning (RL) agent, inspired by cognitive processes observed in animals. To enable future thinking functionality, we first develop a multi-character policy that captures diverse characters with an ensemble of heterogeneous policies. Here, the character of an agent is defined as a different weight combination on reward components, representing distinct behavioral preferences. The future thinking agent collects observation-action trajectories of the target agents and uses the pre-trained multi-character policy to infer their characters. Once the character is inferred, the agent predicts the upcoming actions of target agents and simulates the potential future scenario. This capability allows the agent to adaptively select the optimal action, considering the predicted future scenario in multi-agent interactions. To evaluate the proposed mechanism, we consider the multi-agent autonomous driving scenario with diverse driving traits and multiple particle environments. Simulation results demonstrate that the EFT mechanism with accurate character inference leads to a higher reward than existing multi-agent solutions. We also confirm that the effect of reward improvement remains valid across societies with different levels of character diversity.

Procedural Content Generation (PCG) is defined as the automatic creation of game content using algorithms. PCG has a long history in both the game industry and the academic world. It can increase player engagement and ease the work of game designers. While recent advances in deep learning approaches in PCG have enabled researchers and practitioners to create more sophisticated content, it is the arrival of Large Language Models (LLMs) that truly disrupted the trajectory of PCG advancement. This survey explores the differences between various algorithms used for PCG, including search-based methods, machine learning-based methods, other frequently used methods (e.g., noise functions), and the newcomer, LLMs. We also provide a detailed discussion on combined methods. Furthermore, we compare these methods based on the type of content they generate and the publication dates of their respective papers. Finally, we identify gaps in the existing academic work and suggest possible directions for future research.

Restricted Boltzmann machines (RBM) are generative models capable to learn data with a rich underlying structure. We study the teacher-student setting where a student RBM learns structured data generated by a teacher RBM. The amount of structure in the data is controlled by adjusting the number of hidden units of the teacher and the correlations in the rows of the weights, a.k.a. patterns. In the absence of correlations, we validate the conjecture that the performance is independent of the number of teacher patters and hidden units of the student RBMs, and we argue that the teacher-student setting can be used as a toy model for studying the lottery ticket hypothesis. Beyond this regime, we find that the critical amount of data required to learn the teacher patterns decreases with both their number and correlations. In both regimes, we find that, even with an relatively large dataset, it becomes impossible to learn the teacher patterns if the inference temperature used for regularization is kept too low. In our framework, the student can learn teacher patterns one-to-one or many-to-one, generalizing previous findings about the teacher-student setting with two hidden units to any arbitrary finite number of hidden units.

Infectious diseases occur when pathogens from other individuals or animals infect a person, resulting in harm to both individuals and society as a whole. The outbreak of such diseases can pose a significant threat to human health. However, early detection and tracking of these outbreaks have the potential to reduce the mortality impact. To address these threats, public health authorities have endeavored to establish comprehensive mechanisms for collecting disease data. Many countries have implemented infectious disease surveillance systems, with the detection of epidemics being a primary objective. The clinical healthcare system, local/state health agencies, federal agencies, academic/professional groups, and collaborating governmental entities all play pivotal roles within this system. Moreover, nowadays, search engines and social media platforms can serve as valuable tools for monitoring disease trends. The Internet and social media have become significant platforms where users share information about their preferences and relationships. This real-time information can be harnessed to gauge the influence of ideas and societal opinions, making it highly useful across various domains and research areas, such as marketing campaigns, financial predictions, and public health, among others. This article provides a review of the existing standard methods developed by researchers for detecting outbreaks using time series data. These methods leverage various data sources, including conventional data sources and social media data or Internet data sources. The review particularly concentrates on works published within the timeframe of 2015 to 2022.

Informative path planning (IPP) applied to bathymetric mapping allows AUVs to focus on feature-rich areas to quickly reduce uncertainty and increase mapping efficiency. Existing methods based on Bayesian optimization (BO) over Gaussian Process (GP) maps work well on small scenarios but they are short-sighted and computationally heavy when mapping larger areas, hindering deployment in real applications. To overcome this, we present a 2-layered BO IPP method that performs non-myopic, real-time planning in a tree search fashion over large Stochastic Variational GP maps, while respecting the AUV motion constraints and accounting for localization uncertainty. Our framework outperforms the standard industrial lawn-mowing pattern and a myopic baseline in a set of hardware in the loop (HIL) experiments in an embedded platform over real bathymetry.

Recent works have demonstrated the vulnerability of Deep Reinforcement Learning (DRL) algorithms against training-time, backdoor poisoning attacks. These attacks induce pre-determined, adversarial behavior in the agent upon observing a fixed trigger during deployment while allowing the agent to solve its intended task during training. Prior attacks rely on arbitrarily large perturbations to the agent's rewards to achieve both of these objectives - leaving them open to detection. Thus, in this work, we propose a new class of backdoor attacks against DRL which achieve state of the art performance while minimally altering the agent's rewards. These "inception" attacks train the agent to associate the targeted adversarial behavior with high returns by inducing a disjunction between the agent's chosen action and the true action executed in the environment during training. We formally define these attacks and prove they can achieve both adversarial objectives. We then devise an online inception attack which significantly out-performs prior attacks under bounded reward constraints.

Statistical inference tasks, such as constructing confidence regions or simultaneous confidence intervals, are often addressed by deriving distributional theory such as central limit theorems (CLTs) for the estimator in use. Due to the high dimensionality of modern science and engineering applications, there has been a surge of interests in deriving convergence results that are valid in a finite-sample manner. In Reinforcement Learning (RL), a discipline that underpins many recent machine learning breakthroughs (Agarwal et al. (2019); Sutton and Barto (2018)) one central question is to evaluate with confidence the quality of a given policy, measured by its value function. As RL is often modeled as decision making in Markov decision processes (MDPs), the task of statistical inference needs to accommodate the online nature of the sampling mechanism. Temporal Difference (TD) learning (Sutton (1988)) is arguably the most widely used algorithm designed for this purpose. TD learning, which is an instance of stochastic approximation (SA) method (Robbins and Monro (1951)), approximates the value function of a given policy in an iterative manner. Towards understanding the non-asymptotic convergence rate of TD to the target value function, extensive recent efforts have been made (see, e.g.