The Constrained Markov Decision Process (CMDP) formulation allows to solve safety-critical decision making tasks that are subject to constraints. While CMDPs have been extensively studied in the Reinforcement Learning literature, little attention has been given to sampling-based planning algorithms such as MCTS for solving them. Previous approaches perform conservatively with respect to costs as they avoid constraint violations by using Monte Carlo cost estimates that suffer from high variance. We propose Constrained MCTS (C-MCTS), which estimates cost using a safety critic that is trained with Temporal Difference learning in an offline phase prior to agent deployment. The critic limits exploration by pruning unsafe trajectories within MCTS during deployment. C-MCTS satisfies cost constraints but operates closer to the constraint boundary, achieving higher rewards than previous work. As a nice byproduct, the planner is more efficient w.r.t. planning steps. Most importantly, under model mismatch between the planner and the real world, C-MCTS is less susceptible to cost violations than previous work.

We focus on the problem of imitation learning from visual observations, where the learning agent has access to videos of experts as its sole learning source. The challenges of this framework include the absence of expert actions and the partial observability of the environment, as the ground-truth states can only be inferred from pixels. To tackle this problem, we first conduct a theoretical analysis of imitation learning in partially observable environments. We establish upper bounds on the suboptimality of the learning agent with respect to the divergence between the expert and the agent latent state-transition distributions. Motivated by this analysis, we introduce an algorithm called Latent Adversarial Imitation from Observations, which combines off-policy adversarial imitation techniques with a learned latent representation of the agent's state from sequences of observations. In experiments on high-dimensional continuous robotic tasks, we show that our algorithm matches state-of-the-art performance while providing significant computational advantages. Additionally, we show how our method can be used to improve the efficiency of reinforcement learning from pixels by leveraging expert videos. To ensure reproducibility, we provide free access to our code.

This paper studies the problem of risk-averse receding horizon motion planning for agents with uncertain dynamics, in the presence of stochastic, dynamic obstacles. We propose a model predictive control (MPC) scheme that formulates the obstacle avoidance constraint using coherent risk measures. To handle disturbances, or process noise, in the state dynamics, the state constraints are tightened in a risk-aware manner to provide a disturbance feedback policy. We also propose a waypoint following algorithm that uses the proposed MPC scheme for discrete distributions and prove its risk-sensitive recursive feasibility while guaranteeing finite-time task completion. We further investigate some commonly used coherent risk metrics, namely, conditional value-at-risk (CVaR), entropic value-at-risk (EVaR), and g-entropic risk measures, and propose a tractable incorporation within MPC. We illustrate our framework via simulation studies.

Uncertainty is prevalent in engineering design, statistical learning, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measures of risk and related concepts. We survey the rapid development of risk measures over the last quarter century. From their beginning in financial engineering, we recount the spread to nearly all areas of engineering and applied mathematics. Solidly rooted in convex analysis, risk measures furnish a general framework for handling uncertainty with significant computational and theoretical advantages. We describe the key facts, list several concrete algorithms, and provide an extensive list of references for further reading. The survey recalls connections with utility theory and distributionally robust optimization, points to emerging applications areas such as fair machine learning, and defines measures of reliability.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

This article presents a comprehensive review of the Active Simultaneous Localization and Mapping (A-SLAM) research conducted over the past decade. It explores the formulation, applications, and methodologies employed in A-SLAM, particularly in trajectory generation and control-action selection, drawing on concepts from Information Theory (IT) and the Theory of Optimal Experimental Design (TOED). This review includes both qualitative and quantitative analyses of various approaches, deployment scenarios, configurations, path-planning methods, and utility functions within A-SLAM research. Furthermore, this article introduces a novel analysis of Active Collaborative SLAM (AC-SLAM), focusing on collaborative aspects within SLAM systems. It includes a thorough examination of collaborative parameters and approaches, supported by both qualitative and statistical assessments. This study also identifies limitations in the existing literature and suggests potential avenues for future research. This survey serves as a valuable resource for researchers seeking insights into A-SLAM methods and techniques, offering a current overview of A-SLAM formulation.

This paper addresses the problem of statistical inference for latent continuous-time stochastic processes, which is often intractable, particularly for discrete state space processes described by Markov jump processes. To overcome this issue, we propose a new tractable inference scheme based on an entropic matching framework that can be embedded into the well-known expectation propagation algorithm. We demonstrate the effectiveness of our method by providing closed-form results for a simple family of approximate distributions and apply it to the general class of chemical reaction networks, which are a crucial tool for modeling in systems biology. Moreover, we derive closed form expressions for point estimation of the underlying parameters using an approximate expectation maximization procedure. We evaluate the performance of our method on various chemical reaction network instantiations, including a stochastic Lotka-Voltera example, and discuss its limitations and potential for future improvements. Our proposed approach provides a promising direction for addressing complex continuous-time Bayesian inference problems.

The study of complex networks has significantly advanced our understanding of community structures which serves as a crucial feature of real-world graphs. Detecting communities in graphs is a challenging problem with applications in sociology, biology, and computer science. Despite the efforts of an interdisciplinary community of scientists, a satisfactory solution to this problem has not yet been achieved. This review article delves into the topic of community detection in graphs, which serves as a crucial role in understanding the organization and functioning of complex systems. We begin by introducing the concept of community structure, which refers to the arrangement of vertices into clusters, with strong internal connections and weaker connections between clusters. Then, we provide a thorough exposition of various community detection methods, including a new method designed by us. Additionally, we explore real-world applications of community detection in diverse networks. In conclusion, this comprehensive review provides a deep understanding of community detection in graphs. It serves as a valuable resource for researchers and practitioners in multiple disciplines, offering insights into the challenges, methodologies, and applications of community detection in complex networks.

In many multi-agent and high-dimensional robotic tasks, the controller can be designed in either a centralized or decentralized way. Correspondingly, it is possible to use either single-agent reinforcement learning (SARL) or multi-agent reinforcement learning (MARL) methods to learn such controllers. However, the relationship between these two paradigms remains under-studied in the literature. This work explores research questions in terms of robustness and performance of SARL and MARL approaches to the same task, in order to gain insight into the most suitable methods. We start by analytically showing the equivalence between these two paradigms under the full-state observation assumption. Then, we identify a broad subclass of \textit{Dec-POMDP} tasks where the agents are weakly or partially interacting. In these tasks, we show that partial observations of each agent are sufficient for near-optimal decision-making. Furthermore, we propose to exploit such partially observable MARL to improve the robustness of robots when joint or agent failures occur. Our experiments on both simulated multi-agent tasks and a real robot task with a mobile manipulator validate the presented insights and the effectiveness of the proposed robust robot learning method via partially observable MARL.

Trajectory prediction (TP) plays an important role in supporting the decision-making of Air Traffic Controllers (ATCOs). Traditional TP methods are deterministic and physics-based, with parameters that are calibrated using aircraft surveillance data harvested across the world. These models are, therefore, agnostic to the intentions of the pilots and ATCOs, which can have a significant effect on the observed trajectory, particularly in the lateral plane. This work proposes a generative method for lateral TP, using probabilistic machine learning to model the effect of the epistemic uncertainty arising from the unknown effect of pilot behaviour and ATCO intentions. The models are trained to be specific to a particular sector, allowing local procedures such as coordinated entry and exit points to be modelled. A dataset comprising a week's worth of aircraft surveillance data, passing through a busy sector of the United Kingdom's upper airspace, was used to train and test the models. Specifically, a piecewise linear model was used as a functional, low-dimensional representation of the ground tracks, with its control points determined by a generative model conditioned on partial context. It was found that, of the investigated models, a Bayesian Neural Network using the Laplace approximation was able to generate the most plausible trajectories in order to emulate the flow of traffic through the sector.