--Efficient path optimization for drones in search and rescue operations faces challenges, including limited visibility, time constraints, and complex information gathering in urban environments. We present a comprehensive approach to optimize UA V-based search and rescue operations in neighborhood areas, utilizing both a 3D AirSim-ROS2 simulator and a 2D simulator . The path planning problem is formulated as a partially observable Markov decision process (POMDP), and we propose a novel "Shrinking POMCP" approach to address time constraints. In the AirSim environment, we integrate our approach with a probabilistic world model for belief maintenance and a neu-rosymbolic navigator for obstacle avoidance. The 2D simulator employs surrogate ROS2 nodes with equivalent functionality. We compare trajectories generated by different approaches in the 2D simulator and evaluate performance across various belief types in the 3D AirSim-ROS simulator . Experimental results from both simulators demonstrate that our proposed shrinking POMCP solution achieves significant improvements in search times compared to alternative methods, showcasing its potential for enhancing the efficiency of UA V-assisted search and rescue operations. Search and rescue (SAR) operations are critical, time-sensitive missions conducted in challenging environments like neighborhoods, wilderness [1], or maritime settings [2]. These resource-intensive operations require efficient path planning and optimal routing [3]. In recent years, Unmanned Aerial V ehicles (UA Vs) have become valuable SAR assets, offering advantages such as rapid deployment, extended flight times, and access to hard-to-reach areas. Equipped with sensors and cameras, UA Vs can detect heat signatures, identify objects, and provide real-time aerial imagery to search teams [4]. However, the use of UA Vs in SAR operations presents unique challenges, particularly in path planning and decision-making under uncertainty. Factors such as limited battery life, changing weather conditions, and incomplete information about the search area complicate the task of efficiently coordinating UA V movements to maximize the probability of locating targets [3].

Multiagent systems grapple with partial observability (PO), and the decentralized POMDP (Dec-POMDP) model highlights the fundamental nature of this challenge. Whereas recent approaches to addressing PO have appealed to deep learning models, providing a rigorous understanding of how these models and their approximation errors affect agents' handling of PO and their interactions remain a challenge. In addressing this challenge, we investigate reconstructing global states from local action-observation histories in Dec-POMDPs using diffusion models. We first find that diffusion models conditioned on local history represent possible states as stable fixed points. In collectively observable (CO) Dec-POMDPs, individual diffusion models conditioned on agents' local histories share a unique fixed point corresponding to the global state, while in non-CO settings, the shared fixed points yield a distribution of possible states given joint history. We further find that, with deep learning approximation errors, fixed points can deviate from true states and the deviation is negatively correlated to the Jacobian rank. Inspired by this low-rank property, we bound the deviation by constructing a surrogate linear regression model that approximates the local behavior of diffusion models. With this bound, we propose a composite diffusion process iterating over agents with theoretical convergence guarantees to the true state.

The Dreamer agent provides various benefits of Model-Based Reinforcement Learning (MBRL) such as sample efficiency, reusable knowledge, and safe planning. However, its world model and policy networks inherit the limitations of recurrent neural networks and thus an important question is how an MBRL framework can benefit from the recent advances of transformers and what the challenges are in doing so. In this paper, we propose a transformer-based MBRL agent, called TransDreamer. We first introduce the Transformer State-Space Model, a world model that leverages a transformer for dynamics predictions. We then share this world model with a transformer-based policy network and obtain stability in training a transformer-based RL agent. In experiments, we apply the proposed model to 2D visual RL and 3D first-person visual RL tasks both requiring long-range memory access for memory-based reasoning. We show that the proposed model outperforms Dreamer in these complex tasks.

Statistical process monitoring (SPM) methods are essential tools in quality management to check the stability of industrial processes, i.e., to dynamically classify the process state as in control (IC), under normal operating conditions, or out of control (OC), otherwise. Traditional SPM methods are based on unsupervised approaches, which are popular because in most industrial applications the true OC states of the process are not explicitly known. This hampered the development of supervised methods that could instead take advantage of process data containing labels on the true process state, although they still need improvement in dealing with class imbalance, as OC states are rare in high-quality processes, and the dynamic recognition of unseen classes, e.g., the number of possible OC states. This article presents a novel stream-based active learning strategy for SPM that enhances partially hidden Markov models to deal with data streams. The ultimate goal is to optimize labeling resources constrained by a limited budget and dynamically update the possible OC states. The proposed method performance in classifying the true state of the process is assessed through a simulation and a case study on the SPM of a resistance spot welding process in the automotive industry, which motivated this research.

Reinforcement learning (RL) is a promising method to learn optimal control policies for systems with unknown dynamics. In particular, synthesizing controllers for safety-critical systems based on high-level specifications, such as those expressed in temporal languages like linear temporal logic (LTL), presents a significant challenge in control systems research. Current RL-based methods designed for LTL tasks typically offer only asymptotic guarantees, which provide no insight into the transient performance during the learning phase. While running an RL algorithm, it is crucial to assess how close we are to achieving optimal behavior if we stop learning. In this paper, we present the first regret-free online algorithm for learning a controller that addresses the general class of LTL specifications over Markov decision processes (MDPs) with a finite set of states and actions. We begin by proposing a regret-free learning algorithm to solve infinite-horizon reach-avoid problems. For general LTL specifications, we show that the synthesis problem can be reduced to a reach-avoid problem when the graph structure is known. Additionally, we provide an algorithm for learning the graph structure, assuming knowledge of a minimum transition probability, which operates independently of the main regret-free algorithm.

Retrieving target objects from unknown, confined spaces remains a challenging task that requires integrated, task-driven active sensing and rearrangement planning. Previous approaches have independently addressed active sensing and rearrangement planning, limiting their practicality in real-world scenarios. This paper presents a new, integrated heuristic-based active sensing and Monte-Carlo Tree Search (MCTS)-based retrieval planning approach. These components provide feedback to one another to actively sense critical, unobserved areas suitable for the retrieval planner to plan a sequence for relocating path-blocking obstacles and a collision-free trajectory for retrieving the target object. We demonstrate the effectiveness of our approach using a robot arm equipped with an in-hand camera in both simulated and real-world confined, cluttered scenarios. Our framework is compared against various state-of-the-art methods. The results indicate that our proposed approach outperforms baseline methods by a significant margin in terms of the success rate, the object rearrangement planning time consumption and the number of planning trials before successfully retrieving the target. Videos can be found at https://youtu.be/tea7I-3RtV0.

Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant algebraic approach by listing exactly all the equality constraints on the observed variables. However, this algebraically motivated causal model comprises distributions outside Bayesian networks, and its physical interpretation remains vague. In this work, we inspect the nested Markov model through the lens of generalized probabilistic theory, an axiomatic framework to describe general physical theories. We prove that all the equality constraints defining the nested Markov model hold valid theory-independently. Yet, we show this model generally contains distributions not implementable even within such relaxed physical theories subjected to merely the relativity principles and mild probabilistic rules. To interpret the origin of such a gap, we establish a new causal model that defines valid distributions as projected from a high-dimensional Bell-type causal structure. The new model unveils inequality constraints induced by relativity principles, or equivalently high-dimensional conditional independences, which are absent in the nested Markov model. Nevertheless, we also notice that the restrictions on states and measurements introduced by the generalized probabilistic theory framework can pose additional inequality constraints beyond the new causal model. As a by-product, we discover a new causal structure exhibiting strict gaps between the distribution sets of a Bayesian network, generalized probabilistic theories, and the nested Markov model. We anticipate our results will enlighten further explorations on the unification of algebraic and physical perspectives of causality.

The Pairwise Markov Chain (PMC) is a probabilistic graphical model extending the well-known Hidden Markov Model. This model, although highly effective for many tasks, has been scarcely utilized for continuous value prediction. This is mainly due to the issue of modeling observations inherent in generative probabilistic models. In this paper, we introduce a new algorithm for prediction with the PMC. On the one hand, this algorithm allows circumventing the feature problem, thus fully exploiting the capabilities of the PMC. On the other hand, it enables the PMC to extend any predictive model by introducing hidden states, updated at each time step, and allowing the introduction of non-stationarity for any model. We apply the PMC with its new algorithm for volatility forecasting, which we compare to the highly popular GARCH(1,1) and feedforward neural models across numerous pairs. This is particularly relevant given the regime changes that we can observe in volatility. For each scenario, our algorithm enhances the performance of the extended model, demonstrating the value of our approach.

We consider the fundamental problem of learning the parameters of an undirected graphical model or Markov Random Field (MRF) in the setting where the edge weights are chosen at random. For Ising models, we show that a multiplicative-weight update algorithm due to Klivans and Meka learns the parameters in polynomial time for any inverse temperature $\beta \leq \sqrt{\log n}$. This immediately yields an algorithm for learning the Sherrington-Kirkpatrick (SK) model beyond the high-temperature regime of $\beta < 1$. Prior work breaks down at $\beta = 1$ and requires heavy machinery from statistical physics or functional inequalities. In contrast, our analysis is relatively simple and uses only subgaussian concentration. Our results extend to MRFs of higher order (such as pure $p$-spin models), where even results in the high-temperature regime were not known.

Imagine searching a collection of coins for quarters ($0.25$), dimes ($0.10$), nickels ($0.05$), and pennies ($0.01$)-a hybrid foraging task where observers look for multiple instances of multiple target types. In such tasks, how do target values and their prevalence influence foraging and eye movement behaviors (e.g., should you prioritize rare quarters or common nickels)? To explore this, we conducted human psychophysics experiments, revealing that humans are proficient reward foragers. Their eye fixations are drawn to regions with higher average rewards, fixation durations are longer on more valuable targets, and their cumulative rewards exceed chance, approaching the upper bound of optimal foragers. To probe these decision-making processes of humans, we developed a transformer-based Visual Forager (VF) model trained via reinforcement learning. Our VF model takes a series of targets, their corresponding values, and the search image as inputs, processes the images using foveated vision, and produces a sequence of eye movements along with decisions on whether to collect each fixated item. Our model outperforms all baselines, achieves cumulative rewards comparable to those of humans, and approximates human foraging behavior in eye movements and foraging biases within time-limited environments. Furthermore, stress tests on out-of-distribution tasks with novel targets, unseen values, and varying set sizes demonstrate the VF model's effective generalization. Our work offers valuable insights into the relationship between eye movements and decision-making, with our model serving as a powerful tool for further exploration of this connection. All data, code, and models will be made publicly available.