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We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs). The primary goal of our techniques is to improve performance by avoiding an exhaustive exploration of the state space, instead focussing on particularly relevant areas of the system, guided by heuristics. Our work builds on the previous results of Br{\'{a}}zdil et al., significantly extending it as well as refining several details and fixing errors. The presented framework focuses on probabilistic reachability, which is a core problem in verification, and is instantiated in two distinct scenarios. The first assumes that full knowledge of the MDP is available, in particular precise transition probabilities. It performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP without knowing the exact transition dynamics. Here, we obtain probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. In particular, the latter is an extension of statistical model-checking (SMC) for unbounded properties in MDPs. In contrast to other related approaches, we do not restrict our attention to time-bounded (finite-horizon) or discounted properties, nor assume any particular structural properties of the MDP.

Dynamical low-rank approximation (DLRA) provides a rigorous, cost-effective mathematical framework for solving high-dimensional tensor differential equations (TDEs) on low-rank tensor manifolds. Despite their effectiveness, DLRA-based low-rank approximations lose their computational efficiency when applied to nonlinear TDEs, particularly those exhibiting non-polynomial nonlinearity. In this paper, we present a novel algorithm for the time integration of TDEs on the tensor train and Tucker tensor low-rank manifolds, which are the building blocks of many tensor network decompositions. This paper builds on our previous work (Donello et al., Proceedings of the Royal Society A, Vol. 479, 2023) on solving nonlinear matrix differential equations on low-rank matrix manifolds using CUR decompositions. The methodology we present offers multiple advantages: (i) it leverages cross algorithms based on the discrete empirical interpolation method to strategically sample sparse entries of the time-discrete TDEs to advance the solution in low-rank form. As a result, it offers near-optimal computational savings both in terms of memory and floating-point operations. (ii) The time integration is robust in the presence of small or zero singular values. (iii) The algorithm is remarkably easy to implement, as it requires the evaluation of the full-order model TDE at strategically selected entries and it does not use tangent space projections, whose efficient implementation is intrusive and time-consuming. (iv) We develop high-order explicit Runge-Kutta schemes for the time integration of TDEs on low-rank manifolds. We demonstrate the efficiency of the presented algorithm for several test cases, including a 100-dimensional TDE with non-polynomial nonlinearity.

We give an operational definition of information-theoretic resources within a given multipartite classical or quantum correlation. We present our causal model that serves as the source coding side of this correlation and introduce a novel concept of resource rate. We argue that, beyond classical secrecy, additional resources exist that are useful for the security of distributed computing problems, which can be captured by the resource rate. Furthermore, we establish a relationship between resource rate and an extension of Shannon's logarithmic information measure, namely, total correlation. Subsequently, we present a novel quantum secrecy monotone and investigate a quantum hybrid key distribution system as an extension of our causal model. Finally, we discuss some connections to optimal transport (OT) problem.

We study the sample complexity of learning an $\epsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. For weakly communicating MDPs, we establish the complexity bound $\tilde{O}(SA\frac{H}{\epsilon^2})$, where $H$ is the span of the bias function of the optimal policy and $SA$ is the cardinality of the state-action space. Our result is the first that is minimax optimal (up to log factors) in all parameters $S,A,H$ and $\epsilon$, improving on existing work that either assumes uniformly bounded mixing times for all policies or has suboptimal dependence on the parameters. We further investigate sample complexity in general (non-weakly-communicating) average-reward MDPs. We argue a new transient time parameter $B$ is necessary, establish an $\tilde{O}(SA\frac{B+H}{\epsilon^2})$ complexity bound, and prove a matching (up to log factors) minimax lower bound. Both results are based on reducing the average-reward MDP to a discounted MDP, which requires new ideas in the general setting. To establish the optimality of this reduction, we develop improved bounds for $\gamma$-discounted MDPs, showing that $\tilde{\Omega}\left(SA\frac{H}{(1-\gamma)^2\epsilon^2}\right)$ samples suffice to learn an $\epsilon$-optimal policy in weakly communicating MDPs under the regime that $\gamma\geq 1-1/H$, and $\tilde{\Omega}\left(SA\frac{B+H}{(1-\gamma)^2\epsilon^2}\right)$ samples suffice in general MDPs when $\gamma\geq 1-\frac{1}{B+H}$. Both these results circumvent the well-known lower bound of $\tilde{\Omega}\left(SA\frac{1}{(1-\gamma)^3\epsilon^2}\right)$ for arbitrary $\gamma$-discounted MDPs. Our analysis develops upper bounds on certain instance-dependent variance parameters in terms of the span and transient time parameters. The weakly communicating bounds are tighter than those based on the mixing time or diameter of the MDP and may be of broader use.

This survey provides an exhaustive review of the applications of extended reality (XR) technologies in the field of remote human-computer interaction (HRI). We developed a systematic search strategy based on the PRISMA methodology. From the initial 2,561 articles selected, 100 research papers that met our inclusion criteria were included. We categorized and summarized the domain in detail, delving into XR technologies, including augmented reality (AR), virtual reality (VR), and mixed reality (MR), and their applications in facilitating intuitive and effective remote control and interaction with robotic systems.The survey highlights existing articles on the application of XR technologies, user experience enhancement, and various interaction designs for XR in remote HRI, providing insights into current trends and future directions. We also identified potential gaps and opportunities for future research to improve remote HRI systems through XR technology to guide and inform future XR and robotics research.

Optimal behaviours of a system to perform a specific task can be achieved by leveraging the coupling between trajectory optimization, stabilization, and design optimization. This approach is particularly advantageous for underactuated systems, which are systems that have fewer actuators than degrees of freedom and thus require for more elaborate control systems. This paper proposes a novel co-design algorithm, namely Robust Trajectory Control with Design optimization (RTC-D). An inner optimization layer (RTC) simultaneously performs direct transcription (DIRTRAN) to find a nominal trajectory while computing optimal hyperparameters for a stabilizing time-varying linear quadratic regulator (TVLQR). RTC-D augments RTC with a design optimization layer, maximizing the system's robustness through a time-varying Lyapunov-based region of attraction (ROA) analysis. This analysis provides a formal guarantee of stability for a set of off-nominal states. The proposed algorithm has been tested on two different underactuated systems: the torque-limited simple pendulum and the cart-pole. Extensive simulations of off-nominal initial conditions demonstrate improved robustness, while real-system experiments show increased insensitivity to torque disturbances.

Differentiable physics simulation provides an avenue to tackle previously intractable challenges through gradient-based optimization, thereby greatly improving the efficiency of solving robotics-related problems. To apply differentiable simulation in diverse robotic manipulation scenarios, a key challenge is to integrate various materials in a unified framework. We present SoftMAC, a differentiable simulation framework that couples soft bodies with articulated rigid bodies and clothes. SoftMAC simulates soft bodies with the continuum-mechanics-based Material Point Method (MPM). We provide a novel forecast-based contact model for MPM, which effectively reduces penetration without introducing other artifacts like unnatural rebound. To couple MPM particles with deformable and non-volumetric clothes meshes, we also propose a penetration tracing algorithm that reconstructs the signed distance field in local area. Diverging from previous works, SoftMAC simulates the complete dynamics of each modality and incorporates them into a cohesive system with an explicit and differentiable coupling mechanism. The feature empowers SoftMAC to handle a broader spectrum of interactions, such as soft bodies serving as manipulators and engaging with underactuated systems. We conducted comprehensive experiments to validate the effectiveness and accuracy of the proposed differentiable pipeline in downstream robotic manipulation applications. Supplementary materials and videos are available on our project website at //sites.google.com/view/softmac.

We present a comparative study between cross-encoder and LLMs rerankers in the context of re-ranking effective SPLADE retrievers. We conduct a large evaluation on TREC Deep Learning datasets and out-of-domain datasets such as BEIR and LoTTE. In the first set of experiments, we show how cross-encoder rerankers are hard to distinguish when it comes to re-rerank SPLADE on MS MARCO. Observations shift in the out-of-domain scenario, where both the type of model and the number of documents to re-rank have an impact on effectiveness. Then, we focus on listwise rerankers based on Large Language Models -- especially GPT-4. While GPT-4 demonstrates impressive (zero-shot) performance, we show that traditional cross-encoders remain very competitive. Overall, our findings aim to to provide a more nuanced perspective on the recent excitement surrounding LLM-based re-rankers -- by positioning them as another factor to consider in balancing effectiveness and efficiency in search systems.

Underlying data distributions of natural language, programming code, and mathematical symbols vary vastly, presenting a complex challenge for large language models (LLMs) that strive to achieve high performance across all three domains simultaneously. Achieving a very high level of proficiency for an LLM within a specific domain often requires extensive training with relevant corpora, which is typically accompanied by a sacrifice in performance in other domains. In this paper, we propose to fuse models that are already highly-specialized directly. The proposed fusing framework, UltraFuser, consists of three distinct specialists that are already sufficiently trained on language, coding, and mathematics. A token-level gating mechanism is introduced to blend the specialists' outputs. A two-stage training strategy accompanied by balanced sampling is designed to ensure stability. To effectively train the fused model, we further construct a high-quality supervised instruction tuning dataset, UltraChat 2, which includes text, code, and mathematical content. This dataset comprises approximately 300,000 instructions and covers a wide range of topics in each domain. Experiments show that our model could simultaneously achieve mastery of the three crucial domains.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.