Adaptive mesh refinement (AMR) is necessary for efficient finite element simulations of complex physical phenomenon, as it allocates limited computational budget based on the need for higher or lower resolution, which varies over space and time. We present a novel formulation of AMR as a fully-cooperative Markov game, in which each element is an independent agent who makes refinement and de-refinement choices based on local information. We design a novel deep multi-agent reinforcement learning (MARL) algorithm called Value Decomposition Graph Network (VDGN), which solves the two core challenges that AMR poses for MARL: posthumous credit assignment due to agent creation and deletion, and unstructured observations due to the diversity of mesh geometries. For the first time, we show that MARL enables anticipatory refinement of regions that will encounter complex features at future times, thereby unlocking entirely new regions of the error-cost objective landscape that are inaccessible by traditional methods based on local error estimators. Comprehensive experiments show that VDGN policies significantly outperform error threshold-based policies in global error and cost metrics. We show that learned policies generalize to test problems with physical features, mesh geometries, and longer simulation times that were not seen in training. We also extend VDGN with multi-objective optimization capabilities to find the Pareto front of the tradeoff between cost and error.

符号回归是识别拟合从黑盒过程中观察到的输出的数学表达式的过程。它通常认为是一个离散的优化问题是NP - 硬。解决问题的前提方法包括神经引导的搜索（例如，使用强化学习）和遗传编程。在这项工作中，我们介绍了一种混合神经引导/基因编程方法来象征性回归和其他组合优化问题。我们提出了一种神经引导组件，用于种子随机重启遗传编程组件的起始群体，逐渐学习更好的起始群体。在许多常见的基准任务中从数据集中恢复底层表达式，我们的方法使用相同的实验设置恢复比最近发布的顶部执行模型更多的表达式65％。我们证明在没有对神经引导的组件上的不相互依存的情况下运行许多遗传编程一代，而不是比两个更强烈地耦合的替代配方更好地对象征性回归更好地执行符号回归。最后，我们介绍了一组新的22个符号回归基准问题，而现有的基准难度增加。源代码在www.github.com/brendenpetersen/deep-symbolic -optimization提供。

The performance of inertial navigation systems is largely dependent on the stable flow of external measurements and information to guarantee continuous filter updates and bind the inertial solution drift. Platforms in different operational environments may be prevented at some point from receiving external measurements, thus exposing their navigation solution to drift. Over the years, a wide variety of works have been proposed to overcome this shortcoming, by exploiting knowledge of the system current conditions and turning it into an applicable source of information to update the navigation filter. This paper aims to provide an extensive survey of information aided navigation, broadly classified into direct, indirect, and model aiding. Each approach is described by the notable works that implemented its concept, use cases, relevant state updates, and their corresponding measurement models. By matching the appropriate constraint to a given scenario, one will be able to improve the navigation solution accuracy, compensate for the lost information, and uncover certain internal states, that would otherwise remain unobservable.

We consider infinite horizon Markov decision processes (MDPs) with fast-slow structure, meaning that certain parts of the state space move "fast" (and in a sense, are more influential) while other parts transition more "slowly." Such structure is common in real-world problems where sequential decisions need to be made at high frequencies, yet information that varies at a slower timescale also influences the optimal policy. Examples include: (1) service allocation for a multi-class queue with (slowly varying) stochastic costs, (2) a restless multi-armed bandit with an environmental state, and (3) energy demand response, where both day-ahead and real-time prices play a role in the firm's revenue. Models that fully capture these problems often result in MDPs with large state spaces and large effective time horizons (due to frequent decisions), rendering them computationally intractable. We propose an approximate dynamic programming algorithmic framework based on the idea of "freezing" the slow states, solving a set of simpler finite-horizon MDPs (the lower-level MDPs), and applying value iteration (VI) to an auxiliary MDP that transitions on a slower timescale (the upper-level MDP). We also extend the technique to a function approximation setting, where a feature-based linear architecture is used. On the theoretical side, we analyze the regret incurred by each variant of our frozen-state approach. Finally, we give empirical evidence that the frozen-state approach generates effective policies using just a fraction of the computational cost, while illustrating that simply omitting slow states from the decision modeling is often not a viable heuristic.

In the present work we propose an unsupervised ensemble method consisting of oblique trees that can address the task of auto-encoding, namely Oblique Forest AutoEncoders (briefly OF-AE). Our method is a natural extension of the eForest encoder introduced in [1]. More precisely, by employing oblique splits consisting in multivariate linear combination of features instead of the axis-parallel ones, we will devise an auto-encoder method through the computation of a sparse solution of a set of linear inequalities consisting of feature values constraints. The code for reproducing our results is available at https://github.com/CDAlecsa/Oblique-Forest-AutoEncoders.

When robots learn reward functions using high capacity models that take raw state directly as input, they need to both learn a representation for what matters in the task -- the task ``features" -- as well as how to combine these features into a single objective. If they try to do both at once from input designed to teach the full reward function, it is easy to end up with a representation that contains spurious correlations in the data, which fails to generalize to new settings. Instead, our ultimate goal is to enable robots to identify and isolate the causal features that people actually care about and use when they represent states and behavior. Our idea is that we can tune into this representation by asking users what behaviors they consider similar: behaviors will be similar if the features that matter are similar, even if low-level behavior is different; conversely, behaviors will be different if even one of the features that matter differs. This, in turn, is what enables the robot to disambiguate between what needs to go into the representation versus what is spurious, as well as what aspects of behavior can be compressed together versus not. The notion of learning representations based on similarity has a nice parallel in contrastive learning, a self-supervised representation learning technique that maps visually similar data points to similar embeddings, where similarity is defined by a designer through data augmentation heuristics. By contrast, in order to learn the representations that people use, so we can learn their preferences and objectives, we use their definition of similarity. In simulation as well as in a user study, we show that learning through such similarity queries leads to representations that, while far from perfect, are indeed more generalizable than self-supervised and task-input alternatives.

While the capabilities of autonomous systems have been steadily improving in recent years, these systems still struggle to rapidly explore previously unknown environments without the aid of GPS-assisted navigation. The DARPA Subterranean (SubT) Challenge aimed to fast track the development of autonomous exploration systems by evaluating their performance in real-world underground search-and-rescue scenarios. Subterranean environments present a plethora of challenges for robotic systems, such as limited communications, complex topology, visually-degraded sensing, and harsh terrain. The presented solution enables long-term autonomy with minimal human supervision by combining a powerful and independent single-agent autonomy stack, with higher level mission management operating over a flexible mesh network. The autonomy suite deployed on quadruped and wheeled robots was fully independent, freeing the human supervision to loosely supervise the mission and make high-impact strategic decisions. We also discuss lessons learned from fielding our system at the SubT Final Event, relating to vehicle versatility, system adaptability, and re-configurable communications.

Deep learning models are known to put the privacy of their training data at risk, which poses challenges for their safe and ethical release to the public. Differentially private stochastic gradient descent is the de facto standard for training neural networks without leaking sensitive information about the training data. However, applying it to models for graph-structured data poses a novel challenge: unlike with i.i.d. data, sensitive information about a node in a graph cannot only leak through its gradients, but also through the gradients of all nodes within a larger neighborhood. In practice, this limits privacy-preserving deep learning on graphs to very shallow graph neural networks. We propose to solve this issue by training graph neural networks on disjoint subgraphs of a given training graph. We develop three random-walk-based methods for generating such disjoint subgraphs and perform a careful analysis of the data-generating distributions to provide strong privacy guarantees. Through extensive experiments, we show that our method greatly outperforms the state-of-the-art baseline on three large graphs, and matches or outperforms it on four smaller ones.

Machine learning models are typically evaluated by computing similarity with reference annotations and trained by maximizing similarity with such. Especially in the bio-medical domain, annotations are subjective and suffer from low inter- and intra-rater reliability. Since annotations only reflect the annotation entity's interpretation of the real world, this can lead to sub-optimal predictions even though the model achieves high similarity scores. Here, the theoretical concept of Peak Ground Truth (PGT) is introduced. PGT marks the point beyond which an increase in similarity with the reference annotation stops translating to better Real World Model Performance (RWMP). Additionally, a quantitative technique to approximate PGT by computing inter- and intra-rater reliability is proposed. Finally, three categories of PGT-aware strategies to evaluate and improve model performance are reviewed.

In this paper, we present a novel visual SLAM and long-term localization benchmark for autonomous driving in challenging conditions based on the large-scale 4Seasons dataset. The proposed benchmark provides drastic appearance variations caused by seasonal changes and diverse weather and illumination conditions. While significant progress has been made in advancing visual SLAM on small-scale datasets with similar conditions, there is still a lack of unified benchmarks representative of real-world scenarios for autonomous driving. We introduce a new unified benchmark for jointly evaluating visual odometry, global place recognition, and map-based visual localization performance which is crucial to successfully enable autonomous driving in any condition. The data has been collected for more than one year, resulting in more than 300 km of recordings in nine different environments ranging from a multi-level parking garage to urban (including tunnels) to countryside and highway. We provide globally consistent reference poses with up to centimeter-level accuracy obtained from the fusion of direct stereo-inertial odometry with RTK GNSS. We evaluate the performance of several state-of-the-art visual odometry and visual localization baseline approaches on the benchmark and analyze their properties. The experimental results provide new insights into current approaches and show promising potential for future research. Our benchmark and evaluation protocols will be available at https://www.4seasons-dataset.com/.