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Robotic Information Gathering (RIG) is a foundational research topic that answers how a robot (team) collects informative data to efficiently build an accurate model of an unknown target function under robot embodiment constraints. RIG has many applications, including but not limited to autonomous exploration and mapping, 3D reconstruction or inspection, search and rescue, and environmental monitoring. A RIG system relies on a probabilistic model’s prediction uncertainty to identify critical areas for informative data collection. Gaussian processes (GPs) with stationary kernels have been widely adopted for spatial modeling. However, real-world spatial data is typically non-stationary—different locations do not have the same degree of variability. As a result, the prediction uncertainty does not accurately reveal prediction error, limiting the success of RIG algorithms. We propose a family of non-stationary kernels named Attentive Kernel (AK), which is simple and robust and can extend any existing kernel to a non-stationary one. We evaluate the new kernel in elevation mapping tasks, where AK provides better accuracy and uncertainty quantification over the commonly used stationary kernels and the leading non-stationary kernels. The improved uncertainty quantification guides the downstream informative planner to collect more valuable data around the high-error area, further increasing prediction accuracy. A field experiment demonstrates that the proposed method can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in locations with significant spatial variations, enabling the model to characterize salient environmental features. 

Ensemble models (bagging and gradient-boosting) of relational decision trees have proved to be some of the most effective learning methods in the area of probabilistic logic models (PLMs). While effective, they lose one of the most important benefits of PLMs—interpretability. In this paper we consider the problem of compressing a large set of learned trees into a single explainable model. To this effect, we propose CoTE—Compression of Tree Ensembles—that produces a single small decision list as a compressed representation. CoTE first converts the trees to decision lists and then performs the combination and compression with the aid of the original training set. An experimental evaluation demonstrates the effectiveness of CoTE in several benchmark relational data sets. 

The paper introduces DiSProD, an online planner developed forenvironments with probabilistic transitions in continuous state andaction spaces. DiSProD builds a symbolic graph that captures thedistribution of future trajectories, conditioned on a given policy,using independence assumptions and approximate propagation ofdistributions. The symbolic graph provides a differentiablerepresentation of the policy's value, enabling efficient gradient-basedoptimization for long-horizon search. The propagation of approximatedistributions can be seen as an aggregation of many trajectories, makingit well-suited for dealing with sparse rewards and stochasticenvironments. An extensive experimental evaluation compares DiSProD tostate-of-the-art planners in discrete-time planning and real-timecontrol of robotic systems. The proposed method improves over existingplanners in handling stochastic environments, sensitivity to searchdepth, sparsity of rewards, and large action spaces. Additionalreal-world experiments demonstrate that DiSProD can control groundvehicles and surface vessels to successfully navigate around obstacles. 

The paper provides a thorough investigation of Direct Loss Minimization (DLM), which optimizes the posterior to minimize predictive loss, in sparse Gaussian processes. For the conjugate case, we consider DLM for log-loss and DLM for square loss showing a significant performance improvement in both cases. The application of DLM in non-conjugate cases is more complex because the logarithm of expectation in the log-loss DLM objective is often intractable and simple sampling leads to biased estimates of gradients. The paper makes two technical contributions to address this. First, a new method using product sampling is proposed, which gives unbiased estimates of gradients (uPS) for the objective function. Second, a theoretical analysis of biased Monte Carlo estimates (bMC) shows that stochastic gradient descent converges despite the biased gradients. Experiments demonstrate empirical success of DLM. A comparison of the sampling methods shows that, while uPS is potentially more sample-efficient, bMC provides a better tradeoff in terms of convergence time and computational efficiency.