Model-based reinforcement learning (MBRL) seeks to enhance data efficiency by learning a model of the environment and generating synthetic rollouts from it. However, accumulated model errors during these rollouts can distort the data distribution, negatively impacting policy learning and hindering long-term planning. Thus, the accumulation of model errors is a key bottleneck in current MBRL methods. We propose Infoprop, a model-based rollout mechanism that separates aleatoric from epistemic model uncertainty and reduces the influence of the latter on the data distribution. Further, Infoprop keeps track of accumulated model errors along a model rollout and provides termination criteria to limit data corruption. We demonstrate the capabilities of Infoprop in the Infoprop-Dyna algorithm, reporting state-of-the-art performance in Dyna-style MBRL on common MuJoCo benchmark tasks while substantially increasing rollout length and data quality.

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct *statistical tests of functionals of conditional distributions*. These tests identify the inputs where the functionals differ with high probability, and include tests of conditional moments or two-sample tests. Our key idea is to transform confidence bounds of a learning method into a test of conditional expectations. We instantiate this principle for kernel ridge regression (KRR) with subgaussian noise. An intermediate data embedding then enables more general tests — including *conditional two-sample tests* — via kernel mean embeddings of distributions. To have guarantees in this setting, we generalize existing pointwise-in-time or time-uniform confidence bounds for KRR to previously-inaccessible yet essential cases such as infinite-dimensional outputs with non-trace-class kernels. These bounds also circumvent the need for independent data, allowing for instance online sampling. To make our tests readily applicable in practice, we introduce bootstrapping schemes leveraging the parametric form of testing thresholds identified in theory to avoid tuning inaccessible parameters. We illustrate the tests on examples, including one in process monitoring and comparison of dynamical systems. Overall, our results establish a comprehensive foundation for conditional testing on functionals, from theoretical guarantees to an algorithmic implementation, and advance the state of the art on confidence bounds for vector-valued least squares estimation.

Kernel-based statistical learning on distributional inputs appears in many relevant applications, from medical diagnostics to causal inference, and poses intriguing theoretical questions. While this learning scenario received considerable attention from the machine learning community recently, many gaps in the theory remain. In particular, most works consider only the distributional regression setting, and focus on the regularized least-squares algorithm for this problem. In this work, we start to fill these gaps. We prove two oracle inequalities for kernel machines in general distributional learning scenarios, as well as a generalization result based on algorithmic stability. Our main results are formulated in great generality, utilizing general Hilbertian embeddings, which makes them applicable to a wide array of approaches to distributional learning. Additionally, we specialize our results to the cases of kernel mean embeddings and of the recently introduced Hilbertian embeddings based on sliced Wasserstein distances, providing concrete instances of the general setup. Our results considerably enlarge the scope of theoretically grounded distributional learning, and provide many interesting avenues for future work.

Dyna-style model-based reinforcement learning (MBRL) combines model-free agents with predictive transition models through model-based rollouts. This combination raises a critical question: “When to trust your model?”; i.e., which rollout length results in the model providing useful data? Janner et al. (2019) address this question by gradually increasing rollout lengths throughout the training. While theoretically tempting, uniform model accuracy is a fallacy that collapses at the latest when extrapolating. Instead, we propose asking the question “Where to trust your model?”. Using inherent model uncertainty to consider local accuracy, we obtain the Model-Based Actor-Critic with Uncertainty-Aware Rollout Adaption (MACURA) algorithm. We propose an easy-to-tune rollout mechanism and demonstrate substantial improvements in data efficiency and performance compared to state-of-the-art deep MBRL methods on the MuJoCo benchmark.

The consistency of a learning method is usually established under the assumption that the observations are a realization of an independent and identically distributed (i.i.d.) or mixing process. Yet, kernel methods such as support vector machines (SVMs), Gaussian processes, or conditional kernel mean embeddings (CKMEs) all give excellent performance under sampling schemes that are obviously non-i.i.d., such as when data comes from a dynamical system. We propose the new notion of empirical weak convergence (EWC) as a general assumption explaining such phenomena for kernel methods. It assumes the existence of a random asymptotic data distribution and is a strict weakening of previous assumptions in the field. Our main results then establish consistency of SVMs, kernel mean embeddings, and general Hilbert-space valued empirical expectations with EWC data. Our analysis holds for both finite- and infinite-dimensional outputs, as we extend classical results of statistical learning to the latter case. In particular, it is also applicable to CKMEs. Overall, our results open new classes of processes to statistical learning and can serve as a foundation for a theory of learning beyond i.i.d. and mixing.

Machine learning and deep learning have been used extensively to classify physical surfaces through images and time-series contact data. However, these methods rely on human expertise and entail the time-consuming processes of data and parameter tuning. To overcome these challenges, we propose an easily implemented framework that can directly handle heterogeneous data sources for classification tasks. Our data-versus-data approach automatically quantifies distinctive differences in distributions in a high-dimensional space via kernel two-sample testing between two sets extracted from multimodal data (e.g., images, sounds, haptic signals). We demonstrate the effectiveness of our technique by benchmarking against expertly engineered classifiers for visual-audio-haptic surface recognition due to the industrial relevance, difficulty, and competitive baselines of this application; ablation studies confirm the utility of key components of our pipeline. As shown in our open-source code, we achieve 97.2% accuracy on a standard multi-user dataset with 108 surface classes, outperforming the state-of-the-art machine-learning algorithm by 6% on a more difficult version of the task. The fact that our classifier obtains this performance with minimal data processing in the standard algorithm setting reinforces the powerful nature of kernel methods for learning to recognize complex patterns.Note to Practitioners—We demonstrate how to apply the kernel two-sample test to a surface-recognition task, discuss opportunities for improvement, and explain how to use this framework for other classification problems with similar properties. Automating surface recognition could benefit both surface inspection and robot manipulation. Our algorithm quantifies class similarity and therefore outputs an ordered list of similar surfaces. This technique is well suited for quality assurance and documentation of newly received materials or newly manufactured parts. More generally, our automated classification pipeline can handle heterogeneous data sources including images and high-frequency time-series measurements of vibrations, forces and other physical signals. As our approach circumvents the time-consuming process of feature engineering, both experts and non-experts can use it to achieve high-accuracy classification. It is particularly appealing for new problems without existing models and heuristics. In addition to strong theoretical properties, the algorithm is straightforward to use in practice since it requires only kernel evaluations. Its transparent architecture can provide fast insights into the given use case under different sensing combinations without costly optimization. Practitioners can also use our procedure to obtain the minimum data-acquisition time for independent time-series data from new sensor recordings.