Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using kernel and inference methods. Here we build upon this limit and provide a field-theoretic formalism which covers the generalization properties of infinitely wide networks. We systematically compute generalization properties of linear, non-linear, and deep non-linear networks for kernel matrices with heterogeneous entries. In contrast to currently employed spectral methods we derive the generalization properties from the statistical properties of the input, elucidating the interplay of input dimensionality, size of the training data set, and variability of the data. We show that data variability leads to a non-Gaussian action reminiscent of a ($\varphi^3+\varphi^4$)-theory. Using our formalism on a synthetic task and on MNIST we obtain a homogeneous kernel matrix approximation for the learning curve as well as corrections due to data variability which allow the estimation of the generalization properties and exact results for the bounds of the learning curves in the case of infinitely many training data points.

We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose probability (with respect to the distribution of the uncertain inputs) of belonging to a given set is less than a given threshold. This problem, which we call Quantile Set Inversion (QSI), occurs for instance in the context of robust (reliability-based) optimization problems, when looking for the set of solutions that satisfy the constraints with sufficiently large probability. To solve the QSI problem, we propose a Bayesian strategy based on Gaussian process modeling and the Stepwise Uncertainty Reduction (SUR) principle, to sequentially choose the points at which the function should be evaluated to efficiently approximate the set of interest. We illustrate the performance and interest of the proposed SUR strategy through several numerical experiments.

Causal disentanglement aims to uncover a representation of data using latent variables that are interrelated through a causal model. Such a representation is identifiable if the latent model that explains the data is unique. In this paper, we focus on the scenario where unpaired observational and interventional data are available, with each intervention changing the mechanism of a latent variable. When the causal variables are fully observed, statistically consistent algorithms have been developed to identify the causal model under faithfulness assumptions. We here show that identifiability can still be achieved with unobserved causal variables, given a generalized notion of faithfulness. Our results guarantee that we can recover the latent causal model up to an equivalence class and predict the effect of unseen combinations of interventions, in the limit of infinite data. We implement our causal disentanglement framework by developing an autoencoding variational Bayes algorithm and apply it to the problem of predicting combinatorial perturbation effects in genomics.

Recent advances in reinforcement learning, for partially-observable Markov decision processes (POMDPs), rely on the biologically implausible backpropagation through time algorithm (BPTT) to perform gradient-descent optimisation. In this paper we propose a novel reinforcement learning algorithm that makes use of random feedback local online learning (RFLO), a biologically plausible approximation of realtime recurrent learning (RTRL) to compute the gradients of the parameters of a recurrent neural network in an online manner. By combining it with TD($\lambda$), a variant of temporaldifference reinforcement learning with eligibility traces, we create a biologically plausible, recurrent actor-critic algorithm, capable of solving discrete and continuous control tasks in POMDPs. We compare BPTT, RTRL and RFLO as well as different network architectures, and find that RFLO can perform just as well as RTRL while exceeding even BPTT in terms of complexity. The proposed method, called real-time recurrent reinforcement learning (RTRRL), serves as a model of learning in biological neural networks mimicking reward pathways in the mammalian brain.

This paper considers a class of reinforcement learning problems, which involve systems with two types of states: stochastic and pseudo-stochastic. In such systems, stochastic states follow a stochastic transition kernel while the transitions of pseudo-stochastic states are deterministic given the stochastic states/transitions. We refer to such systems as mixed systems, which are widely used in various applications, including manufacturing systems, communication networks, and queueing networks. We propose a sample efficient RL method that accelerates learning by generating augmented data samples. The proposed algorithm is data-driven and learns the policy from data samples from both real and augmented samples. This method significantly improves learning by reducing the sample complexity such that the dataset only needs to have sufficient coverage of the stochastic states. We analyze the sample complexity of the proposed method under Fitted Q Iteration (FQI) and demonstrate that the optimality gap decreases as $\tilde{\mathcal{O}}(\sqrt{{1}/{n}}+\sqrt{{1}/{m}}),$ where $n$ is the number of real samples and $m$ is the number of augmented samples per real sample. It is important to note that without augmented samples, the optimality gap is $\tilde{\mathcal{O}}(1)$ due to insufficient data coverage of the pseudo-stochastic states. Our experimental results on multiple queueing network applications confirm that the proposed method indeed significantly accelerates learning in both deep Q-learning and deep policy gradient.

Transformers [1] have lead to breakthroughs in training large-scale general representations for computer vision (CV) and natural language processing (NLP) [2], enabling zero-shot adaptation and fast finetuning [3]. At the same time, despite impressive progress, transformer-based representations haven't shown the same versatility for robotic manipulation. Some attribute this gap to the lack of suitable training data for robotics [3]. We argue instead that data relevant to training robotic manipulation models is copious but has important structure that most existing training methods ignore and fail to leverage. These insights lead us to propose a novel transformer-based architecture, called PLEX, that is capable of effective learning from realistically available robotic manipulation datasets. We observe that robotics-relevant data falls into three major categories: (1) Video-only data, which contain high-quality and potentially description-annotated demonstrations for an immense variety of tasks but have no explicit action information for a robot to mimic; (2) Data containing matching sequences of percepts and actions, which are less plentiful than pure videos and don't necessarily correspond to meaningful tasks [4], but capture valuable correlations between a robot's actions and changes in the environment and are easy to collect on a given robot; (3) Small sets of high-quality sensorimotor demonstrations for a target task in a target environment. Thus, a scalable model architecture for robotic manipulation must be able to learn primarily from videos, while being extra data-efficient on sensorimotor training sequences and the small amount target demonstrations. PLEX, the PLanning-EXecution architecture we propose, is designed to take advantage of data sources of these types.

We tackle the challenge of robotic bin packing with irregular objects, such as groceries. Given the diverse physical attributes of these objects and the complex constraints governing their placement and manipulation, employing preprogrammed strategies becomes unfeasible. Our approach is to learn directly from expert demonstrations in order to extract implicit task knowledge and strategies to ensure safe object positioning, efficient use of space, and the generation of human-like behaviors that enhance human-robot trust. We rely on human demonstrations to learn a Markov chain for predicting the object packing sequence for a given set of items and then compare it with human performance. Our experimental results show that the model outperforms human performance by generating sequence predictions that humans classify as human-like more frequently than human-generated sequences. The human demonstrations were collected using our proposed VR platform, BoxED, which is a box packaging environment for simulating real-world objects and scenarios for fast and streamlined data collection with the purpose of teaching robots. We collected data from 43 participants packing a total of 263 boxes with supermarket-like objects, yielding 4644 object manipulations. Our VR platform can be easily adapted to new scenarios and objects, and is publicly available, alongside our dataset, at https://github.com/andrejfsantos4/BoxED.

We present an unbiased method for Bayesian posterior means based on kinetic Langevin dynamics that combines advanced splitting methods with enhanced gradient approximations. Our approach avoids Metropolis correction by coupling Markov chains at different discretization levels in a multilevel Monte Carlo approach. Theoretical analysis demonstrates that our proposed estimator is unbiased, attains finite variance, and satisfies a central limit theorem. It can achieve accuracy $\epsilon>0$ for estimating expectations of Lipschitz functions in $d$ dimensions with $\mathcal{O}(d^{1/4}\epsilon^{-2})$ expected gradient evaluations, without assuming warm start. We exhibit similar bounds using both approximate and stochastic gradients, and our method's computational cost is shown to scale logarithmically with the size of the dataset. The proposed method is tested using a multinomial regression problem on the MNIST dataset and a Poisson regression model for soccer scores. Experiments indicate that the number of gradient evaluations per effective sample is independent of dimension, even when using inexact gradients. For product distributions, we give dimension-independent variance bounds. Our results demonstrate that the unbiased algorithm we present can be much more efficient than the ``gold-standard" randomized Hamiltonian Monte Carlo.

One of the goals of causal inference is to generalize from past experiments and observational data to novel conditions. While it is in principle possible to eventually learn a mapping from a novel experimental condition to an outcome of interest, provided a sufficient variety of experiments is available in the training data, coping with a large combinatorial space of possible interventions is hard. Under a typical sparse experimental design, this mapping is ill-posed without relying on heavy regularization or prior distributions. Such assumptions may or may not be reliable, and can be hard to defend or test. In this paper, we take a close look at how to warrant a leap from past experiments to novel conditions based on minimal assumptions about the factorization of the distribution of the manipulated system, communicated in the well-understood language of factor graph models. A postulated $\textit{interventional factor model}$ (IFM) may not always be informative, but it conveniently abstracts away a need for explicitly modeling unmeasured confounding and feedback mechanisms, leading to directly testable claims. Given an IFM and datasets from a collection of experimental regimes, we derive conditions for identifiability of the expected outcomes of new regimes never observed in these training data. We implement our framework using several efficient algorithms, and apply them on a range of semi-synthetic experiments.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there were finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, many real-world data are not naturally posed in the setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions, and then convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is further developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications.