For robots operating in the real world, it is desirable to learn reusable behaviours that can effectively be transferred and adapted to numerous tasks and scenarios. We propose an approach to learn abstract motor skills from data using a hierarchical mixture latent variable model. In contrast to existing work, our method exploits a three-level hierarchy of both discrete and continuous latent variables, to capture a set of high-level behaviours while allowing for variance in how they are executed. We demonstrate in manipulation domains that the method can effectively cluster offline data into distinct, executable behaviours, while retaining the flexibility of a continuous latent variable model. The resulting skills can be transferred and fine-tuned on new tasks, unseen objects, and from state to vision-based policies, yielding better sample efficiency and asymptotic performance compared to existing skill- and imitation-based methods. We further analyse how and when the skills are most beneficial: they encourage directed exploration to cover large regions of the state space relevant to the task, making them most effective in challenging sparse-reward settings.

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First, the form and the parameters of the kernel function are usually selected blindly, depending seriously on trial-and-error. As a result, there may be serious performance degradation in case of inappropriate selections. Second, at the online monitoring stage, KPCA has much computational burden and poor real-time performance, because the kernel method requires to leverage all the offline training data. In this work, to deal with the two drawbacks, a learnable faster realization of the conventional KPCA is proposed. The core idea is to parameterize all feasible kernel functions using the novel nonlinear DAE-FE (deep autoencoder based feature extraction) framework and propose DAE-PCA (deep autoencoder based principal component analysis) approach in detail. The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs. Furthermore, the online computational efficiency improves by approximately 100 times compared with the conventional KPCA. With the Tennessee Eastman (TE) process benchmark, the effectiveness and superiority of the proposed method is illustrated.

We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes a subset of the processes at any given time instant and obtains a noisy binary indicator of whether or not the corresponding process is anomalous. In this setting, we develop an anomaly detection algorithm that chooses the processes to be observed at a given time instant, decides when to stop taking observations, and declares the decision on anomalous processes. The objective of the detection algorithm is to identify the anomalies with an accuracy exceeding the desired value while minimizing the delay in decision making. We devise a centralized algorithm where the processes are jointly selected by a common agent as well as a decentralized algorithm where the decision of whether to select a process is made independently for each process. Our algorithms rely on a Markov decision process defined using the marginal probability of each process being normal or anomalous, conditioned on the observations. We implement the detection algorithms using the deep actor-critic reinforcement learning framework. Unlike prior work on this topic that has exponential complexity in the number of processes, our algorithms have computational and memory requirements that are both polynomial in the number of processes. We demonstrate the efficacy of these algorithms using numerical experiments by comparing them with state-of-the-art methods.

A main research goal in various studies is to use an observational data set and provide a new set of counterfactual guidelines that can yield causal improvements. Dynamic Treatment Regimes (DTRs) are widely studied to formalize this process. However, available methods in finding optimal DTRs often rely on assumptions that are violated in real-world applications (e.g., medical decision-making or public policy), especially when (a) the existence of unobserved confounders cannot be ignored, and (b) the unobserved confounders are time-varying (e.g., affected by previous actions). When such assumptions are violated, one often faces ambiguity regarding the underlying causal model that is needed to be assumed to obtain an optimal DTR. This ambiguity is inevitable, since the dynamics of unobserved confounders and their causal impact on the observed part of the data cannot be understood from the observed data. Motivated by a case study of finding superior treatment regimes for patients who underwent transplantation in our partner hospital and faced a medical condition known as New Onset Diabetes After Transplantation (NODAT), we extend DTRs to a new class termed Ambiguous Dynamic Treatment Regimes (ADTRs), in which the casual impact of treatment regimes is evaluated based on a "cloud" of potential causal models. We then connect ADTRs to Ambiguous Partially Observable Mark Decision Processes (APOMDPs) proposed by Saghafian (2018), and develop two Reinforcement Learning methods termed Direct Augmented V-Learning (DAV-Learning) and Safe Augmented V-Learning (SAV-Learning), which enable using the observed data to efficiently learn an optimal treatment regime. We establish theoretical results for these learning methods, including (weak) consistency and asymptotic normality. We further evaluate the performance of these learning methods both in our case study and in simulation experiments.

In statistical decision theory, a model is said to be Pareto optimal (or admissible) if no other model carries less risk for at least one state of nature while presenting no more risk for others. How can you rationally aggregate/combine a finite set of Pareto optimal models while preserving Pareto efficiency? This question is nontrivial because weighted model averaging does not, in general, preserve Pareto efficiency. This paper presents an answer in four logical steps: (1) A rational aggregation rule should preserve Pareto efficiency (2) Due to the complete class theorem, Pareto optimal models must be Bayesian, i.e., they minimize a risk where the true state of nature is averaged with respect to some prior. Therefore each Pareto optimal model can be associated with a prior, and Pareto efficiency can be maintained by aggregating Pareto optimal models through their priors. (3) A prior can be interpreted as a preference ranking over models: prior $\pi$ prefers model A over model B if the average risk of A is lower than the average risk of B. (4) A rational/consistent aggregation rule should preserve this preference ranking: If both priors $\pi$ and $\pi'$ prefer model A over model B, then the prior obtained by aggregating $\pi$ and $\pi'$ must also prefer A over B. Under these four steps, we show that all rational/consistent aggregation rules are as follows: Give each individual Pareto optimal model a weight, introduce a weak order/ranking over the set of Pareto optimal models, aggregate a finite set of models S as the model associated with the prior obtained as the weighted average of the priors of the highest-ranked models in S. This result shows that all rational/consistent aggregation rules must follow a generalization of hierarchical Bayesian modeling. Following our main result, we present applications to Kernel smoothing, time-depreciating models, and voting mechanisms.

We consider the problem of Combinatorial Pure Exploration (CPE), which deals with finding a combinatorial set or arms with a high reward, when the rewards of individual arms are unknown in advance and must be estimated using arm pulls. Previous algorithms for this problem, while obtaining sample complexity reductions in many cases, are highly computationally intensive, thus making them impractical even for mildly large problems. In this work, we propose a new CPE algorithm in the PAC setting, which is computationally light weight, and so can easily be applied to problems with tens of thousands of arms. This is achieved since the proposed algorithm requires a very small number of combinatorial oracle calls. The algorithm is based on successive acceptance of arms, along with elimination which is based on the combinatorial structure of the problem. We provide sample complexity guarantees for our algorithm, and demonstrate in experiments its usefulness on large problems, whereas previous algorithms are impractical to run on problems of even a few dozen arms. The code for the algorithms and experiments is provided at https://github.com/noabdavid/csale.

Q-learning is a well-known and commonly used algorithm for reinforcement learning. In recent years, a technique referred to as experience replay [9, 11] has been suggested as a mechanism to improve Q-learning by allowing the learner to access previous experiences, and use them offline as if they were examples currently sampled from the world. It has been suggested that using past experiences in such a way might allow Q-learning to better converge to the optimal Q values, by breaking the time and space correlation structure of experiences as they are sampled from the real world, allowing for policy updates not dependent on the current time and location in the markov decision process. Moreover, using experience replay improves the efficiency of data usage, since every experience is used for learning more than once. This can be useful in situations where data acquirement is costly or difficult.

Using a model of the environment and a value function, an agent can construct many estimates of a state's value, by unrolling the model for different lengths and bootstrapping with its value function. Our key insight is that one can treat this set of value estimates as a type of ensemble, which we call an \emph{implicit value ensemble} (IVE). Consequently, the discrepancy between these estimates can be used as a proxy for the agent's epistemic uncertainty; we term this signal \emph{model-value inconsistency} or \emph{self-inconsistency} for short. Unlike prior work which estimates uncertainty by training an ensemble of many models and/or value functions, this approach requires only the single model and value function which are already being learned in most model-based reinforcement learning algorithms. We provide empirical evidence in both tabular and function approximation settings from pixels that self-inconsistency is useful (i) as a signal for exploration, (ii) for acting safely under distribution shifts, and (iii) for robustifying value-based planning with a model.

In probability, Bayes is a type of conditional probability. It predicts the event based on an event that has already happened. You can use Naive Bayes as a supervised machine learning method for predicting the event based on the evidence present in your dataset. In this tutorial, you will learn how to classify the email as spam or not using the Naive Bayes Classifier. Before doing coding demonstration, Let's know about the Naive Bayes in a brief.

Multiple techniques for producing calibrated predictive probabilities using deep neural networks in supervised learning settings have emerged that leverage approaches to ensemble diverse solutions discovered during cyclic training or training from multiple random starting points (deep ensembles). However, only a limited amount of work has investigated the utility of exploring the local region around each diverse solution (posterior mode). Using three well-known deep architectures on the CIFAR-10 dataset, we evaluate several simple methods for exploring local regions of the weight space with respect to Brier score, accuracy, and expected calibration error. We consider both Bayesian inference techniques (variational inference and Hamiltonian Monte Carlo applied to the softmax output layer) as well as utilizing the stochastic gradient descent trajectory near optima. While adding separate modes to the ensemble uniformly improves performance, we show that the simple mode exploration methods considered here produce little to no improvement over ensembles without mode exploration.