This gives rise to a rich collection oftopological relationships and conditions under which VE models are optimal for planning. Despite this effort, relatively little is known about the planning performance of models that fail to satisfy these conditions.

Model-based reinforcement learning agents must make compromises about which aspects of the environment their models should capture. The value equivalence (VE) principle posits that these compromises should be made considering the model's eventual use in value-based planning. Given sets of functions and policies, a model is said to be order-$k$ VE to the environment if $k$ applications of the Bellman operators induced by the policies produce the correct result when applied to the functions. Prior work investigated the classes of models induced by VE when we vary $k$ and the sets of policies and functions. This gives rise to a rich collection of topological relationships and conditions under which VE models are optimal for planning.

This gives rise to a rich collection of topological relationships and conditions under which VE models are optimal for planning. Despite this effort, relatively little is known about the planning performance of models that fail to satisfy these conditions.

In this supplement we give details of our theoretical results and experiments that had to be left out of the main paper due to space constraints. Section A.1.1 contains derivations of the properties and propositions presented in the main Section A.2 provides a detailed outline of the pipeline used across our experiments in the The numbering of equations, figures and citations resume from what is used in the main paper. This result directly follows from Definitions 1 and 2.Property 2. M( null, V) either contains m We will show the result by contradiction. In order to prove Proposition 2 we will need four lemmas which we state and prove below. It follows that H - dim[B ] = nm rank(A) rank(C).

Model-based reinforcement learning agents must make compromises about which aspects of the environment their models should capture. The value equivalence (VE) principle posits that these compromises should be made considering the model's eventual use in value-based planning. Given sets of functions and policies, a model is said to be order- k VE to the environment if k applications of the Bellman operators induced by the policies produce the correct result when applied to the functions. Prior work investigated the classes of models induced by VE when we vary k and the sets of policies and functions. This gives rise to a rich collection of topological relationships and conditions under which VE models are optimal for planning.

Model-based reinforcement learning agents must make compromises about which aspects of the environment their models should capture. The value equivalence (VE) principle posits that these compromises should be made considering the model's eventual use in value-based planning. Given sets of functions and policies, a model is said to be order- k VE to the environment if k applications of the Bellman operators induced by the policies produce the correct result when applied to the functions. Prior work investigated the classes of models induced by VE when we vary k and the sets of policies and functions. This gives rise to a rich collection of topological relationships and conditions under which VE models are optimal for planning.

Early fault detection and fault prognosis are crucial to ensure efficient and safe operations of complex engineering systems such as the Spallation Neutron Source (SNS) and its power electronics (high voltage converter modulators). Following an advanced experimental facility setup that mimics SNS operating conditions, the authors successfully conducted 21 fault prognosis experiments, where fault precursors are introduced in the system to a degree enough to cause degradation in the waveform signals, but not enough to reach a real fault. Nine different machine learning techniques based on ensemble trees, convolutional neural networks, support vector machines, and hierarchical voting ensembles are proposed to detect the fault precursors. Although all 9 models have shown a perfect and identical performance during the training and testing phase, the performance of most models has decreased in the prognosis phase once they got exposed to real-world data from the 21 experiments. The hierarchical voting ensemble, which features multiple layers of diverse models, maintains a distinguished performance in early detection of the fault precursors with 95% success rate (20/21 tests), followed by adaboost and extremely randomized trees with 52% and 48% success rates, respectively. The support vector machine models were the worst with only 24% success rate (5/21 tests). The study concluded that a successful implementation of machine learning in the SNS or particle accelerator power systems would require a major upgrade in the controller and the data acquisition system to facilitate streaming and handling big data for the machine learning models. In addition, this study shows that the best performing models were diverse and based on the ensemble concept to reduce the bias and hyperparameter sensitivity of individual models.

This paper uses the peridynamic theory, which is well-suited to crack studies, to predict the crack patterns in a moving disk and classify them according to the modes and finally perform regression analysis. In that way, the crack patterns are obtained according to each mode by Molecular Dynamic (MD) simulation using the peridynamics. Image classification and regression studies are conducted through Convolutional Neural Networks (CNNs) and the neural processes. First, we increased the amount and quality of the data using peridynamics, which can theoretically compensate for the problems of the finite element method (FEM) in generating crack pattern images. Second, we did the case study for the PMB, LPS, and VES models that were obtained using the peridynamic theory. Case studies were performed to classify the images using CNNs and determine the PMB, LBS, and VES models' suitability. Finally, we performed the regression analysis for the images of the crack patterns with neural processes to predict the crack patterns. In the regression problem, by representing the results of the variance according to the epochs, it can be confirmed that the result of the variance is decreased by increasing the epoch numbers through the neural processes. The most critical point of this study is that the neural processes make an accurate prediction even if there are missing or insufficient training data.

We look at whether machine learning can predict the final objective function value of a difficult combinatorial optimisation problem from the input. Our context is the pattern reduction problem, one industrially important but difficult aspect of the cutting stock problem. Machine learning appears to have higher prediction accuracy than a na\"ive model, reducing mean absolute percentage error (MAPE) from 12.0% to 8.7%.

Public road authorities and private mobility service providers need information derived from the current and predicted traffic states to act upon the daily urban system and its spatial and temporal dynamics. In this research, a real-time parking area state (occupancy, in- and outflux) prediction model (up to 60 minutes ahead) has been developed using publicly available historic and real time data sources. Based on a case study in a real-life scenario in the city of Arnhem, a Neural Network-based approach outperforms a Random Forest-based one on all assessed performance measures, although the differences are small. Both are outperforming a naive seasonal random walk model. Although the performance degrades with increasing prediction horizon, the model shows a performance gain of over 150% at a prediction horizon of 60 minutes compared with the naive model. Furthermore, it is shown that predicting the in- and outflux is a far more difficult task (i.e. performance gains of 30%) which needs more training data, not based exclusively on occupancy rate. However, the performance of predicting in- and outflux is less sensitive to the prediction horizon. In addition, it is shown that real-time information of current occupancy rate is the independent variable with the highest contribution to the performance, although time, traffic flow and weather variables also deliver a significant contribution. During real-time deployment, the model performs three times better than the naive model on average. As a result, it can provide valuable information for proactive traffic management as well as mobility service providers.