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In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly beneficial in suggesting the most informative data points to be used when fitting a model. Reducing the number of observations needed for model development alleviates both the computational burden required for training and the operational expenses related to labeling. Online active learning, in particular, is useful in high-volume production processes where the decision about the acquisition of the label for a data point needs to be taken within an extremely short time frame. However, despite the recent efforts to develop online active learning strategies, the behavior of these methods in the presence of outliers has not been thoroughly examined. In this work, we investigate the performance of online active linear regression in contaminated data streams. Our study shows that the currently available query strategies are prone to sample outliers, whose inclusion in the training set eventually degrades the predictive performance of the models. To address this issue, we propose a solution that bounds the search area of a conditional D-optimal algorithm and uses a robust estimator. Our approach strikes a balance between exploring unseen regions of the input space and protecting against outliers. Through numerical simulations, we show that the proposed method is effective in improving the performance of online active learning in the presence of outliers, thus expanding the potential applications of this powerful tool.

The proliferation of automated data collection schemes and the advances in sensorics are increasing the amount of data we are able to monitor in real-time. However, given the high annotation costs and the time required by quality inspections, data is often available in an unlabeled form. This is fostering the use of active learning for the development of soft sensors and predictive models. In production, instead of performing random inspections to obtain product information, labels are collected by evaluating the information content of the unlabeled data. Several query strategy frameworks for regression have been proposed in the literature but most of the focus has been dedicated to the static pool-based scenario. In this work, we propose a new strategy for the stream-based scenario, where instances are sequentially offered to the learner, which must instantaneously decide whether to perform the quality check to obtain the label or discard the instance. The approach is inspired by the optimal experimental design theory and the iterative aspect of the decision-making process is tackled by setting a threshold on the informativeness of the unlabeled data points. The proposed approach is evaluated using numerical simulations and the Tennessee Eastman Process simulator. The results confirm that selecting the examples suggested by the proposed algorithm allows for a faster reduction in the prediction error.

Feature selection helps reduce data acquisition costs in ML, but the standard approach is to train models with static feature subsets. Here, we consider the dynamic feature selection (DFS) problem where a model sequentially queries features based on the presently available information. DFS is often addressed with reinforcement learning, but we explore a simpler approach of greedily selecting features based on their conditional mutual information. This method is theoretically appealing but requires oracle access to the data distribution, so we develop a learning approach based on amortized optimization. The proposed method is shown to recover the greedy policy when trained to optimality, and it outperforms numerous existing feature selection methods in our experiments, thus validating it as a simple but powerful approach for this problem.

We consider the problem of continuous-time policy evaluation. This consists in learning through observations the value function associated with an uncontrolled continuous-time stochastic dynamic and a reward function. We propose two original variants of the well-known TD(0) method using vanishing time steps. One is model-free and the other is model-based. For both methods, we prove theoretical convergence rates that we subsequently verify through numerical simulations. Alternatively, those methods can be interpreted as novel reinforcement learning approaches for approximating solutions of linear PDEs (partial differential equations) or linear BSDEs (backward stochastic differential equations).

The shift from the understanding and prediction of processes to their optimization offers great benefits to businesses and other organizations. Precisely timed process interventions are the cornerstones of effective optimization. Prescriptive process monitoring (PresPM) is the sub-field of process mining that concentrates on process optimization. The emerging PresPM literature identifies state-of-the-art methods, causal inference (CI) and reinforcement learning (RL), without presenting a quantitative comparison. Most experiments are carried out using historical data, causing problems with the accuracy of the methods' evaluations and preempting online RL. Our contribution consists of experiments on timed process interventions with synthetic data that renders genuine online RL and the comparison to CI possible, and allows for an accurate evaluation of the results. Our experiments reveal that RL's policies outperform those from CI and are more robust at the same time. Indeed, the RL policies approach perfect policies. Unlike CI, the unaltered online RL approach can be applied to other, more generic PresPM problems such as next best activity recommendations. Nonetheless, CI has its merits in settings where online learning is not an option.

We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this analysis, we then propose new end-to-end learning algorithms for training decision maps that output solutions of empirical risk minimization and distributionally robust optimization problems, two dominant modeling paradigms in optimization under uncertainty. Numerical results for a synthetic newsvendor problem illustrate the key differences between alternative training schemes. We also investigate an economic dispatch problem based on real data to showcase the impact of the neural network architecture of the decision maps on their test performance.

We study a sequential decision making problem between a principal and an agent with incomplete information on both sides. In this model, the principal and the agent interact in a stochastic environment, and each is privy to observations about the state not available to the other. The principal has the power of commitment, both to elicit information from the agent and to provide signals about her own information. The principal and the agent communicate their signals to each other, and select their actions independently based on this communication. Each player receives a payoff based on the state and their joint actions, and the environment moves to a new state. The interaction continues over a finite time horizon, and both players act to optimize their own total payoffs over the horizon. Our model encompasses as special cases stochastic games of incomplete information and POMDPs, as well as sequential Bayesian persuasion and mechanism design problems. We study both computation of optimal policies and learning in our setting. While the general problems are computationally intractable, we study algorithmic solutions under a conditional independence assumption on the underlying state-observation distributions. We present an polynomial-time algorithm to compute the principal's optimal policy up to an additive approximation. Additionally, we show an efficient learning algorithm in the case where the transition probabilities are not known beforehand. The algorithm guarantees sublinear regret for both players.

Online tuning of real-world plants is a complex optimisation problem that continues to require manual intervention by experienced human operators. Autonomous tuning is a rapidly expanding field of research, where learning-based methods, such as Reinforcement Learning-trained Optimisation (RLO) and Bayesian optimisation (BO), hold great promise for achieving outstanding plant performance and reducing tuning times. Which algorithm to choose in different scenarios, however, remains an open question. Here we present a comparative study using a routine task in a real particle accelerator as an example, showing that RLO generally outperforms BO, but is not always the best choice. Based on the study's results, we provide a clear set of criteria to guide the choice of algorithm for a given tuning task. These can ease the adoption of learning-based autonomous tuning solutions to the operation of complex real-world plants, ultimately improving the availability and pushing the limits of operability of these facilities, thereby enabling scientific and engineering advancements.

We introduce the mean inverse integrator (MII), a novel approach to increase the accuracy when training neural networks to approximate vector fields of dynamical systems from noisy data. This method can be used to average multiple trajectories obtained by numerical integrators such as Runge-Kutta methods. We show that the class of mono-implicit Runge-Kutta methods (MIRK) has particular advantages when used in connection with MII. When training vector field approximations, explicit expressions for the loss functions are obtained when inserting the training data in the MIRK formulae, unlocking symmetric and high-order integrators that would otherwise be implicit for initial value problems. The combined approach of applying MIRK within MII yields a significantly lower error compared to the plain use of the numerical integrator without averaging the trajectories. This is demonstrated with experiments using data from several (chaotic) Hamiltonian systems. Additionally, we perform a sensitivity analysis of the loss functions under normally distributed perturbations, supporting the favorable performance of MII.

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.