High sample complexity hampers the successful application of reinforcement learning methods, especially in real-world problems where simulating complex dynamics is computationally demanding. Influence-based abstraction (IBA) was proposed to mitigate this issue by breaking down the global model of large-scale distributed systems, such as traffic control problems, into small local sub-models. Each local model includes only a few state variables and a representation of the influence exerted by the external portion of the system. This approach allows converting a complex simulator into local lightweight simulators, enabling more effective applications of planning and reinforcement learning methods. However, the effectiveness of IBA critically depends on the ability to accurately approximate the influence of each local model. While there are a few examples showing promising results in benchmark problems, the question of whether this approach is feasible in more practical scenarios remains open. In this work, we take steps towards addressing this question by conducting an extensive empirical study of learning models for influence approximations in various realistic domains, and evaluating how these models generalize over long horizons. We find that learning the influence is often a manageable learning task, even for complex and large systems. Additionally, we demonstrate the efficacy of the approximation models for long-horizon problems. By using short trajectories, we can learn accurate influence approximations for much longer horizons.

Lifetime analyses are crucial for ensuring the durability of new Light-emitting Diodes (LEDs) and uncertainty quantification (UQ) is necessary to quantify a lack of usable failure and degradation data. This work presents a new framework for predicting the lifetime of LEDs in terms of lumen maintenance, effectively quantifying the natural variability of lifetimes (aleatory) as well as the reducible uncertainty resulting from data scarcity (epistemic). Non-parametric survival models are employed for UQ of low-magnitude failures, while a new parametric interval prediction model (IPM) is introduced to characterize the uncertainty in high-magnitude lumen depreciation events and long-term extrapolated lifetimes. The width of interval-valued predictions reflects the inherent variability in degradation paths whilst the epistemic uncertainty, arising from data scarcity, is quantified by a statistical bound on the probability of the prediction errors for future degradation trajectories. A modified exponential flux decay model combined with the Arrhenius equation equips the IPM with physical information on the physics of LED luminous flux degradation. The framework is tested and validated on a novel database of LED degradation trajectories and in comparison to well-established probabilistic predictors. The results of this study support the validity of the proposed approach and the usefulness of the additional UQ capabilities.

This work investigates formal generalization error bounds that apply to support vector machines (SVMs) in realizable and agnostic learning problems. We focus on recently observed parallels between probably approximately correct (PAC)-learning bounds, such as compression and complexity-based bounds, and novel error guarantees derived within scenario theory. Scenario theory provides nonasymptotic and distributional-free error bounds for models trained by solving data-driven decision-making problems. Relevant theorems and assumptions are reviewed and discussed. We propose a numerical comparison of the tightness and effectiveness of theoretical error bounds for support vector classifiers trained on several randomized experiments from 13 real-life problems. This analysis allows for a fair comparison of different approaches from both conceptual and experimental standpoints. Based on the numerical results, we argue that the error guarantees derived from scenario theory are often tighter for realizable problems and always yield informative results, i.e., probability bounds tighter than a vacuous [0, 1] interval. This work promotes scenario theory as an alternative tool for model selection, structural-risk minimization, and generalization error analysis of SVMs. In this way, we hope to bring the communities of scenario and statistical learning theory closer, so that they can benefit from each other's insights.