Uncertainty in Physics and AI: Taxonomy, Quantification, and Validation

Reliable uncertainty quantification is essential for the use of machine learning in physics, where scientific discoveries depend on validated probabilistic statements. We provide a structured overview of uncertainty quantification in ML for physics, introducing a unified taxonomy of uncertainty and clarifying the interpretation of predictive and inference uncertainties across frequentist and Bayesian frameworks. We discuss principled validation tools, including coverage, calibration, bias tests, and proper scoring rules, and illustrate them with simple regression and classification examples.

Distributional Active Inference

Optimal control of complex environments with robotic systems faces two complementary and intertwined challenges: efficient organization of sensory state information and far-sighted action planning. Because the reinforcement learning framework addresses only the latter, it tends to deliver sample-inefficient solutions. Active inference is the state-of-the-art process theory that explains how biological brains handle this dual problem. However, its applications to artificial intelligence have thus far been limited to extensions of existing model-based approaches. We present a formal abstraction of reinforcement learning algorithms that spans model-based, distributional, and model-free approaches. This abstraction seamlessly integrates active inference into the distributional reinforcement learning framework, making its performance advantages accessible without transition dynamics modeling.

Improving Plasticity in Non-stationary Reinforcement Learning with Evidential Proximal Policy Optimization

On-policy reinforcement learning algorithms use the most recently learned policy to interact with the environment and update it using the latest gathered trajectories, making them well-suited for adapting to non-stationary environments where dynamics change over time. However, previous studies show that they struggle to maintain plasticity$\unicode{x2013}$the ability of neural networks to adjust their synaptic connections$\unicode{x2013}$with overfitting identified as the primary cause. To address this, we present the first application of evidential learning in an on-policy reinforcement learning setting: $\textit{Evidential Proximal Policy Optimization (EPPO)}$. EPPO incorporates all sources of error in the critic network's approximation$\unicode{x2013}$i.e., the baseline function in advantage calculation$\unicode{x2013}$by modeling the epistemic and aleatoric uncertainty contributions to the approximation's total variance. We achieve this by using an evidential neural network, which serves as a regularizer to prevent overfitting. The resulting probabilistic interpretation of the advantage function enables optimistic exploration, thus maintaining the plasticity. Through experiments on non-stationary continuous control tasks, where the environment dynamics change at regular intervals, we demonstrate that EPPO outperforms state-of-the-art on-policy reinforcement learning variants in both task-specific and overall return.

Latent mixed-effect models for high-dimensional longitudinal data

Modelling longitudinal data is an important yet challenging task. These datasets can be high-dimensional, contain non-linear effects and time-varying covariates. Gaussian process (GP) prior-based variational autoencoders (VAEs) have emerged as a promising approach due to their ability to model time-series data. However, they are costly to train and struggle to fully exploit the rich covariates characteristic of longitudinal data, making them difficult for practitioners to use effectively. In this work, we leverage linear mixed models (LMMs) and amortized variational inference to provide conditional priors for VAEs, and propose LMM-VAE, a scalable, interpretable and identifiable model. We highlight theoretical connections between it and GP-based techniques, providing a unified framework for this class of methods. Our proposal performs competitively compared to existing approaches across simulated and real-world datasets.

Deterministic Uncertainty Propagation for Improved Model-Based Offline Reinforcement Learning

Current approaches to model-based offline Reinforcement Learning (RL) often incorporate uncertainty-based reward penalization to address the distributional shift problem. While these approaches have achieved some success, we argue that this penalization introduces excessive conservatism, potentially resulting in suboptimal policies through underestimation. We identify as an important cause of over-penalization the lack of a reliable uncertainty estimator capable of propagating uncertainties in the Bellman operator. The common approach to calculating the penalty term relies on sampling-based uncertainty estimation, resulting in high variance. To address this challenge, we propose a novel method termed Moment Matching Offline Model-Based Policy Optimization (MOMBO). MOMBO learns a Q-function using moment matching, which allows us to deterministically propagate uncertainties through the Q-function. We evaluate MOMBO's performance across various environments and demonstrate empirically that MOMBO is a more stable and sample-efficient approach.