Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However, weight-space priors are model-specific, can be difficult to interpret and are hard to specify. Instead, we apply a Dirichlet prior in predictive space and perform approximate function-space variational inference. To this end, we interpret conventional categorical predictions from stochastic neural network classifiers as samples from an implicit Dirichlet distribution. By adapting the inference, the same function-space prior can be combined with different models without affecting model architecture or size. We illustrate the flexibility and efficacy of such a prior with toy experiments and demonstrate scalability, improved uncertainty quantification and adversarial robustness with large-scale image classification experiments.

We propose the use of the hypothetical retrospection argumentation procedure, developed by Sven Ove Hansson to improve existing approaches to machine ethical reasoning by accounting for probability and uncertainty from a position of Philosophy that resonates with humans. Actions are represented with a branching set of potential outcomes, each with a state, utility, and either a numeric or poetic probability estimate. Actions are chosen based on comparisons between sets of arguments favouring actions from the perspective of their branches, even those branches that led to an undesirable outcome. This use of arguments allows a variety of philosophical theories for ethical reasoning to be used, potentially in flexible combination with each other. We implement the procedure, applying consequentialist and deontological ethical theories, independently and concurrently, to an autonomous library system use case. We introduce a preliminary framework that seems to meet the varied requirements of a machine ethics system: versatility under multiple theories and a resonance with humans that enables transparency and explainability.

A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system; the Markov decision process transition probabilities are interpreted as couplings and the value functions as deterministic spins that evolve dynamically. Thus, the mean-rewards and transition probabilities are considered to be quenched random variables. The theory reveals that, under certain assumptions, the state-action values are statistically independent across state-action pairs in the asymptotic state space limit, and provides the form of the distribution exactly. The results hold in the finite and discounted infinite horizon settings, for both value iteration and policy evaluation. The state-action value statistics can be computed from a set of mean field equations, which we call dynamic mean field programming (DMFP). For policy evaluation the equations are exact. For value iteration, approximate equations are obtained by appealing to extreme value theory or bounds. The result provides analytic insight into the statistical structure of tabular reinforcement learning, for example revealing the conditions under which reinforcement learning is equivalent to a set of independent multi-armed bandit problems.

Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many problems in the natural sciences incorporate symmetries and involve data living in non-Euclidean spaces. In this work, we extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We do so by a) constructing a noising process which admits, as limiting distribution, a geometric Gaussian process that transforms under the symmetry group of interest, and b) approximating the score with a neural network that is equivariant w.r.t. this group. We show that with these conditions, the generative functional model admits the same symmetry. We demonstrate scalability and capacity of the model, using a novel Langevin-based conditional sampler, to fit complex scalar and vector fields, with Euclidean and spherical codomain, on synthetic and real-world weather data.

Multi-agent influence diagrams (MAIDs) are a popular game-theoretic model based on Bayesian networks. In some settings, MAIDs offer significant advantages over extensive-form game representations. Previous work on MAIDs has assumed that agents employ behavioural policies, which set independent conditional probability distributions over actions for each of their decisions. In settings with imperfect recall, however, a Nash equilibrium in behavioural policies may not exist. We overcome this by showing how to solve MAIDs with forgetful and absent-minded agents using mixed policies and two types of correlated equilibrium. We also analyse the computational complexity of key decision problems in MAIDs, and explore tractable cases. Finally, we describe applications of MAIDs to Markov games and team situations, where imperfect recall is often unavoidable.

The Free Energy Principle (FEP) describes (biological) agents as minimising a variational Free Energy (FE) with respect to a generative model of their environment. Active Inference (AIF) is a corollary of the FEP that describes how agents explore and exploit their environment by minimising an expected FE objective. In two related papers, we describe a scalable, epistemic approach to synthetic AIF agents, by message passing on free-form Forney-style Factor Graphs (FFGs). A companion paper (part I) introduces a Constrained FFG (CFFG) notation that visually represents (generalised) FE objectives for AIF. The current paper (part II) derives message passing algorithms that minimise (generalised) FE objectives on a CFFG by variational calculus. A comparison between simulated Bethe and generalised FE agents illustrates how synthetic AIF induces epistemic behaviour on a T-maze navigation task. With a full message passing account of synthetic AIF agents, it becomes possible to derive and reuse message updates across models and move closer to industrial applications of synthetic AIF.

Bayesian Optimization (BO) is a class of black-box, surrogate-based heuristics that can efficiently optimize problems that are expensive to evaluate, and hence admit only small evaluation budgets. BO is particularly popular for solving numerical optimization problems in industry, where the evaluation of objective functions often relies on time-consuming simulations or physical experiments. However, many industrial problems depend on a large number of parameters. This poses a challenge for BO algorithms, whose performance is often reported to suffer when the dimension grows beyond 15 variables. Although many new algorithms have been proposed to address this problem, it is not well understood which one is the best for which optimization scenario. In this work, we compare five state-of-the-art high-dimensional BO algorithms, with vanilla BO and CMA-ES on the 24 BBOB functions of the COCO environment at increasing dimensionality, ranging from 10 to 60 variables. Our results confirm the superiority of BO over CMA-ES for limited evaluation budgets and suggest that the most promising approach to improve BO is the use of trust regions. However, we also observe significant performance differences for different function landscapes and budget exploitation phases, indicating improvement potential, e.g., through hybridization of algorithmic components.

Abstract--Whereas dedicated scene representations are required for each different task in conventional robotic systems, this paper demonstrates that a unified representation can be used directly for multiple key tasks. We propose the Log-Gaussian Process Implicit Surface for Mapping, Odometry and Planning (Log-GPIS-MOP): a probabilistic framework for surface reconstruction, localisation and navigation based on a unified representation. Our framework applies a logarithmic transformation to a Gaussian Process Implicit Surface (GPIS) formulation to recover a global representation that accurately captures the Euclidean distance field with gradients and, at the same time, the implicit surface. By directly estimating the distance field and its gradient through Log-GPIS inference, the proposed incremental odometry technique computes the optimal alignment of an incoming frame and fuses it globally to produce a map. Concurrently, an optimisation-based planner computes a safe collision-free path using the same Log-GPIS surface representation. We validate the proposed framework on simulated and real datasets in 2D and 3D and benchmark against the state-of-the-art approaches. Our experiments show that Log-GPIS-MOP produces competitive results in sequential odometry, surface mapping and obstacle avoidance. Using the built map and the key objective of the mapping task is to reconstruct an accurate, estimated location, a path planner may produce collision-free dense and high-resolution map of the scene for, e.g., inspection paths for the robot to navigate safely. Path planning similarly requires dense information raises varying requirements leading to dedicated environment such as obstacle occupancy or closest distance to collision representations. The choice of scene representation strongly in order to avoid obstacles. As a unified representation for affects the performance of the localisation, mapping, and path multiple purposes, a feature-based representation such as a set planning tasks. Personal use of this material is permitted.

Inverse UQ is the process to inversely quantify the model input uncertainties based on experimental data. This work focuses on developing an inverse UQ process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the inverse UQ of TRACE physical model parameters using the FEBA transient experimental data. The measurement data is time-dependent peak cladding temperature (PCT). Since the quantity-of-interest (QoI) is time-dependent that corresponds to infinite-dimensional responses, PCA is used to reduce the QoI dimension while preserving the transient profile of the PCT, in order to make the inverse UQ process more efficient. However, conventional PCA applied directly to the PCT time series profiles can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information of the transient PCT profiles before dimensionality reduction. DNNs are then trained using PC scores from functional PCA to build surrogate models of TRACE in order to reduce the computational cost in Markov Chain Monte Carlo sampling. Bayesian neural networks are used to estimate the uncertainties of DNN surrogate model predictions. In this study, we compared four different inverse UQ processes with different dimensionality reduction methods and surrogate models. The proposed approach shows an improvement in reducing the dimension of the TRACE transient simulations, and the forward propagation of inverse UQ results has a better agreement with the experimental data.

The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function given by the neural network's maximum-a-posteriori predictive function and the covariance function induced by the empirical neural tangent kernel. However, while its efficacy has been studied in large-scale tasks like image classification, it has not been studied in sequential decision-making problems like Bayesian optimization where Gaussian processes -- with simple mean functions and kernels such as the radial basis function -- are the de-facto surrogate models. In this work, we study the usefulness of the LLA in Bayesian optimization and highlight its strong performance and flexibility. However, we also present some pitfalls that might arise and a potential problem with the LLA when the search space is unbounded.