An Improved Variational Approximate Posterior for the Deep Wishart Process

Deep kernel processes are a recently introduced class of deep Bayesian models that have the flexibility of neural networks, but work entirely with Gram matrices. They operate by alternately sampling a Gram matrix from a distribution over positive semi-definite matrices, and applying a deterministic transformation. When the distribution is chosen to be Wishart, the model is called a deep Wishart process (DWP). This particular model is of interest because its prior is equivalent to a deep Gaussian process (DGP) prior, but at the same time it is invariant to rotational symmetries, leading to a simpler posterior distribution. Practical inference in the DWP was made possible in recent work ("A variational approximate posterior for the deep Wishart process" Ober and Aitchison 2021a) where the authors used a generalisation of the Bartlett decomposition of the Wishart distribution as the variational approximate posterior. However, predictive performance in that paper was less impressive than one might expect, with the DWP only beating a DGP on a few of the UCI datasets used for comparison. In this paper, we show that further generalising their distribution to allow linear combinations of rows and columns in the Bartlett decomposition results in better predictive performance, while incurring negligible additional computation cost.

Massively Parallel Reweighted Wake-Sleep

Reweighted wake-sleep (RWS) is a machine learning method for performing Bayesian inference in a very general class of models. RWS draws $K$ samples from an underlying approximate posterior, then uses importance weighting to provide a better estimate of the true posterior. RWS then updates its approximate posterior towards the importance-weighted estimate of the true posterior. However, recent work [Chattergee and Diaconis, 2018] indicates that the number of samples required for effective importance weighting is exponential in the number of latent variables. Attaining such a large number of importance samples is intractable in all but the smallest models. Here, we develop massively parallel RWS, which circumvents this issue by drawing $K$ samples of all $n$ latent variables, and individually reasoning about all $K^n$ possible combinations of samples. While reasoning about $K^n$ combinations might seem intractable, the required computations can be performed in polynomial time by exploiting conditional independencies in the generative model. We show considerable improvements over standard "global" RWS, which draws $K$ samples from the full joint.

Taylor TD-learning

Many reinforcement learning approaches rely on temporal-difference (TD) learning to learn a critic. However, TD-learning updates can be high variance due to their sole reliance on Monte Carlo estimates of the updates. Here, we introduce a model-based RL framework, Taylor TD, which reduces this variance. Taylor TD uses a first-order Taylor series expansion of TD updates. This expansion allows to analytically integrate over stochasticity in the action-choice, and some stochasticity in the state distribution for the initial state and action of each TD update. We include theoretical and empirical evidence of Taylor TD updates being lower variance than (standard) TD updates. Additionally, we show that Taylor TD has the same stable learning guarantees as (standard) TD-learning under linear function approximation. Next, we combine Taylor TD with the TD3 algorithm (Fujimoto et al., 2018), into TaTD3. We show TaTD3 performs as well, if not better, than several state-of-the art model-free and model-based baseline algorithms on a set of standard benchmark tasks. Finally, we include further analysis of the settings in which Taylor TD may be most beneficial to performance relative to standard TD-learning.

MONGOOSE: Path-wise Smooth Bayesian Optimisation via Meta-learning

In Bayesian optimisation, we often seek to minimise the black-box objective functions that arise in real-world physical systems. A primary contributor to the cost of evaluating such black-box objective functions is often the effort required to prepare the system for measurement. We consider a common scenario where preparation costs grow as the distance between successive evaluations increases. In this setting, smooth optimisation trajectories are preferred and the jumpy paths produced by the standard myopic (i.e.\ one-step-optimal) Bayesian optimisation methods are sub-optimal. Our algorithm, MONGOOSE, uses a meta-learnt parametric policy to generate smooth optimisation trajectories, achieving performance gains over existing methods when optimising functions with large movement costs.

Decision trees compensate for model misspecification

The best-performing models in ML are not interpretable. If we can explain why they outperform, we may be able to replicate these mechanisms and obtain both interpretability and performance. One example are decision trees and their descendent gradient boosting machines (GBMs). These perform well in the presence of complex interactions, with tree depth governing the order of interactions. However, interactions cannot fully account for the depth of trees found in practice. We confirm 5 alternative hypotheses about the role of tree depth in performance in the absence of true interactions, and present results from experiments on a battery of datasets. Part of the success of tree models is due to their robustness to various forms of mis-specification. We present two methods for robust generalized linear models (GLMs) addressing the composite and mixed response scenarios.

Imitating careful experts to avoid catastrophic events

RL is increasingly being used to control robotic systems that interact closely with humans. This interaction raises the problem of safe RL: how to ensure that a RL-controlled robotic system never, for instance, injures a human. This problem is especially challenging in rich, realistic settings where it is not even possible to clearly write down a reward function which incorporates these outcomes. In these circumstances, perhaps the only viable approach is based on IRL, which infers rewards from human demonstrations. However, IRL is massively underdetermined as many different rewards can lead to the same optimal policies; we show that this makes it difficult to distinguish catastrophic outcomes (such as injuring a human) from merely undesirable outcomes. Our key insight is that humans do display different behaviour when catastrophic outcomes are possible: they become much more careful. We incorporate carefulness signals into IRL, and find that they do indeed allow IRL to disambiguate undesirable from catastrophic outcomes, which is critical to ensuring safety in future real-world human-robot interactions.

Machine learning emulation of a local-scale UK climate model

Climate change is causing the intensification of rainfall extremes. Precipitation projections with high spatial resolution are important for society to prepare for these changes, e.g. to model flooding impacts. Physics-based simulations for creating such projections are very computationally expensive. This work demonstrates the effectiveness of diffusion models, a form of deep generative models, for generating much more cheaply realistic high resolution rainfall samples for the UK conditioned on data from a low resolution simulation. We show for the first time a machine learning model that is able to produce realistic samples of high-resolution rainfall based on a physical model that resolves atmospheric convection, a key process behind extreme rainfall. By adding self-learnt, location-specific information to low resolution relative vorticity, quantiles and time-mean of the samples match well their counterparts from the high-resolution simulation.

Random initialisations performing above chance and how to find them

Neural networks trained with stochastic gradient descent (SGD) starting from different random initialisations typically find functionally very similar solutions, raising the question of whether there are meaningful differences between different SGD solutions. Entezari et al. recently conjectured that despite different initialisations, the solutions found by SGD lie in the same loss valley after taking into account the permutation invariance of neural networks. Concretely, they hypothesise that any two solutions found by SGD can be permuted such that the linear interpolation between their parameters forms a path without significant increases in loss. Here, we use a simple but powerful algorithm to find such permutations that allows us to obtain direct empirical evidence that the hypothesis is true in fully connected networks. Strikingly, we find that two networks already live in the same loss valley at the time of initialisation and averaging their random, but suitably permuted initialisation performs significantly above chance. In contrast, for convolutional architectures, our evidence suggests that the hypothesis does not hold. Especially in a large learning rate regime, SGD seems to discover diverse modes.

What deep reinforcement learning tells us about human motor learning and vice-versa

Machine learning and specifically reinforcement learning (RL) has been extremely successful in helping us to understand neural decision making processes. However, RL's role in understanding other neural processes especially motor learning is much less well explored. To explore this connection, we investigated how recent deep RL methods correspond to the dominant motor learning framework in neuroscience, error-based learning. Error-based learning can be probed using a mirror reversal adaptation paradigm, where it produces distinctive qualitative predictions that are observed in humans. We therefore tested three major families of modern deep RL algorithm on a mirror reversal perturbation. Surprisingly, all of the algorithms failed to mimic human behaviour and indeed displayed qualitatively different behaviour from that predicted by error-based learning. To fill this gap, we introduce a novel deep RL algorithm: model-based deterministic policy gradients (MB-DPG). MB-DPG draws inspiration from error-based learning by explicitly relying on the observed outcome of actions. We show MB-DPG captures (human) error-based learning under mirror-reversal and rotational perturbation. Next, we demonstrate error-based learning in the form of MB-DPG learns faster than canonical model-free algorithms on complex arm-based reaching tasks, while being more robust to (forward) model misspecification than model-based RL. These findings highlight the gap between current deep RL methods and human motor adaptation and offer a route to closing this gap, facilitating future beneficial interaction between between the two fields.