Private Selection with Heterogeneous Sensitivities

Differentially private (DP) selection involves choosing a high-scoring candidate from a finite candidate pool, where each score depends on a sensitive dataset. This problem arises naturally in a variety of contexts including model selection, hypothesis testing, and within many DP algorithms. Classical methods, such as Report Noisy Max (RNM), assume all candidates' scores are equally sensitive to changes in a single individual's data, but this often isn't the case. To address this, algorithms like the Generalised Exponential Mechanism (GEM) leverage variability in candidate sensitivities. However, we observe that while these algorithms can outperform RNM in some situations, they may underperform in others - they can even perform worse than random selection. In this work, we explore how the distribution of scores and sensitivities impacts DP selection mechanisms. In all settings we study, we find that there exists a mechanism that utilises heterogeneity in the candidate sensitivities that outperforms standard mechanisms like RNM. However, no single mechanism uniformly outperforms RNM. We propose using the correlation between the scores and sensitivities as the basis for deciding which DP selection mechanism to use. Further, we design a slight variant of GEM, modified GEM that generally performs well whenever GEM performs poorly. Relying on the correlation heuristic we propose combined GEM, which adaptively chooses between GEM and modified GEM and outperforms both in polarised settings.

Augmented Modular Reinforcement Learning based on Heterogeneous Knowledge

In order to mitigate some of the inefficiencies of Reinforcement Learning (RL), modular approaches composing different decision-making policies to derive agents capable of performing a variety of tasks have been proposed. The modules at the basis of these architectures are generally reusable, also allowing for "plug-and-play" integration. However, such solutions still lack the ability to process and integrate multiple types of information (knowledge), such as rules, sub-goals, and skills. We propose Augmented Modular Reinforcement Learning (AMRL) to address these limitations. This new framework uses an arbitrator to select heterogeneous modules and seamlessly incorporate different types of knowledge. Additionally, we introduce a variation of the selection mechanism, namely the Memory-Augmented Arbitrator, which adds the capability of exploiting temporal information. We evaluate the proposed mechanisms on established as well as new environments and benchmark them against prominent deep RL algorithms. Our results demonstrate the performance improvements that can be achieved by augmenting traditional modular RL with other forms of heterogeneous knowledge.

$\mathcal{F}$-EBM: Energy Based Learning of Functional Data

Energy-Based Models (EBMs) have proven to be a highly effective approach for modelling densities on finite-dimensional spaces. Their ability to incorporate domain-specific choices and constraints into the structure of the model through composition make EBMs an appealing candidate for applications in physics, biology and computer vision and various other fields. In this work, we present a novel class of EBM which is able to learn distributions of functions (such as curves or surfaces) from functional samples evaluated at finitely many points. Two unique challenges arise in the functional context. Firstly, training data is often not evaluated along a fixed set of points. Secondly, steps must be taken to control the behaviour of the model between evaluation points, to mitigate overfitting. The proposed infinite-dimensional EBM employs a latent Gaussian process, which is weighted spectrally by an energy function parameterised with a neural network. The resulting EBM has the ability to utilize irregularly sampled training data and can output predictions at any resolution, providing an effective approach to up-scaling functional data. We demonstrate the efficacy of our proposed approach for modelling a range of datasets, including data collected from Standard and Poor's 500 (S\&P) and UK National grid.