Projecting high-dimensional environment observations into lower-dimensional structured representations can considerably improve data-efficiency for reinforcement learning in domains with limited data such as robotics. Can a single generally useful representation be found? In order to answer this question, it is important to understand how the representation will be used by the agent and what properties such a good representation should have. In this paper we systematically evaluate a number of common learnt and hand-engineered representations in the context of three robotics tasks: lifting, stacking and pushing of 3D blocks. The representations are evaluated in two use-cases: as input to the agent, or as a source of auxiliary tasks. Furthermore, the value of each representation is evaluated in terms of three properties: dimensionality, observability and disentanglement. We can significantly improve performance in both use-cases and demonstrate that some representations can perform commensurate to simulator states as agent inputs. Finally, our results challenge common intuitions by demonstrating that: 1) dimensionality strongly matters for task generation, but is negligible for inputs, 2) observability of task-relevant aspects mostly affects the input representation use-case, and 3) disentanglement leads to better auxiliary tasks, but has only limited benefits for input representations. This work serves as a step towards a more systematic understanding of what makes a good representation for control in robotics, enabling practitioners to make more informed choices for developing new learned or hand-engineered representations.

Concern about how to aggregate sensitive user data without compromising individual privacy is a major barrier to greater availability of data. Differential privacy has emerged as an accepted model to release sensitive information while giving a statistical guarantee for privacy. Many different algorithms are possible to address different target functions. We focus on the core problem of count queries, and seek to design mechanisms to release data associated with a group of n individuals. Prior work has focused on designing mechanisms by raw optimization of a loss function, without regard to the consequences on the results. This can lead to mechanisms with undesirable properties, such as never reporting some outputs (gaps), and overreporting others (spikes). We tame these pathological behaviors by introducing a set of desirable properties that mechanisms can obey. Any combination of these can be satisfied by solving a linear program (LP) which minimizes a cost function, with constraints enforcing the properties. We focus on a particular cost function, and provide explicit constructions that are optimal for certain combinations of properties, and show a closed form for their cost. In the end, there are only a handful of distinct optimal mechanisms to choose between: one is the well-known (truncated) geometric mechanism; the second a novel mechanism that we introduce here, and the remainder are found as the solution to particular LPs. These all avoid the bad behaviors we identify. We demonstrate in a set of experiments on real and synthetic data which is preferable in practice, for different combinations of data distributions, constraints, and privacy parameters.

In this paper, we study the problem of computing $U$-statistics of degree $2$, i.e., quantities that come in the form of averages over pairs of data points, in the local model of differential privacy (LDP). The class of $U$-statistics covers many statistical estimates of interest, including Gini mean difference, Kendall’s tau coefficient and Area under the ROC Curve (AUC), as well as empirical risk measures for machine learning problems such as ranking, clustering and metric learning. We first introduce an LDP protocol based on quantizing the data into bins and applying randomized response, which guarantees an $\epsilon$-LDP estimate with a Mean Squared Error (MSE) of $O(1/\sqrt{n}\epsilon)$ under regularity assumptions on the $U$-statistic or the data distribution. We then propose a specialized protocol for AUC based on a novel use of hierarchical histograms that achieves MSE of $O(\alpha^3/n\epsilon^2)$ for arbitrary data distribution. We also show that 2-party secure computation allows to design a protocol with MSE of $O(1/n\epsilon^2)$, without any assumption on the kernel function or data distribution and with total communication linear in the number of users $n$. Finally, we evaluate the performance of our protocols through experiments on synthetic and real datasets.

Counting the fraction of a population having an input within a specified interval i.e. range count query is a fundamental database operation. Range count queries can also be used to compute other interesting statistics such as quantiles. The framework of differential privacy [6] (DP) is becoming a standard for privacy-preserving data analysis [1]. While many works address the problem of range counting queries in the trusted aggregation model, surprisingly, this problem has not been addressed specifically under untrusted aggregation (local DP [10]). In this work we study the problem of answering 1-dimensional range count queries under the constraint of LDP.

Counting the fraction of a population having an input within a specified interval i.e. a range query, is a fundamental data analysis primitive. Range queries can also be used to compute other core statistics such as quantiles, and to build prediction models. However, frequently the data is subject to privacy concerns when it is drawn from individuals, and relates for example to their financial, health, religious or political status. In this paper, we introduce and analyze methods to support range queries under the local variant of differential privacy [23], an emerging standard for privacy-preserving data analysis. The local model requires that each user releases a noisy view of her private data under a privacy guarantee. While many works address the problem of range queries in the trusted aggregator setting, this problem has not been addressed specifically under untrusted aggregation (local DP) model even though many primitives have been developed recently for estimating a discrete distribution. We describe and analyze two classes of approaches for range queries, based on hierarchical histograms and the Haar wavelet transform. We show that both have strong theoretical accuracy guarantees on variance. In practice, both methods are fast and require minimal computation and communication resources. Our experiments show that the wavelet approach is most accurate in high privacy settings, while the hierarchical approach dominates for weaker privacy requirements.

Concern about how to aggregate sensitive user data without compromising individual privacy is a major barrier to greater availability of data. Differential privacy has emerged as an accepted model to release sensitive information while giving a statistical guarantee for privacy. Many different algorithms are possible to address different target functions. We focus on the core problem of count queries, and seek to design mechanisms to release data associated with a group of n individuals. Prior work has focused on designing mechanisms by raw optimization of a loss function, without regard to the consequences on the results. This can leads to mechanisms with undesirable properties, such as never reporting some outputs (gaps), and overreporting others (spikes). We tame these pathological behaviors by introducing a set of desirable properties that mechanisms can obey. Any combination of these can be satisfied by solving a linear program (LP) which minimizes a cost function, with constraints enforcing the properties. We focus on a particular cost function, and provide explicit constructions that are optimal for certain combinations of properties, and show a closed form for their cost. In the end, there are only a handful of distinct optimal mechanisms to choose between: one is the well-known (truncated) geometric mechanism; the second a novel mechanism that we introduce here, and the remainder are found as the solution to particular LPs. These all avoid the bad behaviors we identify. We demonstrate in a set of experiments on real and synthetic data which is preferable in practice, for different combinations of data distributions, constraints, and privacy parameters.

Advances in deep generative networks have led to impressive results in recent years. Nevertheless, such models can often waste their capacity on the minutiae of datasets, presumably due to weak inductive biases in their decoders. This is where graphics engines may come in handy since they abstract away low-level details and represent images as high-level programs. Current methods that combine deep learning and renderers are limited by hand-crafted likelihood or distance functions, a need for large amounts of supervision, or difficulties in scaling their inference algorithms to richer datasets. To mitigate these issues, we present SPIRAL, an adversarially trained agent that generates a program which is executed by a graphics engine to interpret and sample images. The goal of this agent is to fool a discriminator network that distinguishes between real and rendered data, trained with a distributed reinforcement learning setup without any supervision. A surprising finding is that using the discriminator’s output as a reward signal is the key to allow the agent to make meaningful progress at matching the desired output rendering. To the best of our knowledge, this is the first demonstration of an end-to-end, unsupervised and adversarial inverse graphics agent on challenging real world (MNIST, Omniglot, CelebA) and synthetic 3D datasets. A video of the agent can be found at https://youtu.be/iSyvwAwa7vk.

Local differential privacy (LDP), where users randomly perturb their inputs to provide plausible deniability of their data without the need for a trusted party, has been adopted recently by several major technology organizations, including Google, Apple and Microsoft. This tutorial aims to introduce the key technical underpinnings of these deployed systems, to survey current research that addresses related problems within the LDP model, and to identify relevant open problems and research directions for the community.

Many analysis and machine learning tasks require the availability of marginal statistics on multidimensional datasets while providing strong privacy guarantees for the data subjects. Applications for these statistics range from finding correlations in the data to fitting sophisticated prediction models. In this paper, we provide a set of algorithms for materializing marginal statistics under the strong model of local differential privacy. We prove the first tight theoretical bounds on the accuracy of marginals compiled under each approach, perform empirical evaluation to confirm these bounds, and evaluate them for tasks such as modeling and correlation testing. Our results show that releasing information based on (local) Fourier transformations of the input is preferable to alternatives based directly on (local) marginals.

We investigate the problem of electing a leader in a sparse but well-connected synchronous dynamic network in which up to a fraction of the nodes chosen adversarially can leave/join the network per time step. At this churn rate, all nodes in the network can be replaced by new nodes in a constant number of rounds. Moreover, the adversary can shield a fraction of the nodes (which may include the leader) by repeatedly churning their neighbourhood and thus hinder their communication with the rest of the network. However, empirical studies in peer-to-peer networks have shown that a significant fraction of the nodes are usually stable and well connected. It is, therefore, natural to take advantage of such stability and well-connectedness to establish a leader that can maintain good communication with rest of the nodes. Since the dynamics could change eventually, it is also essential to re-elect a new leader whenever the current leader has either left the network or is not well-connected with rest of the nodes. In such re-elections, care must be taken to avoid premature and spurious leader election resulting in more than one leader present in the network at the same time. We assume a broadcast based communication model in which each node can send up to O(log3n) bits per round and is unaware of its receivers a priori. We present a randomized algorithm that can, in O(log n) rounds, detect and reach consensus about the health of the leader (i.e., whether it is able to maintain good communication with rest of the network). In the event that the network decides that the leader's ability to communicate is unhealthy, a new leader is re-elected in a further O(log2n) rounds. Our running times hold with high probability, and, furthermore, we are guaranteed with high probability that there is at most one leader at any time.