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We propose and study a new privacy definition, termed Probably Approximately Correct (PAC) Security. PAC security characterizes the information-theoretic hardness to recover sensitive data given arbitrary information disclosure/leakage during/after any processing. Unlike the classic cryptographic definition and Differential Privacy (DP), which consider the adversarial (input-independent) worst case, PAC security is a simulatable metric that quantifies the instance-based impossibility of inference. A fully automatic analysis and proof generation framework is proposed: security parameters can be produced with arbitrarily high confidence via Monte-Carlo simulation for any black-box data processing oracle. This appealing automation property enables analysis of complicated data processing, where the worst-case proof in the classic privacy regime could be loose or even intractable. Moreover, we show that the produced PAC security guarantees enjoy simple composition bounds and the automatic analysis framework can be implemented in an online fashion to analyze the composite PAC security loss even under correlated randomness. On the utility side, the magnitude of (necessary) perturbation required in PAC security is not lower bounded by $\Theta(\sqrt{d})$ for a $d$-dimensional release but could be O(1) for many practical data processing tasks, which is in contrast to the input-independent worst-case information-theoretic lower bound. Example applications of PAC security are included with comparisons to existing works.

Task automation of surgical robot has the potentials to improve surgical efficiency. Recent reinforcement learning (RL) based approaches provide scalable solutions to surgical automation, but typically require extensive data collection to solve a task if no prior knowledge is given. This issue is known as the exploration challenge, which can be alleviated by providing expert demonstrations to an RL agent. Yet, how to make effective use of demonstration data to improve exploration efficiency still remains an open challenge. In this work, we introduce Demonstration-guided EXploration (DEX), an efficient reinforcement learning algorithm that aims to overcome the exploration problem with expert demonstrations for surgical automation. To effectively exploit demonstrations, our method estimates expert-like behaviors with higher values to facilitate productive interactions, and adopts non-parametric regression to enable such guidance at states unobserved in demonstration data. Extensive experiments on $10$ surgical manipulation tasks from SurRoL, a comprehensive surgical simulation platform, demonstrate significant improvements in the exploration efficiency and task success rates of our method. Moreover, we also deploy the learned policies to the da Vinci Research Kit (dVRK) platform to show the effectiveness on the real robot. Code is available at //github.com/med-air/DEX.

Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable than marginal ones, they may suffer from slow mixing in infinite mixtures, where some form of truncation, either deterministic or random, is required. In mixtures with random number of components, the exploration of parameter spaces of different dimensions can also be challenging. We tackle these issues by expressing the mixture components in the random order of appearance in an exchangeable sequence directed by the mixing distribution. We derive a sampler that is straightforward to implement for mixing distributions with tractable size-biased ordered weights, and that can be readily adapted to mixture models for which marginal samplers are not available. In infinite mixtures, no form of truncation is necessary. As for finite mixtures with random dimension, a simple updating of the number of components is obtained by a blocking argument, thus, easing challenges found in trans-dimensional moves via Metropolis-Hastings steps. Additionally, sampling occurs in the space of ordered partitions with blocks labelled in the least element order, which endows the sampler with good mixing properties. The performance of the proposed algorithm is evaluated in a simulation study.

Autonomous robots must utilize rich sensory data to make safe control decisions. Often, compute-constrained robots require assistance from remote computation (''the cloud'') if they need to invoke compute-intensive Deep Neural Network perception or control models. Likewise, a robot can be remotely teleoperated by a human during risky scenarios. However, this assistance comes at the cost of a time delay due to network latency, resulting in stale/delayed observations being used in the cloud to compute the control commands for the present robot state. Such communication delays could potentially lead to the violation of essential safety properties, such as collision avoidance. This paper develops methods to ensure the safety of teleoperated robots with stochastic latency. To do so, we use tools from formal verification to construct a shield (i.e., run-time monitor) that provides a list of safe actions for any delayed sensory observation, given the expected and worst-case network latency. Our shield is minimally intrusive and enables networked robots to satisfy key safety constraints, expressed as temporal logic specifications, with high probability. Our approach gracefully improves a teleoperated robot's safety vs. efficiency trade-off as a function of network latency, allowing us to quantify performance gains for WiFi or even future 5G networks. We demonstrate our approach on a real F1/10th autonomous vehicle that navigates in crowded indoor environments and transmits rich LiDAR sensory data over congested WiFi links.

It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are often governed by a second or higher order ODE involving configuration variables and their time derivatives. To apply a collocation method, therefore, the usual practice is to resort to the well known procedure of casting an M th order ODE into M first order ones. This manipulation, which in the continuous domain is perfectly valid, leads to inconsistencies when the problem is discretized. Since the configuration variables and their time derivatives are approximated with polynomials of the same degree, their differential dependencies cannot be fulfilled, and the actual dynamics is not satisfied, not even at the collocation points. This paper draws attention to this problem, and develops improved versions of the trapezoidal and Hermite-Simpson collocation methods that do not present these inconsistencies. In many cases, the new methods reduce the dynamic transcription error in one order of magnitude, or even more, without noticeably increasing the cost of computing the solutions.

Continuous surveillance of a spatial region using distributed robots and sensors is a well-studied application in the area of multi-agent systems. This paper investigates a practically-relevant scenario where robotic sensors are introduced asynchronously and inter-robot communication is discrete, event-driven, local and asynchronous. Furthermore, we work with lazy robots; i.e., the robots seek to minimize their area of responsibility by equipartitioning the domain to be covered. We adapt a well-known algorithm which is practicable and known to generally work well for coverage problems. For a specially chosen geometry of the spatial domain, we show that there exists a non-trivial sequence of inter-robot communication events which leads to an instantaneous loss of coverage when the number of robots exceeds a certain threshold. The same sequence of events preserves coverage and, further, leads to an equipartition of the domain when the number of robots is smaller than the threshold. This result demonstrates that coverage guarantees for a given algorithm might be sensitive to the number of robots and, therefore, may not scale in obvious ways. It also suggests that when such algorithms are to be verified and validated prior to field deployment, the number of robots or sensors used in test scenarios should match that deployed on the field.

Reinforcement learning (RL) and trajectory optimization (TO) present strong complementary advantages. On one hand, RL approaches are able to learn global control policies directly from data, but generally require large sample sizes to properly converge towards feasible policies. On the other hand, TO methods are able to exploit gradient-based information extracted from simulators to quickly converge towards a locally optimal control trajectory which is only valid within the vicinity of the solution. Over the past decade, several approaches have aimed to adequately combine the two classes of methods in order to obtain the best of both worlds. Following on from this line of research, we propose several improvements on top of these approaches to learn global control policies quicker, notably by leveraging sensitivity information stemming from TO methods via Sobolev learning, and augmented Lagrangian techniques to enforce the consensus between TO and policy learning. We evaluate the benefits of these improvements on various classical tasks in robotics through comparison with existing approaches in the literature.

This paper is concerned with offline reinforcement learning (RL), which learns using pre-collected data without further exploration. Effective offline RL would be able to accommodate distribution shift and limited data coverage. However, prior algorithms or analyses either suffer from suboptimal sample complexities or incur high burn-in cost to reach sample optimality, thus posing an impediment to efficient offline RL in sample-starved applications. We demonstrate that the model-based (or "plug-in") approach achieves minimax-optimal sample complexity without burn-in cost for tabular Markov decision processes (MDPs). Concretely, consider a finite-horizon (resp. $\gamma$-discounted infinite-horizon) MDP with $S$ states and horizon $H$ (resp. effective horizon $\frac{1}{1-\gamma}$), and suppose the distribution shift of data is reflected by some single-policy clipped concentrability coefficient $C^{\star}_{\text{clipped}}$. We prove that model-based offline RL yields $\varepsilon$-accuracy with a sample complexity of \[ \begin{cases} \frac{H^{4}SC_{\text{clipped}}^{\star}}{\varepsilon^{2}} & (\text{finite-horizon MDPs}) \frac{SC_{\text{clipped}}^{\star}}{(1-\gamma)^{3}\varepsilon^{2}} & (\text{infinite-horizon MDPs}) \end{cases} \] up to log factor, which is minimax optimal for the entire $\varepsilon$-range. The proposed algorithms are ``pessimistic'' variants of value iteration with Bernstein-style penalties, and do not require sophisticated variance reduction. Our analysis framework is established upon delicate leave-one-out decoupling arguments in conjunction with careful self-bounding techniques tailored to MDPs.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.

We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.