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Multiple hypothesis testing has been widely applied to problems dealing with high-dimensional data, e.g., selecting significant variables and controlling the selection error rate. The most prevailing measure of error rate used in the multiple hypothesis testing is the false discovery rate (FDR). In recent years, local false discovery rate (fdr) has drawn much attention, due to its advantage of accessing the confidence of individual hypothesis. However, most methods estimate fdr through p-values or statistics with known null distributions, which are sometimes not available or reliable. Adopting the innovative methodology of competition-based procedures, e.g., knockoff filter, this paper proposes a new approach, named TDfdr, to local false discovery rate estimation, which is free of the p-values or known null distributions. Simulation results demonstrate that TDfdr can accurately estimate the fdr with two competition-based procedures. In real data analysis, the power of TDfdr on variable selection is verified on two biological datasets.

Mechanical assemblies can exhibit complex relative motions, during which collisions between moving parts and their surroundings must be avoided. To define feasible design spaces for each part's shape, "maximal" collision-free pointsets can be computed using configuration space modeling techniques such as Minkowski operations and sweep/unsweep. For example, for a pair of parts undergoing a given relative motion, to make the problem well-posed, the geometry of one part (chosen arbitrarily) must be fixed to compute the maximal shape of the other part by an unsweep operation. Making such arbitrary choices in a multi-component assembly can place unnecessary restrictions on the design space. A broader family of collision-free pairs of parts can be explored, if fixing the geometry of a component is not required. In this paper, we formalize this family of collision-free shapes and introduce a generic method for generating a broad subset of them. Our procedure, which is an extension of the unsweep, allows for co-generation of a pair of geometries which are modified incrementally and simultaneously to avoid collision. We demonstrate the effectiveness and scalability of our procedure in both 2D and 3D by generating a variety of collision-free shapes. Notably, we show that our approach can automatically generate freeform cam and follower profiles, gear teeth, and screw threads, starting from colliding blocks of materials, solely from a specification of relative motion and without the use of any feature-informed heuristics. Moreover, our approach provides continuous measures of collision that can be incorporated into standard gradient-descent design optimization, allowing for simultaneous collision-free and physics-informed co-design of mechanical parts for assembly.

Meta reinforcement learning (RL) attempts to discover new RL algorithms automatically from environment interaction. In so-called black-box approaches, the policy and the learning algorithm are jointly represented by a single neural network. These methods are very flexible, but they tend to underperform in terms of generalisation to new, unseen environments. In this paper, we explore the role of symmetries in meta-generalisation. We show that a recent successful meta RL approach that meta-learns an objective for backpropagation-based learning exhibits certain symmetries (specifically the reuse of the learning rule, and invariance to input and output permutations) that are not present in typical black-box meta RL systems. We hypothesise that these symmetries can play an important role in meta-generalisation. Building off recent work in black-box supervised meta learning, we develop a black-box meta RL system that exhibits these same symmetries. We show through careful experimentation that incorporating these symmetries can lead to algorithms with a greater ability to generalise to unseen action & observation spaces, tasks, and environments.

The quintessential model-based reinforcement-learning agent iteratively refines its estimates or prior beliefs about the true underlying model of the environment. Recent empirical successes in model-based reinforcement learning with function approximation, however, eschew the true model in favor of a surrogate that, while ignoring various facets of the environment, still facilitates effective planning over behaviors. Recently formalized as the value equivalence principle, this algorithmic technique is perhaps unavoidable as real-world reinforcement learning demands consideration of a simple, computationally-bounded agent interacting with an overwhelmingly complex environment, whose underlying dynamics likely exceed the agent's capacity for representation. In this work, we consider the scenario where agent limitations may entirely preclude identifying an exactly value-equivalent model, immediately giving rise to a trade-off between identifying a model that is simple enough to learn while only incurring bounded sub-optimality. To address this problem, we introduce an algorithm that, using rate-distortion theory, iteratively computes an approximately-value-equivalent, lossy compression of the environment which an agent may feasibly target in lieu of the true model. We prove an information-theoretic, Bayesian regret bound for our algorithm that holds for any finite-horizon, episodic sequential decision-making problem. Crucially, our regret bound can be expressed in one of two possible forms, providing a performance guarantee for finding either the simplest model that achieves a desired sub-optimality gap or, alternatively, the best model given a limit on agent capacity.

In this paper, we introduce a high-level controller synthesis framework that enables teams of heterogeneous agents to assist each other in resolving environmental conflicts that appear at runtime. This conflict resolution method is built upon temporal-logic-based reactive synthesis to guarantee safety and task completion under specific environment assumptions. In heterogeneous multi-agent systems, every agent is expected to complete its own tasks in service of a global team objective. However, at runtime, an agent may encounter un-modeled obstacles (e.g., doors or walls) that prevent it from achieving its own task. To address this problem, we take advantage of the capability of other heterogeneous agents to resolve the obstacle. A controller framework is proposed to redirect agents with the capability of resolving the appropriate obstacles to the required target when such a situation is detected. A set of case studies involving a bipedal robot Digit and a quadcopter are used to evaluate the controller performance in action. Additionally, we implement the proposed framework on a physical multi-agent robotic system to demonstrate its viability for real world applications.

Collision avoidance for multirobot systems is a well-studied problem. Recently, control barrier functions (CBFs) have been proposed for synthesizing controllers that guarantee collision avoidance and goal stabilization for multiple robots. However, it has been noted that reactive control synthesis methods (such as CBFs) are prone to \textit{deadlock}, an equilibrium of system dynamics that causes the robots to stall before reaching their goals. In this paper, we analyze the closed-loop dynamics of robots using CBFs, to characterize controller parameters, initial conditions, and goal locations that invariably lead the system to deadlock. Using tools from duality theory, we derive geometric properties of robot configurations of an $N$ robot system once it is in deadlock and we justify them using the mechanics interpretation of KKT conditions. Our key deductions are that 1) system deadlock is characterized by a force-equilibrium on robots and 2) deadlock occurs to ensure safety when safety is on the brink of being violated. These deductions allow us to interpret deadlock as a subset of the state space, and we show that this set is non-empty and located on the boundary of the safe set. By exploiting these properties, we analyze the number of admissible robot configurations in deadlock and develop a provably-correct decentralized algorithm for deadlock resolution to safely deliver the robots to their goals. This algorithm is validated in simulations as well as experimentally on Khepera-IV robots.

Incrementality, which is used to measure the causal effect of showing an ad to a potential customer (e.g. a user in an internet platform) versus not, is a central object for advertisers in online advertising platforms. This paper investigates the problem of how an advertiser can learn to optimize the bidding sequence in an online manner \emph{without} knowing the incrementality parameters in advance. We formulate the offline version of this problem as a specially structured episodic Markov Decision Process (MDP) and then, for its online learning counterpart, propose a novel reinforcement learning (RL) algorithm with regret at most $\widetilde{O}(H^2\sqrt{T})$, which depends on the number of rounds $H$ and number of episodes $T$, but does not depend on the number of actions (i.e., possible bids). A fundamental difference between our learning problem from standard RL problems is that the realized reward feedback from conversion incrementality is \emph{mixed} and \emph{delayed}. To handle this difficulty we propose and analyze a novel pairwise moment-matching algorithm to learn the conversion incrementality, which we believe is of independent of interest.

Recent years have witnessed significant advances in technologies and services in modern network applications, including smart grid management, wireless communication, cybersecurity as well as multi-agent autonomous systems. Considering the heterogeneous nature of networked entities, emerging network applications call for game-theoretic models and learning-based approaches in order to create distributed network intelligence that responds to uncertainties and disruptions in a dynamic or an adversarial environment. This paper articulates the confluence of networks, games and learning, which establishes a theoretical underpinning for understanding multi-agent decision-making over networks. We provide an selective overview of game-theoretic learning algorithms within the framework of stochastic approximation theory, and associated applications in some representative contexts of modern network systems, such as the next generation wireless communication networks, the smart grid and distributed machine learning. In addition to existing research works on game-theoretic learning over networks, we highlight several new angles and research endeavors on learning in games that are related to recent developments in artificial intelligence. Some of the new angles extrapolate from our own research interests. The overall objective of the paper is to provide the reader a clear picture of the strengths and challenges of adopting game-theoretic learning methods within the context of network systems, and further to identify fruitful future research directions on both theoretical and applied studies.

Since real-world objects and their interactions are often multi-modal and multi-typed, heterogeneous networks have been widely used as a more powerful, realistic, and generic superclass of traditional homogeneous networks (graphs). Meanwhile, representation learning (\aka~embedding) has recently been intensively studied and shown effective for various network mining and analytical tasks. In this work, we aim to provide a unified framework to deeply summarize and evaluate existing research on heterogeneous network embedding (HNE), which includes but goes beyond a normal survey. Since there has already been a broad body of HNE algorithms, as the first contribution of this work, we provide a generic paradigm for the systematic categorization and analysis over the merits of various existing HNE algorithms. Moreover, existing HNE algorithms, though mostly claimed generic, are often evaluated on different datasets. Understandable due to the application favor of HNE, such indirect comparisons largely hinder the proper attribution of improved task performance towards effective data preprocessing and novel technical design, especially considering the various ways possible to construct a heterogeneous network from real-world application data. Therefore, as the second contribution, we create four benchmark datasets with various properties regarding scale, structure, attribute/label availability, and \etc.~from different sources, towards handy and fair evaluations of HNE algorithms. As the third contribution, we carefully refactor and amend the implementations and create friendly interfaces for 13 popular HNE algorithms, and provide all-around comparisons among them over multiple tasks and experimental settings.