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Time is a crucial factor in modelling dynamic behaviours of intelligent agents: activities have a determined temporal duration in a real-world environment, and previous actions influence agents' behaviour. In this paper, we propose a language for modelling concurrent interaction between agents that also allows the specification of temporal intervals in which particular actions occur. Such a language exploits a timed version of Abstract Argumentation Frameworks to realise a shared memory used by the agents to communicate and reason on the acceptability of their beliefs with respect to a given time interval. An interleaving model on a single processor is used for basic computation steps, with maximum parallelism for time elapsing. Following this approach, only one of the enabled agents is executed at each moment. To demonstrate the capabilities of language, we also show how it can be used to model interactions such as debates and dialogue games taking place between intelligent agents. Lastly, we present an implementation of the language that can be accessed via a web interface. Under consideration in Theory and Practice of Logic Programming (TPLP).

We introduce negation under the stable model semantics in DatalogMTL - a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rational timeline, and decidable in EXPSPACE in data complexity over the integer timeline. We also show that, if we restrict our attention to forward-propagating programs, reasoning over the integer timeline becomes PSPACE-complete in data complexity, and hence, no harder than over positive programs; however, reasoning over the rational timeline in this fragment remains undecidable. Under consideration in Theory and Practice of Logic Programming (TPLP).

It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a statistical inference problem where the target estimand is a scalar measure of dissimilarity between the true function-valued parameter and the closest function among all candidate null values. These estimands are typically defined to be zero when the null holds and positive otherwise. While there is well-established theory and methodology for performing efficient inference when one assumes a parametric model for the function-valued parameter, methods for inference in the nonparametric setting are limited. When the null holds, and the target estimand resides at the boundary of the parameter space, existing nonparametric estimators either achieve a non-standard limiting distribution or a sub-optimal convergence rate, making inference challenging. In this work, we propose a strategy for constructing nonparametric estimators with improved asymptotic performance. Notably, our estimators converge at the parametric rate at the boundary of the parameter space and also achieve a tractable null limiting distribution. As illustrations, we discuss how this framework can be applied to perform inference in nonparametric regression problems, and also to perform nonparametric assessment of stochastic dependence.

Hybrid dynamical systems, i.e. systems that have both continuous and discrete states, are ubiquitous in engineering, but are difficult to work with due to their discontinuous transitions. For example, a robot leg is able to exert very little control effort while it is in the air compared to when it is on the ground. When the leg hits the ground, the penetrating velocity instantaneously collapses to zero. These instantaneous changes in dynamics and discontinuities (or jumps) in state make standard smooth tools for planning, estimation, control, and learning difficult for hybrid systems. One of the key tools for accounting for these jumps is called the saltation matrix. The saltation matrix is the sensitivity update when a hybrid jump occurs and has been used in a variety of fields including robotics, power circuits, and computational neuroscience. This paper presents an intuitive derivation of the saltation matrix and discusses what it captures, where it has been used in the past, how it is used for linear and quadratic forms, how it is computed for rigid body systems with unilateral constraints, and some of the structural properties of the saltation matrix in these cases.

There has been growing interest in deep reinforcement learning (DRL) algorithm design, and reward design is one key component of DRL. Among the various techniques, formal methods integrated with DRL have garnered considerable attention due to their expressiveness and ability to define the requirements for the states and actions of the agent. However, the literature of Signal Temporal Logic (STL) in guiding multi-agent reinforcement learning (MARL) reward design remains limited. In this paper, we propose a novel STL-guided multi-agent reinforcement learning algorithm. The STL specifications are designed to include both task specifications according to the objective of each agent and safety specifications, and the robustness values of the STL specifications are leveraged to generate rewards. We validate the advantages of our method through empirical studies. The experimental results demonstrate significant performance improvements compared to MARL without STL guidance, along with a remarkable increase in the overall safety rate of the multi-agent systems.

We study collaborative normal mean estimation, where $m$ strategic agents collect i.i.d samples from a normal distribution $\mathcal{N}(\mu, \sigma^2)$ at a cost. They all wish to estimate the mean $\mu$. By sharing data with each other, agents can obtain better estimates while keeping the cost of data collection small. To facilitate this collaboration, we wish to design mechanisms that encourage agents to collect a sufficient amount of data and share it truthfully, so that they are all better off than working alone. In naive mechanisms, such as simply pooling and sharing all the data, an individual agent might find it beneficial to under-collect and/or fabricate data, which can lead to poor social outcomes. We design a novel mechanism that overcomes these challenges via two key techniques: first, when sharing the others' data with an agent, the mechanism corrupts this dataset proportional to how much the data reported by the agent differs from the others; second, we design minimax optimal estimators for the corrupted dataset. Our mechanism, which is incentive compatible and individually rational, achieves a social penalty (sum of all agents' estimation errors and data collection costs) that is at most a factor 2 of the global minimum. When applied to high dimensional (non-Gaussian) distributions with bounded variance, this mechanism retains these three properties, but with slightly weaker results. Finally, in two special cases where we restrict the strategy space of the agents, we design mechanisms that essentially achieve the global minimum.

The usability of Reinforcement Learning is restricted by the large computation times it requires. Curriculum Reinforcement Learning speeds up learning by defining a helpful order in which an agent encounters tasks, i.e. from simple to hard. Curricula based on Absolute Learning Progress (ALP) have proven successful in different environments, but waste computation on repeating already learned behaviour in new tasks. We solve this problem by introducing a new regularization method based on Self-Paced (Deep) Learning, called Self-Paced Absolute Learning Progress (SPALP). We evaluate our method in three different environments. Our method achieves performance comparable to original ALP in all cases, and reaches it quicker than ALP in two of them. We illustrate possibilities to further improve the efficiency and performance of SPALP.

The $1-N$ generalized Stackelberg game (single-leader multi-follower game) is intricately intertwined with the interaction between a leader and followers (hierarchical interaction) and the interaction among followers (simultaneous interaction). However, obtaining the optimal strategy of the leader is generally challenging due to the complex interactions among the leader and followers. Here, we propose a general methodology to find a generalized Stackelberg equilibrium of a $1-N$ generalized Stackelberg game. Specifically, we first provide the conditions where a generalized Stackelberg equilibrium always exists using the variational equilibrium concept. Next, to find an equilibrium in polynomial time, we transformed the $1-N$ generalized Stackelberg game into a $1-1$ Stackelberg game whose Stackelberg equilibrium is identical to that of the original. Finally, we propose an effective computation procedure based on the projected implicit gradient descent algorithm to find a Stackelberg equilibrium of the transformed $1-1$ Stackelberg game. We validate the proposed approaches using the two problems of deriving operating strategies for EV charging stations: (1) the first problem is optimizing the one-time charging price for EV users, in which a platform operator determines the price of electricity and EV users determine the optimal amount of charging for their satisfaction; and (2) the second problem is to determine the spatially varying charging price to optimally balance the demand and supply over every charging station.

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, robust principal component analysis, phase synchronization, and joint alignment. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.

In this paper, we adopt 3D Convolutional Neural Networks to segment volumetric medical images. Although deep neural networks have been proven to be very effective on many 2D vision tasks, it is still challenging to apply them to 3D tasks due to the limited amount of annotated 3D data and limited computational resources. We propose a novel 3D-based coarse-to-fine framework to effectively and efficiently tackle these challenges. The proposed 3D-based framework outperforms the 2D counterpart to a large margin since it can leverage the rich spatial infor- mation along all three axes. We conduct experiments on two datasets which include healthy and pathological pancreases respectively, and achieve the current state-of-the-art in terms of Dice-S{\o}rensen Coefficient (DSC). On the NIH pancreas segmentation dataset, we outperform the previous best by an average of over 2%, and the worst case is improved by 7% to reach almost 70%, which indicates the reliability of our framework in clinical applications.