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1. Enhancing Vehicle Flow in Random Environments through Dynamic Allocation of Sensing Resources

   S. Kassir and G. de Veciana (September 2022, IEEE Vehicular Technology Conference (VTC))

   This paper presents a theoretical analysis for a self-driving vehicle’s velocity as it navigates through a random environment. We study a stylized environment and vehicle mobility model capturing the essential features of a self-driving vehicle’s behavior, and leverage results from stochastic geometry to characterize the distribution of a typical vehicle’s safe driving velocity, as a function of key network parameters such as the density of objects in the environment and sensing accuracy. We then consider a setting wherein the sensing accuracy is subject to a sensing/communication rate constraint. We propose a procedure that focuses the vehicle’s sensing/communication resources and estimation efforts on the objects that affect its velocity and safety the most so as to optimize its ability to drive faster in uncertain environments. Simulation results show that the proposed methodology achieves considerable gains in the vehicle’s safe driving velocity as compared to uniform rate allocation policies. 

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2. Random Ambiguity

   Lu, Jay (May 2021, Theoretical economics)

   Spiegler, Ran (Ed.)

   We introduce a model of random ambiguity aversion. Choice is stochastic due to unobserved shocks to both information and ambiguity aversion. This is modeled as a random set of beliefs in the maxmin expected utility model of Gilboa and Schmeidler (1989). We characterize the model and show that the distribution of ambiguity aversion can be uniquely identified using binary choices. A novel stochastic order on random sets is introduced that characterizes greater uncertainty aversion under stochastic choice. If the set of priors is the Aumann expectation of the random set, then choices satisfy dynamic consistency. This corresponds to an agent who knows the distribution of signals but is uncertain about how to interpret signal realizations. More broadly, the analysis of stochastic properties of random ambiguity attitudes provides a theoretical foundation for the study of models of random non-linear utility. 

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3. Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos

   Ghosh, Subhroshekhar; Balasubramanian, Krishna; Yang, Xiaochuan (January 2020, Proceedings of Machine Learning Research)

   We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications. FGNs interpolate continuously between the popular purely random geometric graphs (a.k.a. the Poisson Boolean network), and random graphs with increasingly fractal behavior. In fact, they form a parametric family of sparse random geometric graphs that are parametrised by a fractality parameter 𝜈 which governs the strength of the fractal structure. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right. We explore the natural question of detecting the presence of fractality and the problem of parameter estimation based on observed network data. Finally, we explore fractality in community structures by unveiling a natural stochastic block model in the setting of FGNs. 

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4. Learning the model-free linear quadratic regulator via random search

   Hesameddin Mohammadi, Mihailo R. (January 2020, Proceedings of the 2nd Conference on Learning for Dynamics and Control.)

   null (Ed.)

   Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these approaches are often poorly understood because of the nonconvex nature of the underlying optimization problems as well as the lack of exact gradient computation. In this paper, we examine the standard infinite-horizon linear quadratic regulator problem for continuous-time systems with unknown state-space parameters. We provide theoretical bounds on the convergence rate and sample complexity of a random search method. Our results demonstrate that the required simulation time for achieving 𝜖-accuracy in a model-free setup and the total number of function evaluations are both of 𝑂(log(1/𝜖)). 

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5. Online Change Point Detection for Random Dot Product Graphs

   https://doi.org/10.1109/IEEECONF53345.2021.9723374  

   Marenco, Bernardo; Bermolen, Paola; Fiori, Marcelo; Larroca, Federico; Mateos, Gonzalo (October 2021, 2021 55th Asilomar Conference on Signals, Systems, and Computers)

   Given a sequence of random graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. To this end, we adopt the Random Dot Product Graph (RDPG) model which postulates each node has an associated latent vector, and inner products between these vectors dictate the edge formation probabilities. Existing approaches for graph change-point detection (CPD) rely either on extensive computation, or they store and process the entire observed time series. In this paper we consider the cumulative sum of a judicious monitoring function, which quantifies the discrepancy between the streaming graph observations and the nominal model. This reference distribution is inferred via spectral embeddings of the first few graphs in the sequence, and the monitoring function can be updated in an efficient, online fashion. We characterize the distribution of this running statistic, allowing us to select appropriate thresholding parameters that guarantee error-rate control. The end result is a lightweight online CPD algorithm, with a proven capability to flag distribution shifts in the arriving graphs. The novel method is tested on both synthetic and real network data, corroborating its effectiveness in quickly detecting changes in the input graph sequence. 

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