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1. Informing Multi-Modal Planning with Synergistic Discrete Leads

   https://doi.org/10.1109/ICRA40945.2020.9197545  

   Kingston, Zachary; Wells, Andrew M.; Moll, Mark; Kavraki, Lydia E. (April 2020, 2020 IEEE International Conference on Robotics and Automation)

   Robotic manipulation problems are inherently continuous, but typically have underlying discrete structure, e.g., whether or not an object is grasped. This means many problems are multi-modal and in particular have a continuous infinity of modes. For example, in a pick-and-place manipulation domain, every grasp and placement of an object is a mode. Usually manipulation problems require the robot to transition into different modes, e.g., going from a mode with an object placed to another mode with the object grasped. To successfully find a manipulation plan, a planner must find a sequence of valid single-mode motions as well as valid transitions between these modes. Many manipulation planners have been proposed to solve tasks with multi-modal structure. However, these methods require mode-specific planners and fail to scale to very cluttered environments or to tasks that require long sequences of transitions. This paper presents a general layered planning approach to multi-modal planning that uses a discrete “lead” to bias search towards useful mode transitions. The difficulty of achieving specific mode transitions is captured online and used to bias search towards more promising sequences of modes. We demonstrate our planner on complex scenes and show that significant performance improvements are tied to both our discrete “lead” and our continuous representation. 

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2. Numerical Solutions for Detecting Contingency in Modern Power Systems

   https://doi.org/10.1109/ICTC57116.2023.10154790  

   Ma, Xiaohang; Qian, Hongjiang; Wang, Le Yi; Nazari, Masoud H.; Yin, George (May 2023, Proc. 2023 4th IEEE Inform. Comm. Tech. Conference)

   This paper is devoted to the detection of contingencies in modern power systems. Because the systems we consider are under the framework of cyber-physical systems, it is necessary to take into consideration of the information processing aspect and communication networks. A consequence is that noise and random disturbances are unavoidable. The detection problem then becomes one known as quickest detection. In contrast to running the detection problem in a discretetime setting leading to a sequence of detection problems, this work focuses on the problem in a continuous-time setup. We treat stochastic differential equation models. One of the distinct features is that the systems are hybrid involving both continuous states and discrete events that coexist and interact. The discrete event process is modeled by a continuous-time Markov chain representing random environments that are not resented by a continuous sample path. The quickest detection then can be written as an optimal stopping problem. This paper is devoted to finding numerical solutions to the underlying problem. We use a Markov chain approximation method to construct the numerical algorithms. Numerical examples are used to demonstrate the performance. 

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3. Nonlinear Information Bottleneck

   https://doi.org/10.3390/e21121181  

   Kolchinsky, Artemy; Tracey, Brendan D.; Wolpert, David H. (December 2019, Entropy)

   Information bottleneck (IB) is a technique for extracting information in one random variable X that is relevant for predicting another random variable Y. IB works by encoding X in a compressed “bottleneck” random variable M from which Y can be accurately decoded. However, finding the optimal bottleneck variable involves a difficult optimization problem, which until recently has been considered for only two limited cases: discrete X and Y with small state spaces, and continuous X and Y with a Gaussian joint distribution (in which case optimal encoding and decoding maps are linear). We propose a method for performing IB on arbitrarily-distributed discrete and/or continuous X and Y, while allowing for nonlinear encoding and decoding maps. Our approach relies on a novel non-parametric upper bound for mutual information. We describe how to implement our method using neural networks. We then show that it achieves better performance than the recently-proposed “variational IB” method on several real-world datasets. 

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4. Integrating Symbolic Planning and Reinforcement Learning for Following Temporal Logic Specifications

   https://doi.org/10.1109/IJCNN55064.2022.9892304  

   Xu, Duo; Fekri, Faramarz (July 2022, 2022 International Joint Conference on Neural Networks (IJCNN))

   Teaching a deep reinforcement learning (RL) agent to follow instructions in multi-task environments is a challenging problem. We consider that user defines every task by a linear temporal logic (LTL) formula. However, some causal dependencies in complex environments may be unknown to the user in advance. Hence, when human user is specifying instructions, the robot cannot solve the tasks by simply following the given instructions. In this work, we propose a hierarchical reinforcement learning (HRL) framework in which a symbolic transition model is learned to efficiently produce high-level plans that can guide the agent efficiently solve different tasks. Specifically, the symbolic transition model is learned by inductive logic programming (ILP) to capture logic rules of state transitions. By planning over the product of the symbolic transition model and the automaton derived from the LTL formula, the agent can resolve causal dependencies and break a causally complex problem down into a sequence of simpler low-level sub-tasks. We evaluate the proposed framework on three environments in both discrete and continuous domains, showing advantages over previous representative methods. 

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5. Learning the closest product state

   Bakshi, A; Bostanci, J; Kretschmer, W; Landau, Z; Li, J; Liu, A; O'Donnell, R; Tang, E (March 2025, https://doi.org/10.48550/arXiv.2411.04283)

   We study the problem of finding a (pure) product state with optimal fidelity to an unknown n-qubit quantum state ρ, given copies of ρ. This is a basic instance of a fundamental question in quantum learning: is it possible to efficiently learn a simple approximation to an arbitrary state? We give an algorithm which finds a product state with fidelity ε-close to optimal, using N=npoly(1/ε) copies of ρ and poly(N) classical overhead. We further show that estimating the optimal fidelity is NP-hard for error ε=1/poly(n), showing that the error dependence cannot be significantly improved. For our algorithm, we build a carefully-defined cover over candidate product states, qubit by qubit, and then demonstrate that extending the cover can be reduced to approximate constrained polynomial optimization. For our proof of hardness, we give a formal reduction from polynomial optimization to finding the closest product state. Together, these results demonstrate a fundamental connection between these two seemingly unrelated questions. Building on our general approach, we also develop more efficient algorithms in three simpler settings: when the optimal fidelity exceeds 5/6; when we restrict ourselves to a discrete class of product states; and when we are allowed to output a matrix product state. 

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