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Reinforcement learning (RL) algorithms have proven transformative in a range of domains. To tackle real-world domains, these systems often use neural networks to learn policies directly from pixels or other high-dimensional sensory input. By contrast, much theory of RL has focused on discrete state spaces or worst-case analysis, and fundamental questions remain about the dynamics of policy learning in high-dimensional settings. Here, we propose a solvable high-dimensional model of RL that can capture a variety of learning protocols, and derive its typical dynamics as a set of closed-form ordinary differential equations (ODEs). We derive optimal schedules for the learning rates and task difficulty - analogous to annealing schemes and curricula during training in RL - and show that the model exhibits rich behaviour, including delayed learning under sparse rewards; a variety of learning regimes depending on reward baselines; and a speed-accuracy trade-off driven by reward stringency. Experiments on variants of the Procgen game "Bossfight" and Arcade Learning Environment game "Pong" also show such a speed-accuracy trade-off in practice. Together, these results take a step towards closing the gap between theory and practice in high-dimensional RL.

With the advent of Unmanned Aerial Vehicles (UAV) and Micro Aerial Vehicles (MAV) in commercial sectors, their application for transporting and manipulating payloads has attracted many research work. A swarm of agents, cooperatively working to transport and manipulate a payload can overcome the physical limitations of a single agent, adding redundancy and tolerance against failures. In this paper, the dynamics of a swarm connected to a payload via flexible cables are modeled, and a decentralized control is designed using Artificial Potential Field (APF). The swarm is able to transport the payload through an unknown environment to a goal position while avoiding obstacles from the local information received from the onboard sensors. The key contributions are (a) the cables are modelled more accurately using lumped mass model instead of geometric constraints, (b) a decentralized swarm control is designed using potential field approach to ensure hover stability of system without payload state information, (c) the manipulation of payload elevation and azimuth angles are controlled by APF, and (d) the trajectory of the payload for transportation is governed by potential fields generated by goal point and obstacles. The efficacy of the method proposed in this work are evaluated through numerical simulations under the influence of external disturbances and failure of agents.

We propose a logic-informed knowledge-driven modeling framework for human movements by analyzing their trajectories. Our approach is inspired by the fact that human actions are usually driven by their intentions or desires, and are influenced by environmental factors such as the spatial relationships with surrounding objects. In this paper, we introduce a set of spatial-temporal logic rules as knowledge to explain human actions. These rules will be automatically discovered from observational data. To learn the model parameters and the rule content, we design an expectation-maximization (EM) algorithm, which treats the rule content as latent variables. The EM algorithm alternates between the E-step and M-step: in the E-step, the posterior distribution over the latent rule content is evaluated; in the M-step, the rule generator and model parameters are jointly optimized by maximizing the current expected log-likelihood. Our model may have a wide range of applications in areas such as sports analytics, robotics, and autonomous cars, where understanding human movements are essential. We demonstrate the model's superior interpretability and prediction performance on pedestrian and NBA basketball player datasets, both achieving promising results.

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons. We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution, while accounting for the agent's action at every time step. Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also report promising experimental results in dynamics modeling for the scenarios of both model-based planning and model-free RL.

Due to the inherent uncertainty in their deformability during motion, previous methods in rope manipulation often require hundreds of real-world demonstrations to train a manipulation policy for each rope, even for simple tasks such as rope goal reaching, which hinder their applications in our ever-changing world. To address this issue, we introduce GenORM, a framework that allows the manipulation policy to handle different deformable ropes with a single real-world demonstration. To achieve this, we augment the policy by conditioning it on deformable rope parameters and training it with a diverse range of simulated deformable ropes so that the policy can adjust actions based on different rope parameters. At the time of inference, given a new rope, GenORM estimates the deformable rope parameters by minimizing the disparity between the grid density of point clouds of real-world demonstrations and simulations. With the help of a differentiable physics simulator, we require only a single real-world demonstration. Empirical validations on both simulated and real-world rope manipulation setups clearly show that our method can manipulate different ropes with a single demonstration and significantly outperforms the baseline in both environments (62% improvement in in-domain ropes, and 15% improvement in out-of-distribution ropes in simulation, 26% improvement in real-world), demonstrating the effectiveness of our approach in one-shot rope manipulation.

This paper considers a single-trajectory system identification problem for linear systems under general nonlinear and/or time-varying policies with i.i.d. random excitation noises. The problem is motivated by safe learning-based control for constrained linear systems, where the safe policies during the learning process are usually nonlinear and time-varying for satisfying the state and input constraints. In this paper, we provide a non-asymptotic error bound for least square estimation when the data trajectory is generated by any nonlinear and/or time-varying policies as long as the generated state and action trajectories are bounded. This significantly generalizes the existing non-asymptotic guarantees for linear system identification, which usually consider i.i.d. random inputs or linear policies. Interestingly, our error bound is consistent with that for linear policies with respect to the dependence on the trajectory length, system dimensions, and excitation levels. Lastly, we demonstrate the applications of our results by safe learning with robust model predictive control and provide numerical analysis.

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either low-dimensional projections of neural activity, or on learning dynamical systems that explicitly relate to the neural state over time. We discuss how these two approaches are interrelated by considering dynamical systems as representative of flows on a low-dimensional manifold. Building on this concept, we propose a new decomposed dynamical system model that represents complex non-stationary and nonlinear dynamics of time series data as a sparse combination of simpler, more interpretable components. Our model is trained through a dictionary learning procedure, where we leverage recent results in tracking sparse vectors over time. The decomposed nature of the dynamics is more expressive than previous switched approaches for a given number of parameters and enables modeling of overlapping and non-stationary dynamics. In both continuous-time and discrete-time instructional examples we demonstrate that our model can well approximate the original system, learn efficient representations, and capture smooth transitions between dynamical modes, focusing on intuitive low-dimensional non-stationary linear and nonlinear systems. Furthermore, we highlight our model's ability to efficiently capture and demix population dynamics generated from multiple independent subnetworks, a task that is computationally impractical for switched models. Finally, we apply our model to neural "full brain" recordings of C. elegans data, illustrating a diversity of dynamics that is obscured when classified into discrete states.

As a unifying concept in economics, game theory, and operations research, even in the Robotics and AI field, the utility is used to evaluate the level of individual needs, preferences, and interests. Especially for decision-making and learning in multi-agent/robot systems (MAS/MRS), a suitable utility model can guide agents in choosing reasonable strategies to achieve their current needs and learning to cooperate and organize their behaviors, optimizing the system's utility, building stable and reliable relationships, and guaranteeing each group member's sustainable development, similar to the human society. Although these systems' complex, large-scale, and long-term behaviors are strongly determined by the fundamental characteristics of the underlying relationships, there has been less discussion on the theoretical aspects of mechanisms and the fields of applications in Robotics and AI. This paper introduces a utility-orient needs paradigm to describe and evaluate inter and outer relationships among agents' interactions. Then, we survey existing literature in relevant fields to support it and propose several promising research directions along with some open problems deemed necessary for further investigations.

Due to the inherent uncertainty in their deformability during motion, previous methods in rope manipulation often require hundreds of real-world demonstrations to train a manipulation policy for each rope, even for simple tasks such as rope goal reaching, which hinder their applications in our ever-changing world. To address this issue, we introduce GenORM, a framework that allows the manipulation policy to handle different deformable ropes with a single real-world demonstration. To achieve this, we augment the policy by conditioning it on deformable rope parameters and training it with a diverse range of simulated deformable ropes so that the policy can adjust actions based on different rope parameters. At the time of inference, given a new rope, GenORM estimates the deformable rope parameters by minimizing the disparity between the grid density of point clouds of real-world demonstrations and simulations. With the help of a differentiable physics simulator, we require only a single real-world demonstration. Empirical validations on both simulated and real-world rope manipulation setups clearly show that our method can manipulate different ropes with a single demonstration and significantly outperforms the baseline in both environments (62% improvement in in-domain ropes, and 15% improvement in out-of-distribution ropes in simulation, 26% improvement in real-world), demonstrating the effectiveness of our approach in one-shot rope manipulation.