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Learning convex bounds for linear quadratic control policy synthesis

arXiv.org Machine Learning

Learning to make decisions from observed data in dynamic environments remains a problem of fundamental importance in a number of fields, from artificial intelligence and robotics, to medicine and finance. This paper concerns the problem of learning control policies for unknown linear dynamical systems so as to maximize a quadratic reward function. We present a method to optimize the expected value of the reward over the posterior distribution of the unknown system parameters, given data. The algorithm involves sequential convex programing, and enjoys reliable local convergence and robust stability guarantees. Numerical simulations and stabilization of a real-world inverted pendulum are used to demonstrate the approach, with strong performance and robustness properties observed in both.


SABLAS: Learning Safe Control for Black-box Dynamical Systems

#artificialintelligence

Control certificates based on barrier functions have been a powerful tool to generate probably safe control policies for dynamical systems. However, existing methods based on barrier certificates are normally for white-box systems with differentiable dynamics, which makes them inapplicable to many practical applications where the system is a black-box and cannot be accurately modeled. On the other side, model-free reinforcement learning (RL) methods for black-box systems suffer from lack of safety guarantees and low sampling efficiency. In this paper, we propose a novel method that can learn safe control policies and barrier certificates for black-box dynamical systems, without requiring for an accurate system model. Our method re-designs the loss function to back-propagate gradient to the control policy even when the black-box dynamical system is non-differentiable, and we show that the safety certificates hold on the black-box system. Empirical results in simulation show that our method can significantly improve the performance of the learned policies by achieving nearly 100% safety and goal reaching rates using much fewer training samples, compared to state-of-the-art black-box safe control methods. Our learned agents can also generalize to unseen scenarios while keeping the original performance. The source code can be found at https://github.com/Zengyi-Qin/bcbf.


Neural Dynamic Policies for End-to-End Sensorimotor Learning

arXiv.org Machine Learning

The current dominant paradigm in sensorimotor control, whether imitation or reinforcement learning, is to train policies directly in raw action spaces such as torque, joint angle, or end-effector position. This forces the agent to make decisions individually at each timestep in training, and hence, limits the scalability to continuous, high-dimensional, and long-horizon tasks. In contrast, research in classical robotics has, for a long time, exploited dynamical systems as a policy representation to learn robot behaviors via demonstrations. These techniques, however, lack the flexibility and generalizability provided by deep learning or reinforcement learning and have remained under-explored in such settings. In this work, we begin to close this gap and embed the structure of a dynamical system into deep neural network-based policies by reparameterizing action spaces via second-order differential equations. We propose Neural Dynamic Policies (NDPs) that make predictions in trajectory distribution space as opposed to prior policy learning methods where actions represent the raw control space. The embedded structure allows end-to-end policy learning for both reinforcement and imitation learning setups. We show that NDPs outperform the prior state-of-the-art in terms of either efficiency or performance across several robotic control tasks for both imitation and reinforcement learning setups.


SABLAS: Learning Safe Control for Black-box Dynamical Systems

arXiv.org Artificial Intelligence

Control certificates based on barrier functions have been a powerful tool to generate probably safe control policies for dynamical systems. However, existing methods based on barrier certificates are normally for white-box systems with differentiable dynamics, which makes them inapplicable to many practical applications where the system is a black-box and cannot be accurately modeled. On the other side, model-free reinforcement learning (RL) methods for black-box systems suffer from lack of safety guarantees and low sampling efficiency. In this paper, we propose a novel method that can learn safe control policies and barrier certificates for black-box dynamical systems, without requiring for an accurate system model. Our method re-designs the loss function to back-propagate gradient to the control policy even when the black-box dynamical system is non-differentiable, and we show that the safety certificates hold on the black-box system. Empirical results in simulation show that our method can significantly improve the performance of the learned policies by achieving nearly 100% safety and goal reaching rates using much fewer training samples, compared to state-of-the-art black-box safe control methods. Our learned agents can also generalize to unseen scenarios while keeping the original performance. The source code can be found at https://github.com/Zengyi-Qin/bcbf.


Learning to Encode Position for Transformer with Continuous Dynamical Model

arXiv.org Machine Learning

We introduce a new way of learning to encode position information for non-recurrent models, such as Transformer models. Unlike RNN and LSTM, which contain inductive bias by loading the input tokens sequentially, non-recurrent models are less sensitive to position. The main reason is that position information among input units is not inherently encoded, i.e., the models are permutation equivalent; this problem justifies why all of the existing models are accompanied by a sinusoidal encoding/embedding layer at the input. However, this solution has clear limitations: the sinusoidal encoding is not flexible enough as it is manually designed and does not contain any learnable parameters, whereas the position embedding restricts the maximum length of input sequences. It is thus desirable to design a new position layer that contains learnable parameters to adjust to different datasets and different architectures. At the same time, we would also like the encodings to extrapolate in accordance with the variable length of inputs. In our proposed solution, we borrow from the recent Neural ODE approach, which may be viewed as a versatile continuous version of a ResNet. This model is capable of modeling many kinds of dynamical systems. We model the evolution of encoded results along position index by such a dynamical system, thereby overcoming the above limitations of existing methods. We evaluate our new position layers on a variety of neural machine translation and language understanding tasks, the experimental results show consistent improvements over the baselines.