Shared Linear Quadratic Regulation Control: A Reinforcement Learning Approach

We propose controller synthesis for state regulation problems in which a human operator shares control with an autonomy system, running in parallel. The autonomy system continuously improves over human action, with minimal intervention, and can take over full-control. It additively combines user input with an adaptive optimal corrective signal. It is adaptive in that it neither estimates nor requires a model of the human's action policy, or the internal dynamics of the plant, and can adjust to changes in both. Our contribution is twofold; first, a new synthesis for shared control which we formulate as an adaptive optimal control problem for continuous-time linear systems and solve it online as a human-in-the-loop reinforcement learning. The result is an architecture that we call shared linear quadratic regulator (sLQR). Second, we provide new analysis of reinforcement learning for continuous-time linear systems in two parts. In the first analysis part, we avoid learning along a single state-space trajectory which we show leads to data collinearity under certain conditions. We make a clear separation between exploitation of learned policies and exploration of the state-space, and propose an exploration scheme that requires switching to new state-space trajectories rather than injecting noise continuously while learning. This avoidance of continuous noise injection minimizes interference with human action, and avoids bias in the convergence to the stabilizing solution of the underlying algebraic Riccati equation. We show that exploring a minimum number of pairwise distinct state-space trajectories is necessary to avoid collinearity in the learning data. In the second analysis part, we show conditions under which existence and uniqueness of solutions can be established for off-policy reinforcement learning in continuous-time linear systems; namely, prior knowledge of the input matrix.Comment: Accepted by IEEE CDC 201

PAC-Bayes Control: Learning Policies that Provably Generalize to Novel Environments

Our goal is to learn control policies for robots that provably generalize well to novel environments given a dataset of example environments. The key technical idea behind our approach is to leverage tools from generalization theory in machine learning by exploiting a precise analogy (which we present in the form of a reduction) between generalization of control policies to novel environments and generalization of hypotheses in the supervised learning setting. In particular, we utilize the Probably Approximately Correct (PAC)-Bayes framework, which allows us to obtain upper bounds that hold with high probability on the expected cost of (stochastic) control policies across novel environments. We propose policy learning algorithms that explicitly seek to minimize this upper bound. The corresponding optimization problem can be solved using convex optimization (Relative Entropy Programming in particular) in the setting where we are optimizing over a finite policy space. In the more general setting of continuously parameterized policies (e.g., neural network policies), we minimize this upper bound using stochastic gradient descent. We present simulated results of our approach applied to learning (1) reactive obstacle avoidance policies and (2) neural network-based grasping policies. We also present hardware results for the Parrot Swing drone navigating through different obstacle environments. Our examples demonstrate the potential of our approach to provide strong generalization guarantees for robotic systems with continuous state and action spaces, complicated (e.g., nonlinear) dynamics, rich sensory inputs (e.g., depth images), and neural network-based policies.Comment: Extended version of paper presented at the 2018 Conference on Robot Learning (CoRL

Safety-guided deep reinforcement learning via online gaussian process estimation

An important facet of reinforcement learning (RL) has to do with how the agent goes about exploring the environment. Traditional exploration strategies typically focus on efficiency and ignore safety. However, for practical applications, ensuring safety of the agent during exploration is crucial since performing an unsafe action or reaching an unsafe state could result in irreversible damage to the agent. The main challenge of safe exploration is that characterizing the unsafe states and actions is difficult for large continuous state or action spaces and unknown environments. In this paper, we propose a novel approach to incorporate estimations of safety to guide exploration and policy search in deep reinforcement learning. By using a cost function to capture trajectory-based safety, our key idea is to formulate the state-action value function of this safety cost as a candidate Lyapunov function and extend control-theoretic results to approximate its derivative using online Gaussian Process (GP) estimation. We show how to use these statistical models to guide the agent in unknown environments to obtain high-performance control policies with provable stability certificates.Accepted manuscrip

Learning robust control for LQR systems with multiplicative noise via policy gradient

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all recent work in this area, we consider multiplicative noise models, which are increasingly relevant because they explicitly incorporate inherent uncertainty and variation in the system dynamics and thereby improve robustness properties of the controller. Robustness is a critical and poorly understood issue in reinforcement learning; existing methods which do not account for uncertainty can converge to fragile policies or fail to converge at all. Additionally, intentional injection of multiplicative noise into learning algorithms can enhance robustness of policies, as observed in ad hoc work on domain randomization. Although policy gradient algorithms require optimization of a non-convex cost function, we show that the multiplicative noise LQR cost has a special property called gradient domination, which is exploited to prove global convergence of policy gradient algorithms to the globally optimum control policy with polynomial dependence on problem parameters. Results are provided both in the model-known and model-unknown settings where samples of system trajectories are used to estimate policy gradients

SAR: Generalization of Physiological Agility and Dexterity via Synergistic Action Representation

Learning effective continuous control policies in high-dimensional systems, including musculoskeletal agents, remains a significant challenge. Over the course of biological evolution, organisms have developed robust mechanisms for overcoming this complexity to learn highly sophisticated strategies for motor control. What accounts for this robust behavioral flexibility? Modular control via muscle synergies, i.e. coordinated muscle co-contractions, is considered to be one putative mechanism that enables organisms to learn muscle control in a simplified and generalizable action space. Drawing inspiration from this evolved motor control strategy, we use physiologically accurate human hand and leg models as a testbed for determining the extent to which a Synergistic Action Representation (SAR) acquired from simpler tasks facilitates learning more complex tasks. We find in both cases that SAR-exploiting policies significantly outperform end-to-end reinforcement learning. Policies trained with SAR were able to achieve robust locomotion on a wide set of terrains with high sample efficiency, while baseline approaches failed to learn meaningful behaviors. Additionally, policies trained with SAR on a multiobject manipulation task significantly outperformed (>70% success) baseline approaches (<20% success). Both of these SAR-exploiting policies were also found to generalize zero-shot to out-of-domain environmental conditions, while policies that did not adopt SAR failed to generalize. Finally, we establish the generality of SAR on broader high-dimensional control problems using a robotic manipulation task set and a full-body humanoid locomotion task. To the best of our knowledge, this investigation is the first of its kind to present an end-to-end pipeline for discovering synergies and using this representation to learn high-dimensional continuous control across a wide diversity of tasks.Comment: Accepted to RSS 202

CAQL: Continuous Action Q-Learning

Value-based reinforcement learning (RL) methods like Q-learning have shown success in a variety of domains. One challenge in applying Q-learning to continuous-action RL problems, however, is the continuous action maximization (max-Q) required for optimal Bellman backup. In this work, we develop CAQL, a (class of) algorithm(s) for continuous-action Q-learning that can use several plug-and-play optimizers for the max-Q problem. Leveraging recent optimization results for deep neural networks, we show that max-Q can be solved optimally using mixed-integer programming (MIP). When the Q-function representation has sufficient power, MIP-based optimization gives rise to better policies and is more robust than approximate methods (e.g., gradient ascent, cross-entropy search). We further develop several techniques to accelerate inference in CAQL, which despite their approximate nature, perform well. We compare CAQL with state-of-the-art RL algorithms on benchmark continuous-control problems that have different degrees of action constraints and show that CAQL outperforms policy-based methods in heavily constrained environments, often dramatically

Q-Learning in enormous action spaces via amortized approximate maximization

Applying Q-learning to high-dimensional or continuous action spaces can be difficult due to the required maximization over the set of possible actions. Motivated by techniques from amortized inference, we replace the expensive maximization over all actions with a maximization over a small subset of possible actions sampled from a learned proposal distribution. The resulting approach, which we dub Amortized Q-learning (AQL), is able to handle discrete, continuous, or hybrid action spaces while maintaining the benefits of Q-learning. Our experiments on continuous control tasks with up to 21 dimensional actions show that AQL outperforms D3PG (Barth-Maron et al, 2018) and QT-Opt (Kalashnikov et al, 2018). Experiments on structured discrete action spaces demonstrate that AQL can efficiently learn good policies in spaces with thousands of discrete actions.Comment: A previous version of this work appeared at the Deep Reinforcement Learning Workshop, NeurIPS 201

Soft Decomposed Policy-Critic: Bridging the Gap for Effective Continuous Control with Discrete RL

Discrete reinforcement learning (RL) algorithms have demonstrated exceptional performance in solving sequential decision tasks with discrete action spaces, such as Atari games. However, their effectiveness is hindered when applied to continuous control problems due to the challenge of dimensional explosion. In this paper, we present the Soft Decomposed Policy-Critic (SDPC) architecture, which combines soft RL and actor-critic techniques with discrete RL methods to overcome this limitation. SDPC discretizes each action dimension independently and employs a shared critic network to maximize the soft $Q$-function. This novel approach enables SDPC to support two types of policies: decomposed actors that lead to the Soft Decomposed Actor-Critic (SDAC) algorithm, and decomposed $Q$-networks that generate Boltzmann soft exploration policies, resulting in the Soft Decomposed-Critic Q (SDCQ) algorithm. Through extensive experiments, we demonstrate that our proposed approach outperforms state-of-the-art continuous RL algorithms in a variety of continuous control tasks, including Mujoco's Humanoid and Box2d's BipedalWalker. These empirical results validate the effectiveness of the SDPC architecture in addressing the challenges associated with continuous control

Differentiable MPC for End-to-end Planning and Control

We present foundations for using Model Predictive Control (MPC) as a differentiable policy class for reinforcement learning in continuous state and action spaces. This provides one way of leveraging and combining the advantages of model-free and model-based approaches. Specifically, we differentiate through MPC by using the KKT conditions of the convex approximation at a fixed point of the controller. Using this strategy, we are able to learn the cost and dynamics of a controller via end-to-end learning. Our experiments focus on imitation learning in the pendulum and cartpole domains, where we learn the cost and dynamics terms of an MPC policy class. We show that our MPC policies are significantly more data-efficient than a generic neural network and that our method is superior to traditional system identification in a setting where the expert is unrealizable.Comment: NeurIPS 201

Quadratic Q-network for Learning Continuous Control for Autonomous Vehicles

Reinforcement Learning algorithms have recently been proposed to learn time-sequential control policies in the field of autonomous driving. Direct applications of Reinforcement Learning algorithms with discrete action space will yield unsatisfactory results at the operational level of driving where continuous control actions are actually required. In addition, the design of neural networks often fails to incorporate the domain knowledge of the targeting problem such as the classical control theories in our case. In this paper, we propose a hybrid model by combining Q-learning and classic PID (Proportion Integration Differentiation) controller for handling continuous vehicle control problems under dynamic driving environment. Particularly, instead of using a big neural network as Q-function approximation, we design a Quadratic Q-function over actions with multiple simple neural networks for finding optimal values within a continuous space. We also build an action network based on the domain knowledge of the control mechanism of a PID controller to guide the agent to explore optimal actions more efficiently.We test our proposed approach in simulation under two common but challenging driving situations, the lane change scenario and ramp merge scenario. Results show that the autonomous vehicle agent can successfully learn a smooth and efficient driving behavior in both situations.Comment: Machine Learning for Autonomous Driving Workshop on NeurIPS, 201