Control Regularization for Reduced Variance Reinforcement Learning

Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization approach to augmenting model-free RL. In particular, we regularize the behavior of the deep policy to be similar to a policy prior, i.e., we regularize in function space. We show that functional regularization yields a bias-variance trade-off, and propose an adaptive tuning strategy to optimize this trade-off. When the policy prior has control-theoretic stability guarantees, we further show that this regularization approximately preserves those stability guarantees throughout learning. We validate our approach empirically on a range of settings, and demonstrate significantly reduced variance, guaranteed dynamic stability, and more efficient learning than deep RL alone.Comment: Appearing in ICML 201

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

Verifiable Reinforcement Learning via Policy Extraction

While deep reinforcement learning has successfully solved many challenging control tasks, its real-world applicability has been limited by the inability to ensure the safety of learned policies. We propose an approach to verifiable reinforcement learning by training decision tree policies, which can represent complex policies (since they are nonparametric), yet can be efficiently verified using existing techniques (since they are highly structured). The challenge is that decision tree policies are difficult to train. We propose VIPER, an algorithm that combines ideas from model compression and imitation learning to learn decision tree policies guided by a DNN policy (called the oracle) and its Q-function, and show that it substantially outperforms two baselines. We use VIPER to (i) learn a provably robust decision tree policy for a variant of Atari Pong with a symbolic state space, (ii) learn a decision tree policy for a toy game based on Pong that provably never loses, and (iii) learn a provably stable decision tree policy for cart-pole. In each case, the decision tree policy achieves performance equal to that of the original DNN policy

Adding Neural Network Controllers to Behavior Trees without Destroying Performance Guarantees

In this paper, we show how Behavior Trees that have performance guarantees, in terms of safety and goal convergence, can be extended with components that were designed using machine learning, without destroying those performance guarantees. Machine learning approaches such as reinforcement learning or learning from demonstration can be very appealing to AI designers that want efficient and realistic behaviors in their agents. However, those algorithms seldom provide guarantees for solving the given task in all different situations while keeping the agent safe. Instead, such guarantees are often easier to find for manually designed model based approaches. In this paper we exploit the modularity of Behavior trees to extend a given design with an efficient, but possibly unreliable, machine learning component in a way that preserves the guarantees. The approach is illustrated with an inverted pendulum example.Comment: Submitted to IEEE Transactions on Game

Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems

Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge, weakening theoretical guarantees and causing implementation failures on physical systems. This paper develops a machine learning framework centered around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and unmodeled dynamics in general robotic systems. Our proposed method proceeds by iteratively updating estimates of Lyapunov function derivatives and improving controllers, ultimately yielding a stabilizing quadratic program model-based controller. We validate our approach on a planar Segway simulation, demonstrating substantial performance improvements by iteratively refining on a base model-free controller

Reinforcement Learning Based on Real-Time Iteration NMPC

Reinforcement Learning (RL) has proven a stunning ability to learn optimal policies from data without any prior knowledge on the process. The main drawback of RL is that it is typically very difficult to guarantee stability and safety. On the other hand, Nonlinear Model Predictive Control (NMPC) is an advanced model-based control technique which does guarantee safety and stability, but only yields optimality for the nominal model. Therefore, it has been recently proposed to use NMPC as a function approximator within RL. While the ability of this approach to yield good performance has been demonstrated, the main drawback hindering its applicability is related to the computational burden of NMPC, which has to be solved to full convergence. In practice, however, computationally efficient algorithms such as the Real-Time Iteration (RTI) scheme are deployed in order to return an approximate NMPC solution in very short time. In this paper we bridge this gap by extending the existing theoretical framework to also cover RL based on RTI NMPC. We demonstrate the effectiveness of this new RL approach with a nontrivial example modeling a challenging nonlinear system subject to stochastic perturbations with the objective of optimizing an economic cost.Comment: accepted for the IFAC World Congress 202

Understanding Model-Based Reinforcement Learning and its Application in Safe Reinforcement Learning

Model-based reinforcement learning algorithms have been shown to achieve successful results on various continuous control benchmarks, but the understanding of model-based methods is limited. We try to interpret how model-based method works through novel experiments on state-of-the-art algorithms with an emphasis on the model learning part. We evaluate the role of the model learning in policy optimization and propose methods to learn a more accurate model. With a better understanding of model-based reinforcement learning, we then apply model-based methods to solve safe reinforcement learning (RL) problems with near-zero violation of hard constraints throughout training. Drawing an analogy with how humans and animals learn to perform safe actions, we break down the safe RL problem into three stages. First, we train agents in a constraint-free environment to learn a performant policy for reaching high rewards, and simultaneously learn a model of the dynamics. Second, we use model-based methods to plan safe actions and train a safeguarding policy from these actions through imitation. Finally, we propose a factored framework to train an overall policy that mixes the performant policy and the safeguarding policy. This three-step curriculum ensures near-zero violation of safety constraints at all times. As an advantage of model-based method, the sample complexity required at the second and third steps of the process is significantly lower than model-free methods and can enable online safe learning. We demonstrate the effectiveness of our methods in various continuous control problems and analyze the advantages over state-of-the-art approaches

Data-driven Economic NMPC using Reinforcement Learning

Reinforcement Learning (RL) is a powerful tool to perform data-driven optimal control without relying on a model of the system. However, RL struggles to provide hard guarantees on the behavior of the resulting control scheme. In contrast, Nonlinear Model Predictive Control (NMPC) and Economic NMPC (ENMPC) are standard tools for the closed-loop optimal control of complex systems with constraints and limitations, and benefit from a rich theory to assess their closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the quality of the model underlying the control scheme. In this paper, we show that an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system even when using a wrong model. This result also holds for real systems having stochastic dynamics. This entails that ENMPC can be used as a new type of function approximator within RL. Furthermore, we investigate our results in the context of ENMPC and formally connect them to the concept of dissipativity, which is central for the ENMPC stability. Finally, we detail how these results can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply these tools on both a classical linear MPC setting and a standard nonlinear example from the ENMPC literature