Forward invariance is a long-studied property in control theory that is used to certify that a dynamical system stays within some pre-specified set of states for all time, and also admits robustness guarantees (e.g., the certificate holds under perturbations). We propose a general framework for training and provably certifying robust forward invariance in Neural ODEs. We apply this framework to provide certified safety in robust continuous control. To our knowledge, this is the first instance of training Neural ODE policies with such non-vacuous certified guarantees. In addition, we explore the generality of our framework by using it to certify adversarial robustness for image classification.
Policies produced by deep reinforcement learning are typically characterised by their learning curves, but they remain poorly understood in many other respects. ReLU-based policies result in a partitioning of the input space into piecewise linear regions. We seek to understand how observed region counts and their densities evolve during deep reinforcement learning using empirical results that span a range of continuous control tasks and policy network dimensions. Intuitively, we may expect that during training, the region density increases in the areas that are frequently visited by the policy, thereby affording fine-grained control. We use recent theoretical and empirical results for the linear regions induced by neural networks in supervised learning settings for grounding and comparison of our results. Empirically, we find that the region density increases only moderately throughout training, as measured along fixed trajectories coming from the final policy. However, the trajectories themselves also increase in length during training, and thus the region densities decrease as seen from the perspective of the current trajectory. Our findings suggest that the complexity of deep reinforcement learning policies does not principally emerge from a significant growth in the complexity of functions observed on-and-around trajectories of the policy.
Attitude control of a novel regional truss-braced wing aircraft with low stability characteristics is addressed in this paper using Reinforcement Learning (RL). In recent years, RL has been increasingly employed in challenging applications, particularly, autonomous flight control. However, a significant predicament confronting discrete RL algorithms is the dimension limitation of the state-action table and difficulties in defining the elements of the RL environment. To address these issues, in this paper, a detailed mathematical model of the mentioned aircraft is first developed to shape an RL environment. Subsequently, Q-learning, the most prevalent discrete RL algorithm will be implemented in both the Markov Decision Process (MDP), and Partially Observable Markov Decision Process (POMDP) frameworks to control the longitudinal mode of the air vehicle. In order to eliminate residual fluctuations that are a consequence of discrete action selection, and simultaneously track variable pitch angles, a Fuzzy Action Assignment (FAA) method is proposed to generate continuous control commands using the trained Q-table. Accordingly, it will be proved that by defining an accurate reward function, along with observing all crucial states, the performance of the introduced control system surpasses a well-tuned PID controller.
The growing demand for virtual reality (VR) applications requires wireless systems to provide a high transmission rate to support 360-degree video streaming to multiple users simultaneously. In this paper, we propose an intelligent reflecting surface (IRS)-aided rate-splitting (RS) VR streaming system. In the proposed system, RS facilitates the exploitation of the shared interests of the users in VR streaming, and IRS creates additional propagation channels to support the transmission of high-resolution 360-degree videos. IRS also enhances the capability to mitigate the performance bottleneck caused by the requirement that all RS users have to be able to decode the common message. We formulate an optimization problem for maximization of the achievable bitrate of the 360-degree video subject to the quality-of-service (QoS) constraints of the users. We propose a deep deterministic policy gradient with imitation learning (Deep-GRAIL) algorithm, in which we leverage deep reinforcement learning (DRL) and the hidden convexity of the formulated problem to optimize the IRS phase shifts, RS parameters, beamforming vectors, and bitrate selection of the 360-degree video tiles. We also propose RavNet, which is a deep neural network customized for the policy learning in our Deep-GRAIL algorithm. Performance evaluation based on a real-world VR streaming dataset shows that the proposed IRS-aided RS VR streaming system outperforms several baseline schemes in terms of system sum-rate, achievable bitrate of the 360-degree videos, and online execution runtime. Our results also reveal the respective performance gains obtained from RS and IRS for improving the QoS in multiuser VR streaming systems.
Reinforcement learning has been demonstrated as a flexible and effective approach for learning a range of continuous control tasks, such as those used by robots to manipulate objects in their environment. But in robotics particularly, real-world rollouts are costly, and sample efficiency can be a major limiting factor when learning a new skill. In game environments, the use of world models has been shown to improve sample efficiency while still achieving good performance, especially when images or other rich observations are provided. In this project, we explore the use of a world model in a deformable robotic manipulation task, evaluating its effect on sample efficiency when learning to fold a cloth in simulation. We compare the use of RGB image observation with a feature space leveraging built-in structure (keypoints representing the cloth configuration), a common approach in robot skill learning, and compare the impact on task performance and learning efficiency with and without the world model. Our experiments showed that the usage of keypoints increased the performance of the best model on the task by 50%, and in general, the use of a learned or constructed reduced feature space improved task performance and sample efficiency. The use of a state transition predictor(MDN-RNN) in our world models did not have a notable effect on task performance.
While there has been substantial success for solving continuous control with actor-critic methods, simpler critic-only methods such as Q-learning find limited application in the associated high-dimensional action spaces. However, most actor-critic methods come at the cost of added complexity: heuristics for stabilisation, compute requirements and wider hyperparameter search spaces. We show that a simple modification of deep Q-learning largely alleviates these issues. By combining bang-bang action discretization with value decomposition, framing single-agent control as cooperative multi-agent reinforcement learning (MARL), this simple critic-only approach matches performance of state-of-the-art continuous actor-critic methods when learning from features or pixels. We extend classical bandit examples from cooperative MARL to provide intuition for how decoupled critics leverage state information to coordinate joint optimization, and demonstrate surprisingly strong performance across a variety of continuous control tasks.
Direct policy search has been widely applied in modern reinforcement learning and continuous control. However, the theoretical properties of direct policy search on nonsmooth robust control synthesis have not been fully understood. The optimal $\mathcal{H}_\infty$ control framework aims at designing a policy to minimize the closed-loop $\mathcal{H}_\infty$ norm, and is arguably the most fundamental robust control paradigm. In this work, we show that direct policy search is guaranteed to find the global solution of the robust $\mathcal{H}_\infty$ state-feedback control design problem. Notice that policy search for optimal $\mathcal{H}_\infty$ control leads to a constrained nonconvex nonsmooth optimization problem, where the nonconvex feasible set consists of all the policies stabilizing the closed-loop dynamics. We show that for this nonsmooth optimization problem, all Clarke stationary points are global minimum. Next, we identify the coerciveness of the closed-loop $\mathcal{H}_\infty$ objective function, and prove that all the sublevel sets of the resultant policy search problem are compact. Based on these properties, we show that Goldstein's subgradient method and its implementable variants can be guaranteed to stay in the nonconvex feasible set and eventually find the global optimal solution of the $\mathcal{H}_\infty$ state-feedback synthesis problem. Our work builds a new connection between nonconvex nonsmooth optimization theory and robust control, leading to an interesting global convergence result for direct policy search on optimal $\mathcal{H}_\infty$ synthesis.
Policy Optimization (PO) algorithms have been proven particularly suited to handle the high-dimensionality of real-world continuous control tasks. In this context, Trust Region Policy Optimization methods represent a popular approach to stabilize the policy updates. These usually rely on the Kullback-Leibler (KL) divergence to limit the change in the policy. The Wasserstein distance represents a natural alternative, in place of the KL divergence, to define trust regions or to regularize the objective function. However, state-of-the-art works either resort to its approximations or do not provide an algorithm for continuous state-action spaces, reducing the applicability of the method. In this paper, we explore optimal transport discrepancies (which include the Wasserstein distance) to define trust regions, and we propose a novel algorithm - Optimal Transport Trust Region Policy Optimization (OT-TRPO) - for continuous state-action spaces. We circumvent the infinite-dimensional optimization problem for PO by providing a one-dimensional dual reformulation for which strong duality holds. We then analytically derive the optimal policy update given the solution of the dual problem. This way, we bypass the computation of optimal transport costs and of optimal transport maps, which we implicitly characterize by solving the dual formulation. Finally, we provide an experimental evaluation of our approach across various control tasks. Our results show that optimal transport discrepancies can offer an advantage over state-of-the-art approaches.
A long-term goal of reinforcement learning is to design agents that can autonomously interact and learn in the world. A critical challenge to such autonomy is the presence of irreversible states which require external assistance to recover from, such as when a robot arm has pushed an object off of a table. While standard agents require constant monitoring to decide when to intervene, we aim to design proactive agents that can request human intervention only when needed. To this end, we propose an algorithm that efficiently learns to detect and avoid states that are irreversible, and proactively asks for help in case the agent does enter them. On a suite of continuous control environments with unknown irreversible states, we find that our algorithm exhibits better sample- and intervention-efficiency compared to existing methods. Our code is publicly available at https://sites.google.com/view/proactive-interventions
Behavior cloning of expert demonstrations can speed up learning optimal policies in a more sample-efficient way over reinforcement learning. However, the policy cannot extrapolate well to unseen states outside of the demonstration data, creating covariate shift (agent drifting away from demonstrations) and compounding errors. In this work, we tackle this issue by extending the region of attraction around the demonstrations so that the agent can learn how to get back onto the demonstrated trajectories if it veers off-course. We train a generative backwards dynamics model and generate short imagined trajectories from states in the demonstrations. By imitating both demonstrations and these model rollouts, the agent learns the demonstrated paths and how to get back onto these paths. With optimal or near-optimal demonstrations, the learned policy will be both optimal and robust to deviations, with a wider region of attraction. On continuous control domains, we evaluate the robustness when starting from different initial states unseen in the demonstration data. While both our method and other imitation learning baselines can successfully solve the tasks for initial states in the training distribution, our method exhibits considerably more robustness to different initial states.
We investigate the task of object goal navigation in unknown environments where the target is specified by a semantic label (e.g. find a couch). Such a navigation task is especially challenging as it requires understanding of semantic context in diverse settings. Most of the prior work tackles this problem under the assumption of a discrete action policy whereas we present an approach with continuous control which brings it closer to real world applications. We propose a deep neural network architecture and loss function to predict dense cost maps that implicitly contain semantic context and guide the robot towards the semantic goal. We also present a novel way of fusing mid-level visual representations in our architecture to provide additional semantic cues for cost map prediction. The estimated cost maps are then used by a sampling-based model predictive controller (MPC) for generating continuous robot actions. The preliminary experiments suggest that the cost maps generated by our network are suitable for the MPC and can guide the agent to the semantic goal more efficiently than a baseline approach. The results also indicate the importance of mid-level representations for navigation by improving the success rate by 7 percentage points.
Reinforcement learning algorithms are typically designed to learn a performant policy that can repeatedly and autonomously complete a task, usually starting from scratch. However, in many real-world situations, the goal might not be to learn a policy that can do the task repeatedly, but simply to perform a new task successfully once in a single trial. For example, imagine a disaster relief robot tasked with retrieving an item from a fallen building, where it cannot get direct supervision from humans. It must retrieve this object within one test-time trial, and must do so while tackling unknown obstacles, though it may leverage knowledge it has of the building before the disaster. We formalize this problem setting, which we call single-life reinforcement learning (SLRL), where an agent must complete a task within a single episode without interventions, utilizing its prior experience while contending with some form of novelty. SLRL provides a natural setting to study the challenge of autonomously adapting to unfamiliar situations, and we find that algorithms designed for standard episodic reinforcement learning often struggle to recover from out-of-distribution states in this setting. Motivated by this observation, we propose an algorithm, $Q$-weighted adversarial learning (QWALE), which employs a distribution matching strategy that leverages the agent's prior experience as guidance in novel situations. Our experiments on several single-life continuous control problems indicate that methods based on our distribution matching formulation are 20-60% more successful because they can more quickly recover from novel states.
Providing densely shaped reward functions for RL algorithms is often exceedingly challenging, motivating the development of RL algorithms that can learn from easier-to-specify sparse reward functions. This sparsity poses new exploration challenges. One common way to address this problem is using demonstrations to provide initial signal about regions of the state space with high rewards. However, prior RL from demonstrations algorithms introduce significant complexity and many hyperparameters, making them hard to implement and tune. We introduce Monte Carlo Augmented Actor Critic (MCAC), a parameter free modification to standard actor-critic algorithms which initializes the replay buffer with demonstrations and computes a modified $Q$-value by taking the maximum of the standard temporal distance (TD) target and a Monte Carlo estimate of the reward-to-go. This encourages exploration in the neighborhood of high-performing trajectories by encouraging high $Q$-values in corresponding regions of the state space. Experiments across $5$ continuous control domains suggest that MCAC can be used to significantly increase learning efficiency across $6$ commonly used RL and RL-from-demonstrations algorithms. See https://sites.google.com/view/mcac-rl for code and supplementary material.
In offline model-based reinforcement learning (offline MBRL), we learn a dynamic model from historically collected data, and subsequently utilize the learned model and fixed datasets for policy learning, without further interacting with the environment. Offline MBRL algorithms can improve the efficiency and stability of policy learning over the model-free algorithms. However, in most of the existing offline MBRL algorithms, the learning objectives for the dynamic models and the policies are isolated from each other. Such an objective mismatch may lead to inferior performance of the learned agents. In this paper, we address this issue by developing an iterative offline MBRL framework, where we maximize a lower bound of the true expected return, by alternating between dynamic-model training and policy learning. With the proposed unified model-policy learning framework, we achieve competitive performance on a wide range of continuous-control offline reinforcement learning datasets. Source code is publicly released.
We consider the problem of learning control policies in discrete-time stochastic systems which guarantee that the system stabilizes within some specified stabilization region with probability~$1$. Our approach is based on the novel notion of stabilizing ranking supermartingales (sRSMs) that we introduce in this work. Our sRSMs overcome the limitation of methods proposed in previous works whose applicability is restricted to systems in which the stabilizing region cannot be left once entered under any control policy. We present a learning procedure that learns a control policy together with an sRSM that formally certifies probability~$1$ stability, both learned as neural networks. We show that this procedure can also be adapted to formally verifying that, under a given Lipschitz continuous control policy, the stochastic system stabilizes within some stabilizing region with probability~$1$. Our experimental evaluation shows that our learning procedure can successfully learn provably stabilizing policies in practice.
Offline reinforcement learning (RL) addresses the problem of learning a performant policy from a fixed batch of data collected by following some behavior policy. Model-based approaches are particularly appealing in the offline setting since they can extract more learning signals from the logged dataset by learning a model of the environment. However, the performance of existing model-based approaches falls short of model-free counterparts, due to the compounding of estimation errors in the learned model. Driven by this observation, we argue that it is critical for a model-based method to understand when to trust the model and when to rely on model-free estimates, and how to act conservatively w.r.t. both. To this end, we derive an elegant and simple methodology called conservative Bayesian model-based value expansion for offline policy optimization (CBOP), that trades off model-free and model-based estimates during the policy evaluation step according to their epistemic uncertainties, and facilitates conservatism by taking a lower bound on the Bayesian posterior value estimate. On the standard D4RL continuous control tasks, we find that our method significantly outperforms previous model-based approaches: e.g., MOPO by $116.4$%, MOReL by $23.2$% and COMBO by $23.7$%. Further, CBOP achieves state-of-the-art performance on $11$ out of $18$ benchmark datasets while doing on par on the remaining datasets.
High variances in reinforcement learning have shown impeding successful convergence and hurting task performance. As reward signal plays an important role in learning behavior, multi-step methods have been considered to mitigate the problem, and are believed to be more effective than single step methods. However, there is a lack of comprehensive and systematic study on this important aspect to demonstrate the effectiveness of multi-step methods in solving highly complex continuous control problems. In this study, we introduce a new long $N$-step surrogate stage (LNSS) reward approach to effectively account for complex environment dynamics while previous methods are usually feasible for limited number of steps. The LNSS method is simple, low computational cost, and applicable to value based or policy gradient reinforcement learning. We systematically evaluate LNSS in OpenAI Gym and DeepMind Control Suite to address some complex benchmark environments that have been challenging to obtain good results by DRL in general. We demonstrate performance improvement in terms of total reward, convergence speed, and coefficient of variation (CV) by LNSS. We also provide analytical insights on how LNSS exponentially reduces the upper bound on the variances of Q value from a respective single step method
Gradient-based methods have been widely used for system design and optimization in diverse application domains. Recently, there has been a renewed interest in studying theoretical properties of these methods in the context of control and reinforcement learning. This article surveys some of the recent developments on policy optimization, a gradient-based iterative approach for feedback control synthesis, popularized by successes of reinforcement learning. We take an interdisciplinary perspective in our exposition that connects control theory, reinforcement learning, and large-scale optimization. We review a number of recently-developed theoretical results on the optimization landscape, global convergence, and sample complexity of gradient-based methods for various continuous control problems such as the linear quadratic regulator (LQR), $\mathcal{H}_\infty$ control, risk-sensitive control, linear quadratic Gaussian (LQG) control, and output feedback synthesis. In conjunction with these optimization results, we also discuss how direct policy optimization handles stability and robustness concerns in learning-based control, two main desiderata in control engineering. We conclude the survey by pointing out several challenges and opportunities at the intersection of learning and control.
We consider how to most efficiently leverage teleoperator time to collect data for learning robust image-based value functions and policies for sparse reward robotic tasks. To accomplish this goal, we modify the process of data collection to include more than just successful demonstrations of the desired task. Instead we develop a novel protocol that we call Visual Backtracking Teleoperation (VBT), which deliberately collects a dataset of visually similar failures, recoveries, and successes. VBT data collection is particularly useful for efficiently learning accurate value functions from small datasets of image-based observations. We demonstrate VBT on a real robot to perform continuous control from image observations for the deformable manipulation task of T-shirt grasping. We find that by adjusting the data collection process we improve the quality of both the learned value functions and policies over a variety of baseline methods for data collection. Specifically, we find that offline reinforcement learning on VBT data outperforms standard behavior cloning on successful demonstration data by 13% when both methods are given equal-sized datasets of 60 minutes of data from the real robot.
Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a time-varying propensity score that can detect gradual shifts in the distribution of data which allows us to selectively sample past data to update the model -- not just similar data from the past like that of a standard propensity score but also data that evolved in a similar fashion in the past. The time-varying propensity score is quite general: we demonstrate different ways of implementing it and evaluate it on a variety of problems ranging from supervised learning (e.g., image classification problems) where data undergoes a sequence of gradual shifts, to reinforcement learning tasks (e.g., robotic manipulation and continuous control) where data shifts as the policy or the task changes.