Domain randomization (DR) is a successful technique for learning robust policies for robot systems, when the dynamics of the target robot system are unknown. The success of policies trained with domain randomization however, is highly dependent on the correct selection of the randomization distribution. The majority of success stories typically use real world data in order to carefully select the DR distribution, or incorporate real world trajectories to better estimate appropriate randomization distributions. In this paper, we consider the problem of finding good domain randomization parameters for simulation, without prior access to data from the target system. We explore the use of gradient-based search methods to learn a domain randomization with the following properties: 1) The trained policy should be successful in environments sampled from the domain randomization distribution 2) The domain randomization distribution should be wide enough so that the experience similar to the target robot system is observed during training, while addressing the practicality of training finite capacity models. These two properties aim to ensure the trajectories encountered in the target system are close to those observed during training, as existing methods in machine learning are better suited for interpolation than extrapolation. We show how adapting the domain randomization distribution while training context-conditioned policies results in improvements on jump-start and asymptotic performance when transferring a learned policy to the target environment.
@cite_10 propose a related approach for learning robust policies over a distribution of simulator models. The proposed approach, based on the the @math -percentile conditional value at risk (CVaR) @cite_11 objective, improves the policy performance on a small proportion of environments where the policy performs the worst. The authors propose an algorithm that updates the distribution of simulation models to maximize the likelihood of real-world trajectories, via Bayesian inference. The combination of worst-case performance optimization and Bayesian updates ensures that the resulting policy is robust to errors in the estimation of the simulation model parameters. Our method can be combined with the CVaR objective to encourage diversity of the learned DR distribution.
@cite_10 @cite_11
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In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in costs in addition to minimizing a standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk measure that addresses some of the shortcomings of the well-known variance-related risk measures, and because of its computational efficiencies has gained popularity in finance and operations research. In this paper, we consider the mean-CVaR optimization problem in MDPs. We first derive a formula for computing the gradient of this risk-sensitive objective function. We then devise policy gradient and actor-critic algorithms that each uses a specific method to estimate this gradient and updates the policy parameters in the descent direction. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in an optimal stopping problem. Many Stochastic Optimal Control (SOC) approaches rely on samples to either obtain an estimate of the value function or a linearisation of the underlying system model. However, these approaches typically neglect the fact that the accuracy of the policy update depends on the closeness of the resulting trajectory distribution to these samples. The greedy operator does not consider such closeness constraint to the samples. Hence, the greedy operator can lead to oscillations or even instabilities in the policy updates. Such undesired behaviour is likely to result in an inferior performance of the estimated policy. We reuse inspiration from the reinforcement learning community and relax the greedy operator used in SOC with an information theoretic bound that limits the ‘distance’ of two subsequent trajectory distributions in a policy update. The introduced bound ensures a smooth and stable policy update. Our method is also well suited for model-based reinforcement learning, where we estimate the system dynamics model from data. As this model is likely to be inaccurate, it might be dangerous to exploit the model greedily. Instead, our bound ensures that we generate new data in the vicinity of the current data, such that we can improve our estimate of the system dynamics model. We show that our approach outperforms several state of the art approaches on challenging simulated robot control tasks. A partially observable Markov decision process has been proposed as a dialogue model that enables robustness to speech recognition errors and automatic policy optimisation using reinforcement learning (RL). However, conventional RL algorithms require a very large number of dialogues, necessitating a user simulator. Recently, Gaussian processes have been shown to substantially speed up the optimisation, making it possible to learn directly from interaction with human users. However, early studies have been limited to very low dimensional spaces and the learning has exhibited convergence problems. Here we investigate learning from human interaction using the Bayesian Update of Dialogue State system. This dynamic Bayesian network based system has an optimisation space covering more than one hundred features, allowing a wide range of behaviours to be learned. Using an improved policy model and a more robust reward function, we show that stable learning can be achieved that significantly outperforms a simulator trained policy. Policy gradient methods have been successfully applied to a variety of reinforcement learning tasks. However, while learning in a simulator, these methods do not utilise the opportunity to improve learning by adjusting certain environment variables: unobservable state features that are randomly determined by the environment in a physical setting, but that are controllable in a simulator. This can lead to slow learning, or convergence to highly suboptimal policies. In this paper, we present contextual policy optimisation (CPO). The central idea is to use Bayesian optimisation to actively select the distribution of the environment variable that maximises the improvement generated by each iteration of the policy gradient method. To make this Bayesian optimisation practical, we contribute two easy-to-compute low-dimensional fingerprints of the current policy. We apply CPO to a number of continuous control tasks of varying difficulty and show that CPO can efficiently learn policies that are robust to significant rare events, which are unlikely to be observable under random sampling but are key to learning good policies. Deep neural networks coupled with fast simulation and improved computation have led to recent successes in the field of reinforcement learning (RL). However, most current RL-based approaches fail to generalize since: (a) the gap between simulation and real world is so large that policy-learning approaches fail to transfer; (b) even if policy learning is done in real world, the data scarcity leads to failed generalization from training to test scenarios (e.g., due to different friction or object masses). Inspired from H∞ control methods, we note that both modeling errors and differences in training and test scenarios can be viewed as extra forces disturbances in the system. This paper proposes the idea of robust adversarial reinforcement learning (RARL), where we train an agent to operate in the presence of a destabilizing adversary that applies disturbance forces to the system. The jointly trained adversary is reinforced - that is, it learns an optimal destabilization policy. We formulate the policy learning as a zero-sum, minimax objective function. Extensive experiments in multiple environments (InvertedPendulum, HalfCheetah, Swimmer, Hopper, Walker2d and Ant) conclusively demonstrate that our method (a) improves training stability; (b) is robust to differences in training test conditions; and c) outperform the baseline even in the absence of the adversary. Deep neural networks coupled with fast simulation and improved computation have led to recent successes in the field of reinforcement learning (RL). However, most current RL-based approaches fail to generalize since: (a) the gap between simulation and real world is so large that policy-learning approaches fail to transfer; (b) even if policy learning is done in real world, the data scarcity leads to failed generalization from training to test scenarios (e.g., due to different friction or object masses). Inspired from H-infinity control methods, we note that both modeling errors and differences in training and test scenarios can be viewed as extra forces disturbances in the system. This paper proposes the idea of robust adversarial reinforcement learning (RARL), where we train an agent to operate in the presence of a destabilizing adversary that applies disturbance forces to the system. The jointly trained adversary is reinforced -- that is, it learns an optimal destabilization policy. We formulate the policy learning as a zero-sum, minimax objective function. Extensive experiments in multiple environments (InvertedPendulum, HalfCheetah, Swimmer, Hopper and Walker2d) conclusively demonstrate that our method (a) improves training stability; (b) is robust to differences in training test conditions; and c) outperform the baseline even in the absence of the adversary. Sample complexity and safety are major challenges when learning policies with reinforcement learning for real-world tasks, especially when the policies are represented using rich function approximators like deep neural networks. Model-based methods where the real-world target domain is approximated using a simulated source domain provide an avenue to tackle the above challenges by augmenting real data with simulated data. However, discrepancies between the simulated source domain and the target domain pose a challenge for simulated training. We introduce the EPOpt algorithm, which uses an ensemble of simulated source domains and a form of adversarial training to learn policies that are robust and generalize to a broad range of possible target domains, including to unmodeled effects. Further, the probability distribution over source domains in the ensemble can be adapted using data from the target domain and approximate Bayesian methods, to progressively make it a better approximation. Thus, learning on a model ensemble, along with source domain adaptation, provides the benefit of both robustness and learning. Sample complexity and safety are major challenges when learning policies with reinforcement learning for real-world tasks, especially when the policies are represented using rich function approximators like deep neural networks. Model-based methods where the real-world target domain is approximated using a simulated source domain provide an avenue to tackle the above challenges by augmenting real data with simulated data. However, discrepancies between the simulated source domain and the target domain pose a challenge for simulated training. We introduce the EPOpt algorithm, which uses an ensemble of simulated source domains and a form of adversarial training to learn policies that are robust and generalize to a broad range of possible target domains, including unmodeled effects. Further, the probability distribution over source domains in the ensemble can be adapted using data from target domain and approximate Bayesian methods, to progressively make it a better approximation. Thus, learning on a model ensemble, along with source domain adaptation, provides the benefit of both robustness and learning adaptation. Conditional Value at Risk (CVaR) is a prominent risk measure that is being used extensively in various domains. We develop a new formula for the gradient of the CVaR in the form of a conditional expectation. Based on this formula, we propose a novel sampling-based estimator for the CVaR gradient, in the spirit of the likelihood-ratio method. We analyze the bias of the estimator, and prove the convergence of a corresponding stochastic gradient descent algorithm to a local CVaR optimum. Our method allows to consider CVaR optimization in new domains. As an example, we consider a reinforcement learning application, and learn a risk-sensitive controller for the game of Tetris. Specifying a numeric reward function for reinforcement learning typically requires a lot of hand-tuning from a human expert. In contrast, preference-based reinforcement learning (PBRL) utilizes only pairwise comparisons between trajectories as a feedback signal, which are often more intuitive to specify. Currently available approaches to PBRL for control problems with continuous state action spaces require a known or estimated model, which is often not available and hard to learn. In this paper, we integrate preference-based estimation of the reward function into a model-free reinforcement learning (RL) algorithm, resulting in a model-free PBRL algorithm. Our new algorithm is based on Relative Entropy Policy Search (REPS), enabling us to utilize stochastic policies and to directly control the greediness of the policy update. REPS decreases exploration of the policy slowly by limiting the relative entropy of the policy update, which ensures that the algorithm is provided with a versatile set of trajectories, and consequently with informative preferences. The preference-based estimation is computed using a sample-based Bayesian method, which can also estimate the uncertainty of the utility. Additionally, we also compare to a linear solvable approximation, based on inverse RL. We show that both approaches perform favourably to the current state-of-the-art. The overall result is an algorithm that can learn non-parametric continuous action policies from a small number of preferences. With the goal to generate more scalable algorithms with higher efficiency and fewer open parameters, reinforcement learning (RL) has recently moved towards combining classical techniques from optimal control and dynamic programming with modern learning techniques from statistical estimation theory. In this vein, this paper suggests to use the framework of stochastic optimal control with path integrals to derive a novel approach to RL with parameterized policies. While solidly grounded in value function estimation and optimal control based on the stochastic Hamilton-Jacobi-Bellman (HJB) equations, policy improvements can be transformed into an approximation problem of a path integral which has no open algorithmic parameters other than the exploration noise. The resulting algorithm can be conceived of as model-based, semi-model-based, or even model free, depending on how the learning problem is structured. The update equations have no danger of numerical instabilities as neither matrix inversions nor gradient learning rates are required. Our new algorithm demonstrates interesting similarities with previous RL research in the framework of probability matching and provides intuition why the slightly heuristically motivated probability matching approach can actually perform well. Empirical evaluations demonstrate significant performance improvements over gradient-based policy learning and scalability to high-dimensional control problems. Finally, a learning experiment on a simulated 12 degree-of-freedom robot dog illustrates the functionality of our algorithm in a complex robot learning scenario. We believe that Policy Improvement with Path Integrals (PI2) offers currently one of the most efficient, numerically robust, and easy to implement algorithms for RL based on trajectory roll-outs. We propose a new constrained Markov decision process framework with risk-type constraints. The risk metric we use is Conditional Value-at-Risk (CVaR), which is gaining popularity in finance. It is a conditional expectation but the conditioning is defined in terms of the level of the tail probability. We propose an iterative offline algorithm to find the risk-contrained optimal control policy. A stochastic approximation-inspired ‘learning’ variant is also sketched. In this work we propose an approach to learn a robust policy for solving the pivoting task. Recently, several model-free continuous control algorithms were shown to learn successful policies without prior knowledge of the dynamics of the task. However, obtaining successful policies required thousands to millions of training episodes, limiting the applicability of these approaches to real hardware. We developed a training procedure that allows us to use a simple custom simulator to learn policies robust to the mismatch of simulation vs robot. In our experiments, we demonstrate that the policy learned in the simulator is able to pivot the object to the desired target angle on the real robot. We also show generalization to an object with different inertia, shape, mass and friction properties than those used during training. This result is a step towards making model-free reinforcement learning available for solving robotics tasks via pre-training in simulators that offer only an imprecise match to the real-world dynamics. Simulations are attractive environments for training agents as they provide an abundant source of data and alleviate certain safety concerns during the training process. But the behaviours developed by agents in simulation are often specific to the characteristics of the simulator. Due to modeling error, strategies that are successful in simulation may not transfer to their real world counterparts. In this paper, we demonstrate a simple method to bridge this "reality gap." By randomizing the dynamics of the simulator during training, we are able to develop policies that are capable of adapting to very different dynamics, including ones that differ significantly from the dynamics on which the policies were trained. This adaptivity enables the policies to generalize to the dynamics of the real world without any training on the physical system. Our approach is demonstrated on an object pushing task using a robotic arm. Despite being trained exclusively in simulation, our policies are able to maintain a similar level of performance when deployed on a real robot, reliably moving an object to a desired location from random initial configurations. We explore the impact of various design decisions and show that the resulting policies are robust to significant calibration error. This letter proposes a new reinforcement learning (RL) paradigm that explicitly takes into account input disturbance as well as modeling errors. The use of environmental models in RL is quite popular for both offline learning using simulations and for online action planning. However, the difference between the model and the real environment can lead to unpredictable, and often unwanted, results. Based on the theory of H∞ control, we consider a differential game in which a "disturbing" agent tries to make the worst possible disturbance while a "control" agent tries to make the best control input. The problem is formulated as finding a min-max solution of a value function that takes into account the amount of the reward and the norm of the disturbance. We derive online learning algorithms for estimating the value function and for calculating the worst disturbance and the best control in reference to the value function. We tested the paradigm, which we call robust reinforcement learning (RRL), on the control task of an inverted pendulum. In the linear domain, the policy and the value function learned by online algorithms coincided with those derived analytically by the linear H∞ control theory. For a fully nonlinear swing-up task, RRL achieved robust performance with changes in the pendulum weight and friction, while a standard reinforcement learning algorithm could not deal with these changes. We also applied RRL to the cart-pole swing-up task, and a robust swing-up policy was acquired. We investigate the control of constrained stochastic linear systems when faced with limited information regarding the disturbance process, i.e., when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. In the first case, we require that the constraints hold with a given probability for all disturbance distributions sharing the known moments. These constraints are commonly referred to as distributionally robust chance constraints. In the second case, we impose conditional value-at-risk (CVaR) constraints to bound the expected constraint violation for all disturbance distributions consistent with the given moment information. Such constraints are referred to as distributionally robust CVaR constraints with second-order moment specifications. We propose a method for designing linear controllers for systems with such constraints that is both computationally tractable and practically meaningful for both finite and infinite horizon problems. We prove in the infinite horizon case that our design procedure produces the globally optimal linear output feedback controller for distributionally robust CVaR and chance constrained problems. The proposed methods are illustrated for a wind blade control design case study for which distributionally robust constraints constitute sensible design objectives. Model-free policy learning has enabled robust performance of complex tasks with relatively simple algorithms. However, this simplicity comes at the cost of requiring an Oracle and arguably very poor sample complexity. This renders such methods unsuitable for physical systems. Variants of model-based methods address this problem through the use of simulators, however, this gives rise to the problem of policy transfer from simulated to the physical system. Model mismatch due to systematic parameter shift and unmodelled dynamics error may cause sub-optimal or unsafe behavior upon direct transfer. We introduce the Adaptive Policy Transfer for Stochastic Dynamics (ADAPT) algorithm that achieves provably safe and robust, dynamically-feasible zero-shot transfer of RL-policies to new domains with dynamics error. ADAPT combines the strengths of offline policy learning in a black-box source simulator with online tube-based MPC to attenuate bounded model mismatch between the source and target dynamics. ADAPT allows online transfer of policy, trained solely in a simulation offline, to a family of unknown targets without fine-tuning. We also formally show that (i) ADAPT guarantees state and control safety through state-action tubes under the assumption of Lipschitz continuity of the divergence in dynamics and, (ii) ADAPT results in a bounded loss of reward accumulation relative to a policy trained and evaluated in the source environment. We evaluate ADAPT on 2 continuous, non-holonomic simulated dynamical systems with 4 different disturbance models, and find that ADAPT performs between 50 -300 better on mean reward accrual than direct policy transfer. The goal of reinforcement learning (RL) is to let an agent learn an optimal control policy in an unknown environment so that future expected rewards are maximized. The model-free RL approach directly learns the policy based on data samples. Although using many samples tends to improve the accuracy of policy learning, collecting a large number of samples is often expensive in practice. On the other hand, the model-based RL approach first estimates the transition model of the environment and then learns the policy based on the estimated transition model. Thus, if the transition model is accurately learned from a small amount of data, the model-based approach is a promising alternative to the model-free approach. In this paper, we propose a novel model-based RL method by combining a recently proposed model-free policy search method called policy gradients with parameter-based exploration and the state-of-the-art transition model estimator called least-squares conditional density estimation. Through experiments, we demonstrate the practical usefulness of the proposed method. We propose a method to forecast a vehicle’s ego-motion as a distribution over spatiotemporal paths, conditioned on features (e.g., from LIDAR and images) embedded in an overhead map. The method learns a policy inducing a distribution over simulated trajectories that is both “diverse” (produces most of the likely paths) and “precise” (mostly produces likely paths). This balance is achieved through minimization of a symmetrized cross-entropy between the distribution and demonstration data. By viewing the simulated-outcome distribution as the pushforward of a simple distribution under a simulation operator, we obtain expressions for the cross-entropy metrics that can be efficiently evaluated and differentiated, enabling stochastic-gradient optimization. We propose concrete policy architectures for this model, discuss our evaluation metrics relative to previously-used degenerate metrics, and demonstrate the superiority of our method relative to state-of-the-art methods in both the Kitti dataset and a similar but novel and larger real-world dataset explicitly designed for the vehicle forecasting domain. Policy search is a subfield in reinforcement learning which focuses on finding good parameters for a given policy parametrization. It is well suited for robotics as it can cope with high-dimensional state and action spaces, one of the main challenges in robot learning. We review recent successes of both model-free and model-based policy search in robot learning.Model-free policy search is a general approach to learn policies based on sampled trajectories. We classify model-free methods based on their policy evaluation strategy, policy update strategy, and exploration strategy and present a unified view on existing algorithms. Learning a policy is often easier than learning an accurate forward model, and, hence, model-free methods are more frequently used in practice. However, for each sampled trajectory, it is necessary to interact with the robot, which can be time consuming and challenging in practice. Model-based policy search addresses this problem by first learning a simulator of the robot's dynamics from data. Subsequently, the simulator generates trajectories that are used for policy learning. For both model-free and model-based policy search methods, we review their respective properties and their applicability to robotic systems.