Meta-learning allows an intelligent agent to leverage prior learning episodes as a basis for quickly improving performance on a novel task. Bayesian hierarchical modeling provides a theoretical framework for formalizing meta-learning as inference for a set of parameters that are shared across tasks. Here, we reformulate the model-agnostic meta-learning algorithm (MAML) of Finn et al. (2017) as a method for probabilistic inference in a hierarchical Bayesian model. In contrast to prior methods for meta-learning via hierarchical Bayes, MAML is naturally applicable to complex function approximators through its use of a scalable gradient descent procedure for posterior inference. Furthermore, the identification of MAML as hierarchical Bayes provides a way to understand the algorithm's operation as a meta-learning procedure, as well as an opportunity to make use of computational strategies for efficient inference. We use this opportunity to propose an improvement to the MAML algorithm that makes use of techniques from approximate inference and curvature estimation.

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Learning to learn is a powerful paradigm for enabling models to learn from data more effectively and efficiently. A popular approach to meta-learning is to train a recurrent model to read in a training dataset as input and output the parameters of a learned model, or output predictions for new test inputs. Alternatively, a more recent approach to meta-learning aims to acquire deep representations that can be effectively fine-tuned, via standard gradient descent, to new tasks. In this paper, we consider the meta-learning problem from the perspective of universality, formalizing the notion of learning algorithm approximation and comparing the expressive power of the aforementioned recurrent models to the more recent approaches that embed gradient descent into the meta-learner. In particular, we seek to answer the following question: does deep representation combined with standard gradient descent have sufficient capacity to approximate any learning algorithm? We find that this is indeed true, and further find, in our experiments, that gradient-based meta-learning consistently leads to learning strategies that generalize more widely compared to those represented by recurrent models.

* ICLR 2018
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A key challenge in scaling up robot learning to many skills and environments is removing the need for human supervision, so that robots can collect their own data and improve their own performance without being limited by the cost of requesting human feedback. Model-based reinforcement learning holds the promise of enabling an agent to learn to predict the effects of its actions, which could provide flexible predictive models for a wide range of tasks and environments, without detailed human supervision. We develop a method for combining deep action-conditioned video prediction models with model-predictive control that uses entirely unlabeled training data. Our approach does not require a calibrated camera, an instrumented training set-up, nor precise sensing and actuation. Our results show that our method enables a real robot to perform nonprehensile manipulation -- pushing objects -- and can handle novel objects not seen during training.

* ICRA 2017. Supplementary video: https://sites.google.com/site/robotforesight/
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Recent advances in one-shot learning have produced models that can learn from a handful of labeled examples, for passive classification and regression tasks. This paper combines reinforcement learning with one-shot learning, allowing the model to decide, during classification, which examples are worth labeling. We introduce a classification task in which a stream of images are presented and, on each time step, a decision must be made to either predict a label or pay to receive the correct label. We present a recurrent neural network based action-value function, and demonstrate its ability to learn how and when to request labels. Through the choice of reward function, the model can achieve a higher prediction accuracy than a similar model on a purely supervised task, or trade prediction accuracy for fewer label requests.

* NIPS 2016, Deep Reinforcement Learning Workshop, Barcelona, Spain. See https://cs.stanford.edu/~woodward/ for the poster and a short video description of the paper
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Humans and animals can learn complex predictive models that allow them to accurately and reliably reason about real-world phenomena, and they can adapt such models extremely quickly in the face of unexpected changes. Deep neural network models allow us to represent very complex functions, but lack this capacity for rapid online adaptation. The goal in this paper is to develop a method for continual online learning from an incoming stream of data, using deep neural network models. We formulate an online learning procedure that uses stochastic gradient descent to update model parameters, and an expectation maximization algorithm with a Chinese restaurant process prior to develop and maintain a mixture of models to handle non-stationary task distributions. This allows for all models to be adapted as necessary, with new models instantiated for task changes and old models recalled when previously seen tasks are encountered again. Furthermore, we observe that meta-learning can be used to meta-train a model such that this direct online adaptation with SGD is effective, which is otherwise not the case for large function approximators. In this work, we apply our meta-learning for online learning (MOLe) approach to model-based reinforcement learning, where adapting the predictive model is critical for control; we demonstrate that MOLe outperforms alternative prior methods, and enables effective continuous adaptation in non-stationary task distributions such as varying terrains, motor failures, and unexpected disturbances.

* Project website: https://sites.google.com/berkeley.edu/onlineviameta
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Meta-learning for few-shot learning entails acquiring a prior over previous tasks and experiences, such that new tasks be learned from small amounts of data. However, a critical challenge in few-shot learning is task ambiguity: even when a powerful prior can be meta-learned from a large number of prior tasks, a small dataset for a new task can simply be too ambiguous to acquire a single model (e.g., a classifier) for that task that is accurate. In this paper, we propose a probabilistic meta-learning algorithm that can sample models for a new task from a model distribution. Our approach extends model-agnostic meta-learning, which adapts to new tasks via gradient descent, to incorporate a parameter distribution that is trained via a variational lower bound. At meta-test time, our algorithm adapts via a simple procedure that injects noise into gradient descent, and at meta-training time, the model is trained such that this stochastic adaptation procedure produces samples from the approximate model posterior. Our experimental results show that our method can sample plausible classifiers and regressors in ambiguous few-shot learning problems.

* First two authors contributed equally. Supplementary results available at https://sites.google.com/view/probabilistic-maml/
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We propose an algorithm for meta-learning that is model-agnostic, in the sense that it is compatible with any model trained with gradient descent and applicable to a variety of different learning problems, including classification, regression, and reinforcement learning. The goal of meta-learning is to train a model on a variety of learning tasks, such that it can solve new learning tasks using only a small number of training samples. In our approach, the parameters of the model are explicitly trained such that a small number of gradient steps with a small amount of training data from a new task will produce good generalization performance on that task. In effect, our method trains the model to be easy to fine-tune. We demonstrate that this approach leads to state-of-the-art performance on two few-shot image classification benchmarks, produces good results on few-shot regression, and accelerates fine-tuning for policy gradient reinforcement learning with neural network policies.

* ICML 2017. Code at https://github.com/cbfinn/maml, Videos of RL results at https://sites.google.com/view/maml, Blog post at http://bair.berkeley.edu/blog/2017/07/18/learning-to-learn/
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A core challenge for an agent learning to interact with the world is to predict how its actions affect objects in its environment. Many existing methods for learning the dynamics of physical interactions require labeled object information. However, to scale real-world interaction learning to a variety of scenes and objects, acquiring labeled data becomes increasingly impractical. To learn about physical object motion without labels, we develop an action-conditioned video prediction model that explicitly models pixel motion, by predicting a distribution over pixel motion from previous frames. Because our model explicitly predicts motion, it is partially invariant to object appearance, enabling it to generalize to previously unseen objects. To explore video prediction for real-world interactive agents, we also introduce a dataset of 59,000 robot interactions involving pushing motions, including a test set with novel objects. In this dataset, accurate prediction of videos conditioned on the robot's future actions amounts to learning a "visual imagination" of different futures based on different courses of action. Our experiments show that our proposed method produces more accurate video predictions both quantitatively and qualitatively, when compared to prior methods.

* To appear in NIPS '16; Video results, code, and data available at: http://www.sites.google.com/site/robotprediction
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Reinforcement learning can acquire complex behaviors from high-level specifications. However, defining a cost function that can be optimized effectively and encodes the correct task is challenging in practice. We explore how inverse optimal control (IOC) can be used to learn behaviors from demonstrations, with applications to torque control of high-dimensional robotic systems. Our method addresses two key challenges in inverse optimal control: first, the need for informative features and effective regularization to impose structure on the cost, and second, the difficulty of learning the cost function under unknown dynamics for high-dimensional continuous systems. To address the former challenge, we present an algorithm capable of learning arbitrary nonlinear cost functions, such as neural networks, without meticulous feature engineering. To address the latter challenge, we formulate an efficient sample-based approximation for MaxEnt IOC. We evaluate our method on a series of simulated tasks and real-world robotic manipulation problems, demonstrating substantial improvement over prior methods both in terms of task complexity and sample efficiency.

* International Conference on Machine Learning (ICML), 2016, to appear
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Recently, nested dropout was proposed as a method for ordering representation units in autoencoders by their information content, without diminishing reconstruction cost. However, it has only been applied to training fully-connected autoencoders in an unsupervised setting. We explore the impact of nested dropout on the convolutional layers in a CNN trained by backpropagation, investigating whether nested dropout can provide a simple and systematic way to determine the optimal representation size with respect to the desired accuracy and desired task and data complexity.

* 4 pages, 2 figures. Accepted as a workshop contribution at ICLR 2015
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While reinforcement learning (RL) has the potential to enable robots to autonomously acquire a wide range of skills, in practice, RL usually requires manual, per-task engineering of reward functions, especially in real world settings where aspects of the environment needed to compute progress are not directly accessible. To enable robots to autonomously learn skills, we instead consider the problem of reinforcement learning without access to rewards. We aim to learn an unsupervised embedding space under which the robot can measure progress towards a goal for itself. Our approach explicitly optimizes for a metric space under which action sequences that reach a particular state are optimal when the goal is the final state reached. This enables learning effective and control-centric representations that lead to more autonomous reinforcement learning algorithms. Our experiments on three simulated environments and two real-world manipulation problems show that our method can learn effective goal metrics from unlabeled interaction, and use the learned goal metrics for autonomous reinforcement learning.

* Videos available at https://sites.google.com/view/dpn-public/
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We consider the problem of learning multi-stage vision-based tasks on a real robot from a single video of a human performing the task, while leveraging demonstration data of subtasks with other objects. This problem presents a number of major challenges. Video demonstrations without teleoperation are easy for humans to provide, but do not provide any direct supervision. Learning policies from raw pixels enables full generality but calls for large function approximators with many parameters to be learned. Finally, compound tasks can require impractical amounts of demonstration data, when treated as a monolithic skill. To address these challenges, we propose a method that learns both how to learn primitive behaviors from video demonstrations and how to dynamically compose these behaviors to perform multi-stage tasks by "watching" a human demonstrator. Our results on a simulated Sawyer robot and real PR2 robot illustrate our method for learning a variety of order fulfillment and kitchen serving tasks with novel objects and raw pixel inputs.

* Video results available at https://sites.google.com/view/one-shot-hil
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Reinforcement learning and planning methods require an objective or reward function that encodes the desired behavior. Yet, in practice, there is a wide range of scenarios where an objective is difficult to provide programmatically, such as tasks with visual observations involving unknown object positions or deformable objects. In these cases, prior methods use engineered problem-specific solutions, e.g., by instrumenting the environment with additional sensors to measure a proxy for the objective. Such solutions require a significant engineering effort on a per-task basis, and make it impractical for robots to continuously learn complex skills outside of laboratory settings. We aim to find a more general and scalable solution for specifying goals for robot learning in unconstrained environments. To that end, we formulate the few-shot objective learning problem, where the goal is to learn a task objective from only a few example images of successful end states for that task. We propose a simple solution to this problem: meta-learn a classifier that can recognize new goals from a few examples. We show how this approach can be used with both model-free reinforcement learning and visual model-based planning and show results in three domains: rope manipulation from images in simulation, visual navigation in a simulated 3D environment, and object arrangement into user-specified configurations on a real robot.

* Videos available at https://sites.google.com/view/few-shot-goals
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Meta-learning is a powerful tool that builds on multi-task learning to learn how to quickly adapt a model to new tasks. In the context of reinforcement learning, meta-learning algorithms can acquire reinforcement learning procedures to solve new problems more efficiently by meta-learning prior tasks. The performance of meta-learning algorithms critically depends on the tasks available for meta-training: in the same way that supervised learning algorithms generalize best to test points drawn from the same distribution as the training points, meta-learning methods generalize best to tasks from the same distribution as the meta-training tasks. In effect, meta-reinforcement learning offloads the design burden from algorithm design to task design. If we can automate the process of task design as well, we can devise a meta-learning algorithm that is truly automated. In this work, we take a step in this direction, proposing a family of unsupervised meta-learning algorithms for reinforcement learning. We describe a general recipe for unsupervised meta-reinforcement learning, and describe an effective instantiation of this approach based on a recently proposed unsupervised exploration technique and model-agnostic meta-learning. We also discuss practical and conceptual considerations for developing unsupervised meta-learning methods. Our experimental results demonstrate that unsupervised meta-reinforcement learning effectively acquires accelerated reinforcement learning procedures without the need for manual task design, significantly exceeds the performance of learning from scratch, and even matches performance of meta-learning methods that use hand-specified task distributions.

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Generative adversarial networks (GANs) are a recently proposed class of generative models in which a generator is trained to optimize a cost function that is being simultaneously learned by a discriminator. While the idea of learning cost functions is relatively new to the field of generative modeling, learning costs has long been studied in control and reinforcement learning (RL) domains, typically for imitation learning from demonstrations. In these fields, learning cost function underlying observed behavior is known as inverse reinforcement learning (IRL) or inverse optimal control. While at first the connection between cost learning in RL and cost learning in generative modeling may appear to be a superficial one, we show in this paper that certain IRL methods are in fact mathematically equivalent to GANs. In particular, we demonstrate an equivalence between a sample-based algorithm for maximum entropy IRL and a GAN in which the generator's density can be evaluated and is provided as an additional input to the discriminator. Interestingly, maximum entropy IRL is a special case of an energy-based model. We discuss the interpretation of GANs as an algorithm for training energy-based models, and relate this interpretation to other recent work that seeks to connect GANs and EBMs. By formally highlighting the connection between GANs, IRL, and EBMs, we hope that researchers in all three communities can better identify and apply transferable ideas from one domain to another, particularly for developing more stable and scalable algorithms: a major challenge in all three domains.

* NIPS 2016 Workshop on Adversarial Training. First two authors contributed equally
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Policy search methods can allow robots to learn control policies for a wide range of tasks, but practical applications of policy search often require hand-engineered components for perception, state estimation, and low-level control. In this paper, we aim to answer the following question: does training the perception and control systems jointly end-to-end provide better performance than training each component separately? To this end, we develop a method that can be used to learn policies that map raw image observations directly to torques at the robot's motors. The policies are represented by deep convolutional neural networks (CNNs) with 92,000 parameters, and are trained using a partially observed guided policy search method, which transforms policy search into supervised learning, with supervision provided by a simple trajectory-centric reinforcement learning method. We evaluate our method on a range of real-world manipulation tasks that require close coordination between vision and control, such as screwing a cap onto a bottle, and present simulated comparisons to a range of prior policy search methods.

* updating with revisions for JMLR final version
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In order to autonomously learn wide repertoires of complex skills, robots must be able to learn from their own autonomously collected data, without human supervision. One learning signal that is always available for autonomously collected data is prediction: if a robot can learn to predict the future, it can use this predictive model to take actions to produce desired outcomes, such as moving an object to a particular location. However, in complex open-world scenarios, designing a representation for prediction is difficult. In this work, we instead aim to enable self-supervised robotic learning through direct video prediction: instead of attempting to design a good representation, we directly predict what the robot will see next, and then use this model to achieve desired goals. A key challenge in video prediction for robotic manipulation is handling complex spatial arrangements such as occlusions. To that end, we introduce a video prediction model that can keep track of objects through occlusion by incorporating temporal skip-connections. Together with a novel planning criterion and action space formulation, we demonstrate that this model substantially outperforms prior work on video prediction-based control. Our results show manipulation of objects not seen during training, handling multiple objects, and pushing objects around obstructions. These results represent a significant advance in the range and complexity of skills that can be performed entirely with self-supervised robotic learning.

* accepted at the Conference on Robot Learning (CoRL) 2017
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A significant challenge for the practical application of reinforcement learning in the real world is the need to specify an oracle reward function that correctly defines a task. Inverse reinforcement learning (IRL) seeks to avoid this challenge by instead inferring a reward function from expert behavior. While appealing, it can be impractically expensive to collect datasets of demonstrations that cover the variation common in the real world (e.g. opening any type of door). Thus in practice, IRL must commonly be performed with only a limited set of demonstrations where it can be exceedingly difficult to unambiguously recover a reward function. In this work, we exploit the insight that demonstrations from other tasks can be used to constrain the set of possible reward functions by learning a "prior" that is specifically optimized for the ability to infer expressive reward functions from limited numbers of demonstrations. We demonstrate that our method can efficiently recover rewards from images for novel tasks and provide intuition as to how our approach is analogous to learning a prior.

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A longstanding challenge in robot learning for manipulation tasks has been the ability to generalize to varying initial conditions, diverse objects, and changing objectives. Learning based approaches have shown promise in producing robust policies, but require heavy supervision to efficiently learn precise control, especially from visual inputs. We propose a novel self-supervision technique that uses time-reversal to learn goals and provide a high level plan to reach them. In particular, we introduce the time-reversal model (TRM), a self-supervised model which explores outward from a set of goal states and learns to predict these trajectories in reverse. This provides a high level plan towards goals, allowing us to learn complex manipulation tasks with no demonstrations or exploration at test time. We test our method on the domain of assembly, specifically the mating of tetris-style block pairs. Using our method operating atop visual model predictive control, we are able to assemble tetris blocks on a physical robot using only uncalibrated RGB camera input, and generalize to unseen block pairs. sites.google.com/view/time-reversal

* 7 pages, 10 figures
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A key challenge in complex visuomotor control is learning abstract representations that are effective for specifying goals, planning, and generalization. To this end, we introduce universal planning networks (UPN). UPNs embed differentiable planning within a goal-directed policy. This planning computation unrolls a forward model in a latent space and infers an optimal action plan through gradient descent trajectory optimization. The plan-by-gradient-descent process and its underlying representations are learned end-to-end to directly optimize a supervised imitation learning objective. We find that the representations learned are not only effective for goal-directed visual imitation via gradient-based trajectory optimization, but can also provide a metric for specifying goals using images. The learned representations can be leveraged to specify distance-based rewards to reach new target states for model-free reinforcement learning, resulting in substantially more effective learning when solving new tasks described via image-based goals. We were able to achieve successful transfer of visuomotor planning strategies across robots with significantly different morphologies and actuation capabilities.

* Videos available at https://sites.google.com/view/upn-public/home
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