Conventional wisdom holds that model-based planning is a powerful approach to sequential decision-making. It is often very challenging in practice, however, because while a model can be used to evaluate a plan, it does not prescribe how to construct a plan. Here we introduce the "Imagination-based Planner", the first model-based, sequential decision-making agent that can learn to construct, evaluate, and execute plans. Before any action, it can perform a variable number of imagination steps, which involve proposing an imagined action and evaluating it with its model-based imagination. All imagined actions and outcomes are aggregated, iteratively, into a "plan context" which conditions future real and imagined actions. The agent can even decide how to imagine: testing out alternative imagined actions, chaining sequences of actions together, or building a more complex "imagination tree" by navigating flexibly among the previously imagined states using a learned policy. And our agent can learn to plan economically, jointly optimizing for external rewards and computational costs associated with using its imagination. We show that our architecture can learn to solve a challenging continuous control problem, and also learn elaborate planning strategies in a discrete maze-solving task. Our work opens a new direction toward learning the components of a model-based planning system and how to use them.
The game of Go has long been viewed as the most challenging of classic games for artificial intelligence owing to its enormous search space and the difficulty of evaluating board positions and moves. Here we introduce a new approach to computer Go that uses ‘value networks’ to evaluate board positions and ‘policy networks’ to select moves. These deep neural networks are trained by a novel combination of supervised learning from human expert games, and reinforcement learning from games of self-play. Without any lookahead search, the neural networks play Go at the level of stateof-the-art Monte Carlo tree search programs that simulate thousands of random games of self-play. We also introduce a new search algorithm that combines Monte Carlo simulation with value and policy networks. Using this search algorithm, our program AlphaGo achieved a 99.8 winning rate against other Go programs, and defeated the human European Go champion by 5 games to 0. This is the first time that a computer program has defeated a human professional player in the full-sized game of Go, a feat previously thought to be at least a decade away. If one possesses a model of a controlled deterministic system, then from any state, one may consider the set of all possible reachable states starting from that state and using any sequence of actions. This forms a tree whose size is exponential in the planning time horizon. Here we ask the question: given finite computational resources (e.g. CPU time), which may not be known ahead of time, what is the best way to explore this tree, such that once all resources have been used, the algorithm would be able to propose an action (or a sequence of actions) whose performance is as close as possible to optimality? The performance with respect to optimality is assessed in terms of the regret (with respect to the sum of discounted future rewards) resulting from choosing the action returned by the algorithm instead of an optimal action. In this paper we investigate an optimistic exploration of the tree, where the most promising states are explored first, and compare this approach to a naive uniform exploration. Bounds on the regret are derived both for uniform and optimistic exploration strategies. Numerical simulations illustrate the benefit of optimistic planning. 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. We introduce Embed to Control (E2C), a method for model learning and control of non-linear dynamical systems from raw pixel images. E2C consists of a deep generative model, belonging to the family of variational autoencoders, that learns to generate image trajectories from a latent space in which the dynamics is constrained to be locally linear. Our model is derived directly from an optimal control formulation in latent space, supports long-term prediction of image sequences and exhibits strong performance on a variety of complex control problems. Designing controllers for tasks with complex nonlinear dynamics is extremely challenging, time-consuming, and in many cases, infeasible. This difficulty is exacerbated in tasks such as robotic food-cutting, in which dynamics might vary both with environmental properties, such as material and tool class, and with time while acting. In this work, we present DeepMPC, an online real-time model-predictive control approach designed to handle such difficult tasks. Rather than hand-design a dynamics model for the task, our approach uses a novel deep architecture and learning algorithm, learning controllers for complex tasks directly from data. We validate our method in experiments on a large-scale dataset of 1488 material cuts for 20 diverse classes, and in 450 real-world robotic experiments, demonstrating significant improvement over several other approaches. From household appliances to applications in robotics, engineered systems involving complex dynamics can only be as effective as the algorithms that control them. While Dynamic Programming (DP) has provided researchers with a way to optimally solve decision and control problems involving complex dynamic systems, its practical value was limited by algorithms that lacked the capacity to scale up to realistic problems. However, in recent years, dramatic developments in Reinforcement Learning (RL), the model-free counterpart of DP, changed our understanding of what is possible. Those developments led to the creation of reliable methods that can be applied even when a mathematical model of the system is unavailable, allowing researchers to solve challenging control problems in engineering, as well as in a variety of other disciplines, including economics, medicine, and artificial intelligence. Reinforcement Learning and Dynamic Programming Using Function Approximators provides a comprehensive and unparalleled exploration of the field of RL and DP. With a focus on continuous-variable problems, this seminal text details essential developments that have substantially altered the field over the past decade. In its pages, pioneering experts provide a concise introduction to classical RL and DP, followed by an extensive presentation of the state-of-the-art and novel methods in RL and DP with approximation. Combining algorithm development with theoretical guarantees, they elaborate on their work with illustrative examples and insightful comparisons. Three individual chapters are dedicated to representative algorithms from each of the major classes of techniques: value iteration, policy iteration, and policy search. The features and performance of these algorithms are highlighted in extensive experimental studies on a range of control applications. The recent development of applications involving complex systems has led to a surge of interest in RL and DP methods and the subsequent need for a quality resource on the subject. For graduate students and others new to the field, this book offers a thorough introduction to both the basics and emerging methods. And for those researchers and practitioners working in the fields of optimal and adaptive control, machine learning, artificial intelligence, and operations research, this resource offers a combination of practical algorithms, theoretical analysis, and comprehensive examples that they will be able to adapt and apply to their own work. Access the authors' website at www.dcsc.tudelft.nl rlbook for additional material, including computer code used in the studies and information concerning new developments. We consider a global optimization problem of a deterministic function f in a semi-metric space, given a finite budget of n evaluations. The function f is assumed to be locally smooth (around one of its global maxima) with respect to a semi-metric l We describe two algorithms based on optimistic exploration that use a hierarchical partitioning of the space at all scales. A first contribution is an algorithm, DOO, that requires the knowledge of l. We report a finite-sample performance bound in terms of a measure of the quantity of near-optimal states. We then define a second algorithm, SOO, which does not require the knowledge of the semi-metric l under which f is smooth, and whose performance is almost as good as DOO optimally-fitted.