We present a unified framework for learning continuous control policies using backpropagation. It supports stochastic control by treating stochasticity in the Bellman equation as a deterministic function of exogenous noise. The product is a spectrum of general policy gradient algorithms that range from model-free methods with value functions to model-based methods without value functions. We use learned models but only require observations from the environment in- stead of observations from model-predicted trajectories, minimizing the impact of compounded model errors. We apply these algorithms first to a toy stochastic control problem and then to several physics-based control problems in simulation. One of these variants, SVG(1), shows the effectiveness of learning models, value functions, and policies simultaneously in continuous domains.
Writing the noise variables as exogenous inputs to the system to allow direct differentiation with respect to the system state (equation ) is a known device in control theory @cite_12 @cite_7 where the model is given analytically. The idea of using a model to optimize a parametric policy around real trajectories is presented heuristically in @cite_29 and @cite_17 for deterministic policies and models. Also in the limit of deterministic policies and models, the recursions we have derived in Algorithm reduce to those of @cite_14 . Werbos defines an actor-critic algorithm called Heuristic Dynamic Programming that uses a deterministic model to roll-forward one step to produce a state prediction that is evaluated by a value function @cite_1 . have used Gaussian process models to compute policy gradients that are sensitive to model-uncertainty @cite_24 , and have optimized impressive policies with the aid of a non-parametric trajectory optimizer and locally-linear models @cite_20 . Our work in contrast has focused on using global, neural network models conjoined to value function approximators.
@cite_14 @cite_7 @cite_29 @cite_1 @cite_24 @cite_20 @cite_12 @cite_17
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We provide efficient algorithms to calculate first and second order gradients of the cost of a control law with respect to its parameters, to speed up policy optimization. We achieve robustness by simultaneously designing one control law for multiple models with potentially different model structures, which represent model uncertainty and unmodeled dynamics. Providing explicit examples of possible unmodeled dynamics during the control design process is easier for the designer and is more effective than providing simulated perturbations to increase robustness, as is currently done in machine learning. Our approach supports the design of deterministic nonlinear and time varying controllers for both deterministic and stochastic nonlinear and time varying systems, including policies with internal state such as observers or other state estimators. We highlight the benefit of control laws made up of collections of simple policies where only one component policy is active at a time. Controller optimization and learning is particularly fast and effective in this situation because derivatives are decoupled. We describe an Adaptive Dynamic Programming algorithm VGL(λ) for learning a critic function over a large continuous state space. The algorithm, which requires a learned model of the environment, extends Dual Heuristic Dynamic Programming to include a bootstrapping parameter analogous to that used in the reinforcement learning algorithm TD(λ). We provide on-line and batch mode implementations of the algorithm, and summarise the theoretical relationships and motivations of using this method over its precursor algorithms Dual Heuristic Dynamic Programming and TD(λ). Experiments for control problems using a neural network and greedy policy are provided. It is demonstrated that neural networks can be used effectively for the identification and control of nonlinear dynamical systems. The emphasis is on models for both identification and control. Static and dynamic backpropagation methods for the adjustment of parameters are discussed. In the models that are introduced, multilayer and recurrent networks are interconnected in novel configurations, and hence there is a real need to study them in a unified fashion. Simulation results reveal that the identification and adaptive control schemes suggested are practically feasible. Basic concepts and definitions are introduced throughout, and theoretical questions that have to be addressed are also described. > This chapter contains sections titled: Introduction and Overview, A Simple Two-Component Adaptive Critic Design, HDP and Dynamic Programming, Alternative Ways to Figure 3.2 in Adapting the Action Network, Alternatives to HDP in Adapting the Critic Network, Some Topics for Further Research, Equations and Code For Implementation, References In this paper, we introduce PILCO, a practical, data-efficient model-based policy search method. PILCO reduces model bias, one of the key problems of model-based reinforcement learning, in a principled way. By learning a probabilistic dynamics model and explicitly incorporating model uncertainty into long-term planning, PILCO can cope with very little data and facilitates learning from scratch in only a few trials. Policy evaluation is performed in closed form using state-of-the-art approximate inference. Furthermore, policy gradients are computed analytically for policy improvement. We report unprecedented learning efficiency on challenging and high-dimensional control tasks. We present a policy search method that uses iteratively refitted local linear models to optimize trajectory distributions for large, continuous problems. These trajectory distributions can be used within the framework of guided policy search to learn policies with an arbitrary parameterization. Our method fits time-varying linear dynamics models to speed up learning, but does not rely on learning a global model, which can be difficult when the dynamics are complex and discontinuous. We show that this hybrid approach requires many fewer samples than model-free methods, and can handle complex, nonsmooth dynamics that can pose a challenge for model-based techniques. We present experiments showing that our method can be used to learn complex neural network policies that successfully execute simulated robotic manipulation tasks in partially observed environments with numerous contact discontinuities and underactuation. In the model-based policy search approach to reinforcement learning (RL), policies are found using a model (or "simulator") of the Markov decision process. However, for high-dimensional continuous-state tasks, it can be extremely difficult to build an accurate model, and thus often the algorithm returns a policy that works in simulation but not in real-life. The other extreme, model-free RL, tends to require infeasibly large numbers of real-life trials. In this paper, we present a hybrid algorithm that requires only an approximate model, and only a small number of real-life trials. The key idea is to successively "ground" the policy evaluations using real-life trials, but to rely on the approximate model to suggest local changes. Our theoretical results show that this algorithm achieves near-optimal performance in the real system, even when the model is only approximate. Empirical results also demonstrate that---when given only a crude model and a small number of real-life trials---our algorithm can obtain near-optimal performance in the real system.