Nonlinear optimal control problems are often solved with numerical methods that require knowledge of system's dynamics which may be difficult to infer, and that carry a large computational cost associated with iterative calculations. We present a novel neurobiologically inspired hierarchical learning framework, Reinforcement Learning Optimal Control, which operates on two levels of abstraction and utilises a reduced number of controllers to solve nonlinear systems with unknown dynamics in continuous state and action spaces. Our approach is inspired by research at two levels of abstraction: first, at the level of limb coordination human behaviour is explained by linear optimal feedback control theory. Second, in cognitive tasks involving learning symbolic level action selection, humans learn such problems using model-free and model-based reinforcement learning algorithms. We propose that combining these two levels of abstraction leads to a fast global solution of nonlinear control problems using reduced number of controllers. Our framework learns the local task dynamics from naive experience and forms locally optimal infinite horizon Linear Quadratic Regulators which produce continuous low-level control. A top-level reinforcement learner uses the controllers as actions and learns how to best combine them in state space while maximising a long-term reward. A single optimal control objective function drives high-level symbolic learning by providing training signals on desirability of each selected controller. We show that a small number of locally optimal linear controllers are able to solve global nonlinear control problems with unknown dynamics when combined with a reinforcement learner in this hierarchical framework. Our algorithm competes in terms of computational cost and solution quality with sophisticated control algorithms and we illustrate this with solutions to benchmark problems.
Another class of models combines model-free and model-based algorithms, known as hybrid models. These have been applied to learning reward functions from demonstration @cite_14 , and to obtaining approximate models of the dynamics used in differential dynamic programming and policy gradient evaluations, which required only a small number of real-life trials @cite_44 . More recently @cite_23 , designed an algorithm which learnt stationary nonlinear policies for solutions to unknown dynamical systems using priors and an improved iLQG algorithm. As compared to hybrid models, RLOC offers an alternative framework which learns linear and nonlinear plant dynamics on-line and does not rely on approximate models. We show using two low-dimensional standard benchmark problems that RLOC outperforms matches the benchmark algorithms: naive switching, LQR, state-of-the-art iLQR and state-of-the-art PILCO, in terms of accuracy and computational requirements, thus forming a promising framework for addressing this important class on nonlinear control problems with unknown dynamics.
@cite_44 @cite_14 @cite_23
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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. This book examines Gaussian processes in both model-based reinforcement learning (RL) and inference in nonlinear dynamic systems. First, we introduce PILCO, a fully Bayesian approach for efficient RL in continuous-valued state and action spaces when no expert knowledge is available. PILCO takes model uncertainties consistently into account during long-term planning to reduce model bias. Second, we propose principled algorithms for robust filtering and smoothing in GP dynamic systems. Model-free deep reinforcement learning (RL) methods have been successful in a wide variety of simulated domains. However, a major obstacle facing deep RL in the real world is their high sample complexity. Batch policy gradient methods offer stable learning, but at the cost of high variance, which often requires large batches. TD-style methods, such as off-policy actor-critic and Q-learning, are more sample-efficient but biased, and often require costly hyperparameter sweeps to stabilize. In this work, we aim to develop methods that combine the stability of policy gradients with the efficiency of off-policy RL. We present Q-Prop, a policy gradient method that uses a Taylor expansion of the off-policy critic as a control variate. Q-Prop is both sample efficient and stable, and effectively combines the benefits of on-policy and off-policy methods. We analyze the connection between Q-Prop and existing model-free algorithms, and use control variate theory to derive two variants of Q-Prop with conservative and aggressive adaptation. We show that conservative Q-Prop provides substantial gains in sample efficiency over trust region policy optimization (TRPO) with generalized advantage estimation (GAE), and improves stability over deep deterministic policy gradient (DDPG), the state-of-the-art on-policy and off-policy methods, on OpenAI Gym's MuJoCo continuous control environments. 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.