In many robotic applications, some aspects of the system dynamics can be modeled accurately while others are difficult to obtain or model. We present a novel reinforcement learning (RL) method for continuous state and action spaces that learns with partial knowledge of the system and without active exploration. It solves linearly-solvable Markov decision processes (L-MDPs), which are well suited for continuous state and action spaces, based on an actor-critic architecture. Compared to previous RL methods for L-MDPs and path integral methods which are model based, the actor-critic learning does not need a model of the uncontrolled dynamics and, importantly, transition noise levels; however, it requires knowing the control dynamics for the problem. We evaluate our method on two synthetic test problems, and one real-world problem in simulation and using real traffic data. Our experiments demonstrate improved learning and policy performance.
Path integral control also learns a policy based on linearized Bellman equation @cite_7 @cite_2 . Unlike approaches for L-MDPs, path integral control can directly optimize the policy. However, the approach has to sample sample many trajectories under a training policy from a certain initial state. As we mentioned previously, we seek to avoid such active and potentially unsafe explorations in the real world.
@cite_7 @cite_2
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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. Path integral (PI) control defines a general class of control problems for which the optimal control computation is equivalent to an inference problem that can be solved by evaluation of a path integral over state trajectories. However, this potential is mostly unused in real-world problems because of two main limitations: first, current approaches can typically only be applied to learn open-loop controllers and second, current sampling procedures are inefficient and not scalable to high dimensional systems. We introduce the efficient Path Integral Relative-Entropy Policy Search (PI-REPS) algorithm for learning feedback policies with PI control. Our algorithm is inspired by information theoretic policy updates that are often used in policy search. We use these updates to approximate the state trajectory distribution that is known to be optimal from the PI control theory. Our approach allows for a principled treatment of different sampling distributions and can be used to estimate many types of parametric or non-parametric feedback controllers. We show that PI-REPS significantly outperforms current methods and is able to solve tasks that are out of reach for current methods.