Model-Based Reinforcement Learning with Continuous States and Actions

Finding an optimal policy in a reinforcement learning (RL) framework with continuous state and action spaces is challenging. Approximate solutions are often inevitable. GPDP is an approximate dynamic programming algorithm based on Gaussian process (GP) models for the value functions. In this paper, we extend GPDP to the case of unknown transition dynamics. After building a GP model for the transition dynamics, we apply GPDP to this model and determine a continuous-valued policy in the entire state space. We apply the resulting controller to the underpowered pendulum swing up. Moreover, we compare our results on this RL task to a nearly optimal discrete DP solution in a fully known environment

Model-based Reinforcement Learning with Parametrized Physical Models and Optimism-Driven Exploration

In this paper, we present a robotic model-based reinforcement learning method that combines ideas from model identification and model predictive control. We use a feature-based representation of the dynamics that allows the dynamics model to be fitted with a simple least squares procedure, and the features are identified from a high-level specification of the robot's morphology, consisting of the number and connectivity structure of its links. Model predictive control is then used to choose the actions under an optimistic model of the dynamics, which produces an efficient and goal-directed exploration strategy. We present real time experimental results on standard benchmark problems involving the pendulum, cartpole, and double pendulum systems. Experiments indicate that our method is able to learn a range of benchmark tasks substantially faster than the previous best methods. To evaluate our approach on a realistic robotic control task, we also demonstrate real time control of a simulated 7 degree of freedom arm.Comment: 8 page

Reinforcement Learning: A Survey

This paper surveys the field of reinforcement learning from a computer-science perspective. It is written to be accessible to researchers familiar with machine learning. Both the historical basis of the field and a broad selection of current work are summarized. Reinforcement learning is the problem faced by an agent that learns behavior through trial-and-error interactions with a dynamic environment. The work described here has a resemblance to work in psychology, but differs considerably in the details and in the use of the word ``reinforcement.'' The paper discusses central issues of reinforcement learning, including trading off exploration and exploitation, establishing the foundations of the field via Markov decision theory, learning from delayed reinforcement, constructing empirical models to accelerate learning, making use of generalization and hierarchy, and coping with hidden state. It concludes with a survey of some implemented systems and an assessment of the practical utility of current methods for reinforcement learning.Comment: See http://www.jair.org/ for any accompanying file

Certified Reinforcement Learning with Logic Guidance

This paper proposes the first model-free Reinforcement Learning (RL) framework to synthesise policies for unknown, and continuous-state Markov Decision Processes (MDPs), such that a given linear temporal property is satisfied. We convert the given property into a Limit Deterministic Buchi Automaton (LDBA), namely a finite-state machine expressing the property. Exploiting the structure of the LDBA, we shape a synchronous reward function on-the-fly, so that an RL algorithm can synthesise a policy resulting in traces that probabilistically satisfy the linear temporal property. This probability (certificate) is also calculated in parallel with policy learning when the state space of the MDP is finite: as such, the RL algorithm produces a policy that is certified with respect to the property. Under the assumption of finite state space, theoretical guarantees are provided on the convergence of the RL algorithm to an optimal policy, maximising the above probability. We also show that our method produces ''best available'' control policies when the logical property cannot be satisfied. In the general case of a continuous state space, we propose a neural network architecture for RL and we empirically show that the algorithm finds satisfying policies, if there exist such policies. The performance of the proposed framework is evaluated via a set of numerical examples and benchmarks, where we observe an improvement of one order of magnitude in the number of iterations required for the policy synthesis, compared to existing approaches whenever available.Comment: This article draws from arXiv:1801.08099, arXiv:1809.0782

Robust satisfaction of temporal logic specifications via reinforcement learning

We consider the problem of steering a system with unknown, stochastic dynamics to satisfy a rich, temporally-layered task given as a signal temporal logic formula. We represent the system as a finite-memory Markov decision process with unknown transition probabilities and whose states are built from a partition of the state space. We present provably convergent reinforcement learning algorithms to maximize the probability of satisfying a given specification and to maximize the average expected robustness, i.e. a measure of how strongly the formula is satisfied. Robustness allows us to quantify progress towards satisfying a given specification. We demonstrate via a pair of robot navigation simulation case studies that, due to the quantification of progress towards satisfaction, reinforcement learning with robustness maximization performs better than probability maximization in terms of both probability of satisfaction and expected robustness with a low number of training examples