### Learning to Control in Metric Space with Optimal Regret

We study online reinforcement learning for finite-horizon deterministic control systems with {\it arbitrary} state and action spaces. Suppose that the transition dynamics and reward function is unknown, but the state and action space is endowed with a metric that characterizes the proximity between different states and actions. We provide a surprisingly simple upper-confidence reinforcement learning algorithm that uses a function approximation oracle to estimate optimistic Q functions from experiences. We show that the regret of the algorithm after $K$ episodes is $O(HL(KH)^{\frac{d-1}{d}})$ where $L$ is a smoothness parameter, and $d$ is the doubling dimension of the state-action space with respect to the given metric. We also establish a near-matching regret lower bound. The proposed method can be adapted to work for more structured transition systems, including the finite-state case and the case where value functions are linear combinations of features, where the method also achieve the optimal regret.

### Towards An Understanding of What is Learned: Extracting Multi-Abstraction-Level Knowledge from Learning Agents

Machine Learning approaches used in the context of agents (like Reinforcement Learning) commonly result in weighted state-action pair representations (where the weights determine which action should be performed, given a perceived state). The weighted state-action pairs are stored, e.g., in tabular form or as approximated functions which makes the learned knowledge hard to comprehend by humans, since the number of state-action pairs can be extremely high. In this paper, a knowledge extraction approach is presented which extracts compact and comprehensible knowledge bases from such weighted state-action pairs. For this purpose, so-called Hierarchical Knowledge Bases are described which allow for a top-down view on the learned knowledge at an adequate level of abstraction. The approach can be applied to gain structural insights into a problem and its solution and it can be easily transformed into common knowledge representation formalisms, like normal logic programs.

### Reinforcement Learning for Mixed Open-loop and Closed-loop Control

Closed-loop control relies on sensory feedback that is usually assumed tobe free . But if sensing incurs a cost, it may be costeffective totake sequences of actions in open-loop mode. We describe a reinforcement learning algorithm that learns to combine open-loop and closed-loop control when sensing incurs a cost. Although weassume reliable sensors, use of open-loop control means that actions must sometimes be taken when the current state of the controlled system is uncertain. This is a special case of the hidden-state problem in reinforcement learning, and to cope, our algorithm relies on short-term memory.

### Asynchronous n-steps Q-learning

Q-learning is the most famous Temporal Difference algorithm. Original Q-learning algorithm tries to determine the state-action value function that minimizes the error below. We will use an optimizer (the simplest one- Gradient Descent) to compute the values of the state-action function. First of all we need to compute the gradient of the loss function. Gradient descent finds the minimum of a function by subtracting the gradient, with respect to the parameters of the function, from the parameters.

### Pretraining Deep Actor-Critic Reinforcement Learning Algorithms With Expert Demonstrations

Pretraining with expert demonstrations have been found useful in speeding up the training process of deep reinforcement learning algorithms since less online simulation data is required. Some people use supervised learning to speed up the process of feature learning, others pretrain the policies by imitating expert demonstrations. However, these methods are unstable and not suitable for actor-critic reinforcement learning algorithms. Also, some existing methods rely on the global optimum assumption, which is not true in most scenarios. In this paper, we employ expert demonstrations in a actor-critic reinforcement learning framework, and meanwhile ensure that the performance is not affected by the fact that expert demonstrations are not global optimal. We theoretically derive a method for computing policy gradients and value estimators with only expert demonstrations. Our method is theoretically plausible for actor-critic reinforcement learning algorithms that pretrains both policy and value functions. We apply our method to two of the typical actor-critic reinforcement learning algorithms, DDPG and ACER, and demonstrate with experiments that our method not only outperforms the RL algorithms without pretraining process, but also is more simulation efficient.