Air traffic control is becoming a more and more complex task due to the increasing number of aircraft. Current air traffic control methods are not suitable for managing this increased traffic. Autonomous air traffic control is deemed a promising alternative. In this paper an air traffic control model is presented that guides an arbitrary number of aircraft across a three-dimensional, unstructured airspace while avoiding conflicts and collisions. This is done utilizing the power of graph based deep learning approaches. These approaches offer significant advantages over current approaches to this task, such as invariance to the input ordering of aircraft and the ability to easily cope with a varying number of aircraft. Results acquired using these approaches show that the air traffic control model performs well on realistic traffic densities; it is capable of managing the airspace by avoiding 100% of potential collisions and preventing 89.8% of potential conflicts.

A long-term goal of reinforcement learning agents is to be able to perform tasks in complex real-world scenarios. The use of external information is one way of scaling agents to more complex problems. However, there is a general lack of collaboration or interoperability between different approaches using external information. In this work, we propose a conceptual framework and taxonomy for assisted reinforcement learning, aimed at fostering such collaboration by classifying and comparing various methods that use external information in the learning process. The proposed taxonomy details the relationship between the external information source and the learner agent, highlighting the process of information decomposition, structure, retention, and how it can be used to influence agent learning. As well as reviewing state-of-the-art methods, we identify current streams of reinforcement learning that use external information in order to improve the agent's performance and its decision-making process. These include heuristic reinforcement learning, interactive reinforcement learning, learning from demonstration, transfer learning, and learning from multiple sources, among others. These streams of reinforcement learning operate with the shared objective of scaffolding the learner agent. Lastly, we discuss further possibilities for future work in the field of assisted reinforcement learning systems.

In this paper we provide a general framework for designing, analyzing and implementing such algorithms in the episodic reinforcement learning problem. This framework is built upon Lagrangian duality, and demonstrates that every model-optimistic algorithm that constructs an optimistic MDP has an equivalent representation as a value-optimistic dynamic programming algorithm. Typically, it was thought that these two classes of algorithms were distinct, with model-optimistic algorithms benefiting from a cleaner probabilistic analysis while value-optimistic algorithms are easier to implement and thus more practical. With the framework developed in this paper, we show that it is possible to get the best of both worlds by providing a class of algorithms which have a computationally efficient dynamic-programming implementation and also a simple probabilistic analysis. Besides being able to capture many existing algorithms in the tabular setting, our framework can also address largescale problems under realizable function approximation, where it enables a simple model-based analysis of some recently proposed methods.

The construction of replication strategies for contingent claims in the presence of risk and market friction is a key problem of financial engineering. In real markets, continuous replication, such as in the model of Black, Scholes and Merton, is not only unrealistic but it is also undesirable due to high transaction costs. Over the last decades stochastic optimal-control methods have been developed to balance between effective replication and losses. More recently, with the rise of artificial intelligence, temporal-difference Reinforcement Learning, in particular variations of $Q$-learning in conjunction with Deep Neural Networks, have attracted significant interest. From a practical point of view, however, such methods are often relatively sample inefficient, hard to train and lack performance guarantees. This motivates the investigation of a stable benchmark algorithm for hedging. In this article, the hedging problem is viewed as an instance of a risk-averse contextual $k$-armed bandit problem, for which a large body of theoretical results and well-studied algorithms are available. We find that the $k$-armed bandit model naturally fits to the $P\&L$ formulation of hedging, providing for a more accurate and sample efficient approach than $Q$-learning and reducing to the Black-Scholes model in the absence of transaction costs and risks.

In optical coherence tomography (OCT) volumes of retina, the sequential acquisition of the individual slices makes this modality prone to motion artifacts, misalignments between adjacent slices being the most noticeable. Any distortion in OCT volumes can bias structural analysis and influence the outcome of longitudinal studies. On the other hand, presence of speckle noise that is characteristic of this imaging modality, leads to inaccuracies when traditional registration techniques are employed. Also, the lack of a well-defined ground truth makes supervised deep-learning techniques ill-posed to tackle the problem. In this paper, we tackle these issues by using deep reinforcement learning to correct inter-frame movements in an unsupervised manner. Specifically, we use dueling deep Q-network to train an artificial agent to find the optimal policy, i.e. a sequence of actions, that best improves the alignment by maximizing the sum of reward signals. Instead of relying on the ground-truth of transformation parameters to guide the rewarding system, for the first time, we use a combination of intensity based image similarity metrics. Further, to avoid the agent bias towards speckle noise, we ensure the agent can see retinal layers as part of the interacting environment. For quantitative evaluation, we simulate the eye movement artifacts by applying 2D rigid transformations on individual B-scans. The proposed model achieves an average of 0.985 and 0.914 for normalized mutual information and correlation coefficient, respectively. We also compare our model with elastix intensity based medical image registration approach, where significant improvement is achieved by our model for both noisy and denoised volumes.

In this paper, we analyze the convergence rate of the gradient temporal difference learning (GTD) family of algorithms. Previous analyses of this class of algorithms use ODE techniques to prove asymptotic convergence, and to the best of our knowledge, no finite-sample analysis has been done. Moreover, there has been not much work on finite-sample analysis for convergent off-policy reinforcement learning algorithms. In this paper, we formulate GTD methods as stochastic gradient algorithms w.r.t.~a primal-dual saddle-point objective function, and then conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Two revised algorithms are also proposed, namely projected GTD2 and GTD2-MP, which offer improved convergence guarantees and acceleration, respectively. The results of our theoretical analysis show that the GTD family of algorithms are indeed comparable to the existing LSTD methods in off-policy learning scenarios.

In continuing tasks, average-reward reinforcement learning may be a more appropriate problem formulation than the more common discounted reward formulation. As usual, learning an optimal policy in this setting typically requires a large amount of training experiences. Reward shaping is a common approach for incorporating domain knowledge into reinforcement learning in order to speed up convergence to an optimal policy. However, to the best of our knowledge, the theoretical properties of reward shaping have thus far only been established in the discounted setting. This paper presents the first reward shaping framework for average-reward learning and proves that, under standard assumptions, the optimal policy under the original reward function can be recovered. In order to avoid the need for manual construction of the shaping function, we introduce a method for utilizing domain knowledge expressed as a temporal logic formula. The formula is automatically translated to a shaping function that provides additional reward throughout the learning process. We evaluate the proposed method on three continuing tasks. In all cases, shaping speeds up the average-reward learning rate without any reduction in the performance of the learned policy compared to relevant baselines.

Resolving the exploration-exploitation trade-off remains a fundamental problem in the design and implementation of reinforcement learning (RL) algorithms. In this paper, we focus on model-free RL using the epsilon-greedy exploration policy, which despite its simplicity, remains one of the most frequently used forms of exploration. However, a key limitation of this policy is the specification of $\varepsilon$. In this paper, we provide a novel Bayesian perspective of $\varepsilon$ as a measure of the uniformity of the Q-value function. We introduce a closed-form Bayesian model update based on Bayesian model combination (BMC), based on this new perspective, which allows us to adapt $\varepsilon$ using experiences from the environment in constant time with monotone convergence guarantees. We demonstrate that our proposed algorithm, $\varepsilon$-\texttt{BMC}, efficiently balances exploration and exploitation on different problems, performing comparably or outperforming the best tuned fixed annealing schedules and an alternative data-dependent $\varepsilon$ adaptation scheme proposed in the literature.

Deep reinforcement learning algorithms (Sutton & Barto, 1998) are effective at learning, often from raw sensor inputs, control policies that optimize for a quantitative reward signal. Learning these policies can require experiencing millions of unsafe actions. Even if a safe policy is finally learned - which will happen only if the reward signal reflects all relevant safety priorities - providing a purely statistical guarantee that the optimal policy is safe requires an unrealistic amount of training data (Kalra & Paddock, 2016). The difficulty of establishing the safety of these algorithms makes it difficult to justify the use of reinforcement learning in safety-critical domains where industry standards demand strong evidence of safety prior to deployment (ISO-26262, 2011). Formal verification provides a rigorous way of establishing safety for traditional control systems (Clarke et al., 2018). The problem of providing formal guarantees in RL is called formally constrained reinforcement learning (FCRL).

Determination of inspection and maintenance policies for minimizing long-term risks and costs in deteriorating engineering environments constitutes a complex optimization problem. Major computational challenges include the (i) curse of dimensionality, due to exponential scaling of state/action set cardinalities with the number of components; (ii) curse of history, related to exponentially growing decision-trees with the number of decision-steps; (iii) presence of state uncertainties, induced by inherent environment stochasticity and variability of inspection/monitoring measurements; (iv) presence of constraints, pertaining to stochastic long-term limitations, due to resource scarcity and other infeasible/undesirable system responses. In this work, these challenges are addressed within a joint framework of constrained Partially Observable Markov Decision Processes (POMDP) and multi-agent Deep Reinforcement Learning (DRL). POMDPs optimally tackle (ii)-(iii), combining stochastic dynamic programming with Bayesian inference principles. Multi-agent DRL addresses (i), through deep function parametrizations and decentralized control assumptions. Challenge (iv) is herein handled through proper state augmentation and Lagrangian relaxation, with emphasis on life-cycle risk-based constraints and budget limitations. The underlying algorithmic steps are provided, and the proposed framework is found to outperform well-established policy baselines and facilitate adept prescription of inspection and intervention actions, in cases where decisions must be made in the most resource- and risk-aware manner.