Policy evaluation is a key process in Reinforcement Learning (RL). It assesses a given policy by estimating the corresponding value function. When using parameterized value functions, common approaches minimize the sum of squared Bellman temporal-difference errors and receive a point-estimate for the parameters. Kalman-based and Gaussian-processes based frameworks were suggested to evaluate the policy by treating the value as a random variable. These frameworks can learn uncertainties over the value parameters and exploit them for policy exploration. When adopting these frameworks to solve deep RL tasks, several limitations are revealed: excessive computations in each optimization step, difficulty with handling batches of samples which slows training and the effect of memory in stochastic environments which prevents off-policy learning. In this work, we discuss these limitations and propose to overcome them by an alternative general framework, based on the extended Kalman filter. We devise an optimization method, called Kalman Optimization for Value Approximation (KOVA) that can be incorporated as a policy evaluation component in policy optimization algorithms. KOVA minimizes a regularized objective function that concerns both parameter and noisy return uncertainties. We analyze the properties of KOVA and present its performance on deep RL control tasks.

We develop provably efficient reinforcement learning algorithms for two-player zero-sum Markov games in which the two players simultaneously take actions. To incorporate function approximation, we consider a family of Markov games where the reward function and transition kernel possess a linear structure. Both the offline and online settings of the problems are considered. In the offline setting, we control both players and the goal is to find the Nash Equilibrium efficiently by minimizing the worst-case duality gap. In the online setting, we control a single player to play against an arbitrary opponent and the goal is to minimize the regret. For both settings, we propose an optimistic variant of the least-squares minimax value iteration algorithm. We show that our algorithm is computationally efficient and provably achieves an $\tilde O(\sqrt{d^3 H^3 T})$ upper bound on the duality gap and regret, without requiring additional assumptions on the sampling model. We highlight that our setting requires overcoming several new challenges that are absent in Markov decision processes or turn-based Markov games. In particular, to achieve optimism in simultaneous-move Marko games, we construct both upper and lower confidence bounds of the value function, and then compute the optimistic policy by solving a general-sum matrix game with these bounds as the payoff matrices. As finding the Nash Equilibrium of such a general-sum game is computationally hard, our algorithm instead solves for a Coarse Correlated Equilibrium (CCE), which can be obtained efficiently via linear programming. To our best knowledge, such a CCE-based scheme for implementing optimism has not appeared in the literature and might be of interest in its own right.

Deep reinforcement learning has the potential to train robots to perform complex tasks in the real world without requiring accurate models of the robot or its environment. A practical approach is to train agents in simulation, and then transfer them to the real world. One popular method for achieving transferability is to use domain randomisation, which involves randomly perturbing various aspects of a simulated environment in order to make trained agents robust to the reality gap. However, less work has gone into understanding such agents - which are deployed in the real world - beyond task performance. In this work we examine such agents, through qualitative and quantitative comparisons between agents trained with and without visual domain randomisation. We train agents for Fetch and Jaco robots on a visuomotor control task and evaluate how well they generalise using different testing conditions. Finally, we investigate the internals of the trained agents by using a suite of interpretability techniques. Our results show that the primary outcome of domain randomisation is more robust, entangled representations, accompanied with larger weights with greater spatial structure; moreover, the types of changes are heavily influenced by the task setup and presence of additional proprioceptive inputs. Additionally, we demonstrate that our domain randomised agents require higher sample complexity, can overfit and more heavily rely on recurrent processing. Furthermore, even with an improved saliency method introduced in this work, we show that qualitative studies may not always correspond with quantitative measures, necessitating the combination of inspection tools in order to provide sufficient insights into the behaviour of trained agents.

The current paper studies the problem of agnostic $Q$-learning with function approximation in deterministic systems where the optimal $Q$-function is approximable by a function in the class $\mathcal{F}$ with approximation error $\delta \ge 0$. We propose a novel recursion-based algorithm and show that if $\delta = O\left(\rho/\sqrt{\dim_E}\right)$, then one can find the optimal policy using $O\left(\dim_E\right)$ trajectories, where $\rho$ is the gap between the optimal $Q$-value of the best actions and that of the second-best actions and $\dim_E$ is the Eluder dimension of $\mathcal{F}$. Our result has two implications: 1) In conjunction with the lower bound in [Du et al., ICLR 2020], our upper bound suggests that the condition $\delta = \widetilde{\Theta}\left(\rho/\sqrt{\mathrm{dim}_E}\right)$ is necessary and sufficient for algorithms with polynomial sample complexity. 2) In conjunction with the lower bound in [Wen and Van Roy, NIPS 2013], our upper bound suggests that the sample complexity $\widetilde{\Theta}\left(\mathrm{dim}_E\right)$ is tight even in the agnostic setting. Therefore, we settle the open problem on agnostic $Q$-learning proposed in [Wen and Van Roy, NIPS 2013]. We further extend our algorithm to the stochastic reward setting and obtain similar results.

Policy gradient reinforcement learning (RL) algorithms have achieved impressive performance in challenging learning tasks such as continuous control, but suffer from high sample complexity. Experience replay is a commonly used approach to improve sample efficiency, but gradient estimators using past trajectories typically have high variance. Existing sampling strategies for experience replay like uniform sampling or prioritised experience replay do not explicitly try to control the variance of the gradient estimates. In this paper, we propose an online learning algorithm, adaptive experience selection (AES), to adaptively learn an experience sampling distribution that explicitly minimises this variance. Using a regret minimisation approach, AES iteratively updates the experience sampling distribution to match the performance of a competitor distribution assumed to have optimal variance. Sample non-stationarity is addressed by proposing a dynamic (i.e. time changing) competitor distribution for which a closed-form solution is proposed. We demonstrate that AES is a low-regret algorithm with reasonable sample complexity. Empirically, AES has been implemented for deep deterministic policy gradient and soft actor critic algorithms, and tested on 8 continuous control tasks from the OpenAI Gym library. Ours results show that AES leads to significantly improved performance compared to currently available experience sampling strategies for policy gradient.

The choice of the control frequency of a system has a relevant impact on the ability of reinforcement learning algorithms to learn a highly performing policy. In this paper, we introduce the notion of action persistence that consists in the repetition of an action for a fixed number of decision steps, having the effect of modifying the control frequency. We start analyzing how action persistence affects the performance of the optimal policy, and then we present a novel algorithm, Persistent Fitted Q-Iteration (PFQI), that extends FQI, with the goal of learning the optimal value function at a given persistence. After having provided a theoretical study of PFQI and a heuristic approach to identify the optimal persistence, we present an experimental campaign on benchmark domains to show the advantages of action persistence and proving the effectiveness of our persistence selection method.

Algorithms that tackle deep exploration -- an important challenge in reinforcement learning -- have relied on epistemic uncertainty representation through ensembles or other hypermodels, exploration bonuses, or visitation count distributions. An open question is whether deep exploration can be achieved by an incremental reinforcement learning algorithm that tracks a single point estimate, without additional complexity required to account for epistemic uncertainty. We answer this question in the affirmative. In particular, we develop Langevin DQN, a variation of DQN that differs only in perturbing parameter updates with Gaussian noise, and demonstrate through a computational study that the algorithm achieves deep exploration. We also provide an intuition for why Langevin DQN performs deep exploration.

In this paper, we present an approach based on reinforcement learning for eye tracking data manipulation. It is based on two opposing agents, where one tries to classify the data correctly and the second agent looks for patterns in the data, which get manipulated to hide specific information. We show that our approach is successfully applicable to preserve the privacy of a subject. In addition, our approach allows to evaluate the importance of temporal, as well as spatial, information of eye tracking data for specific classification goals. In general, this approach can also be used for stimuli manipulation, making it interesting for gaze guidance. For this purpose, this work provides the theoretical basis, which is why we have also integrated a section on how to apply this method for gaze guidance.

Reinforcement learning is field that keeps growing and not only because of the breakthroughs in deep learning. Sure if we talk about deep reinforcement learning, it uses neural networks underneath, but there is more to it than that. In our journey through the world of reinforcement learning we focused on one of the most popular reinforcement learning algorithms out there Q-Learning. This approach is considered one of the biggest breakthroughs in Temporal Difference control. In this article, we are going to explore one variation and improvement of this algorithm – Double Q-Learning.

Transferring knowledge among various environments is important to efficiently learn multiple tasks online. Most existing methods directly use the previously learned models or previously learned optimal policies to learn new tasks. However, these methods may be inefficient when the underlying models or optimal policies are substantially different across tasks. In this paper, we propose Template Learning (TempLe), the first PAC-MDP method for multi-task reinforcement learning that could be applied to tasks with varying state/action space. TempLe generates transition dynamics templates, abstractions of the transition dynamics across tasks, to gain sample efficiency by extracting similarities between tasks even when their underlying models or optimal policies have limited commonalities. We present two algorithms for an "online" and a "finite-model" setting respectively. We prove that our proposed TempLe algorithms achieve much lower sample complexity than single-task learners or state-of-the-art multi-task methods. We show via systematically designed experiments that our TempLe method universally outperforms the state-of-the-art multi-task methods (PAC-MDP or not) in various settings and regimes.