Since its introduction, the reward prediction error (RPE) theory of dopamine has explained a wealth of empirical phenomena, providing a unifying framework for understanding the representation of reward and value in the brain 1-3 . According to the now canonical theory, reward predictions are represented as a single scalar quantity, which supports learning about the expectation, or mean, of stochastic outcomes. In the present work, we propose a novel account of dopamine-based reinforcement learning. Inspired by recent artificial intelligence research on distributional reinforcement learning 4-6 , we hypothesized that the brain represents possible future rewards not as a single mean, but instead as a probability distribution, effectively representing multiple future outcomes simultaneously and in parallel. This idea leads immediately to a set of empirical predictions, which we tested using single-unit recordings from mouse ventral tegmental area. Our findings provide strong evidence for a neural realization of distributional reinforcement learning.The RPE theory of dopamine derives from work in the artificial intelligence (AI) field of reinforcement learning (RL) 7 . Since the link to neuroscience was first made, however, RL has made substantial advances 8,9 , revealing factors that radically enhance the effectiveness of RL algorithms 10 . In some cases, the relevant mechanisms invite comparison with neural function, suggesting new hypotheses concerning reward-based learning in the brain [11][12][13] . Here, we examine one particularly promising recent development in AI research and

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The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret. The proof is accompanied by a numerical comparison with other optimal policies, experiments that have been lacking in the literature until now for the Bernoulli case.

We consider optimal sequential allocation in the context of the so-called stochastic multi-armed bandit model. We describe a generic index policy, in the sense of Gittins [J. R. Stat. Soc. Ser. B Stat. Methodol. 41 (1979) 148-177], based on upper confidence bounds of the arm payoffs computed using the Kullback-Leibler divergence. We consider two classes of distributions for which instances of this general idea are analyzed: the kl-UCB algorithm is designed for oneparameter exponential families and the empirical KL-UCB algorithm for bounded and finitely supported distributions. Our main contribution is a unified finite-time analysis of the regret of these algorithms that asymptotically matches the lower bounds of Lai and Robbins [Adv. in Appl. Math. 6 (1985) 4-22] and Burnetas and Katehakis [Adv. in Appl. Math. 17 (1996) 122-142], respectively. We also investigate the behavior of these algorithms when used with general bounded rewards, showing in particular that they provide significant improvements over the state-of-the-art.

In this work we aim to solve a large collection of tasks using a single reinforcement learning agent with a single set of parameters. A key challenge is to handle the increased amount of data and extended training time. We have developed a new distributed agent IMPALA (Importance Weighted Actor-Learner Architecture) that not only uses resources more efficiently in singlemachine training but also scales to thousands of machines without sacrificing data efficiency or resource utilisation. We achieve stable learning at high throughput by combining decoupled acting and learning with a novel off-policy correction method called V-trace. We demonstrate the effectiveness of IMPALA for multi-task reinforcement learning on DMLab-30 (a set of 30 tasks from the DeepMind Lab environment (Beattie et al., 2016)) and Atari-57 (all available Atari games in Arcade Learning Environment (Bellemare et al., 2013a)). Our results show that IMPALA is able to achieve better performance than previous agents with less data, and crucially exhibits positive transfer between tasks as a result of its multi-task approach. The source code is publicly available at github.com/deepmind/scalable agent.

To cite this version:Andras Antos, Csaba Szepesvari, Rémi Munos. Learning near-optimal policies with Bellman-residual minimization based fitted policy iteration and a single sample path. Machine Learning Journal, Springer, 2008, pp.71:89-129. The date of receipt and acceptance will be inserted by the editor Abstract We consider the problem of finding a near-optimal policy using value-function methods in continuous space, discounted Markovian Decision Problems (MDP) when only a single trajectory underlying some policy can be used as the input. Since the state-space is continuous, one must resort to the use of function approximation. In this paper we study a policy iteration algorithm iterating over action-value functions where the iterates are obtained by empirical risk minimization, where the loss function used penalizes high magnitudes of the Bellman-residual. It turns out that when a linear parameterization is used the algorithm is equivalent to least-squares policy iteration. Our main result is a finite-sample, high-probability bound on the performance of the computed policy that depends on the mixing rate of the trajectory, the capacity of the function set as measured by a novel capacity concept (the VC-crossing dimension), the approximation power of the function set and the controllability properties of the MDP. To the best of our knowledge this is the first theoretical result for off-policy control learning over continuous state-spaces using a single trajectory.

We consider the framework of stochastic multi-armed bandit problems and study the possibilities and limitations of strategies that explore sequentially the arms. The strategies are assessed not in terms of their cumulative regrets, as is usually the case, but through quantities referred to as simple regrets. The latter are related to the (expected) gains of the decisions that the strategies would recommend for a new one-shot instance of the same multi-armed bandit problem. Here, exploration is only constrained by the number of available rounds (not necessarily known in advance), in contrast to the case when cumulative regrets are considered and when exploitation needs to be performed at the same time. We start by indicating the links between simple and cumulative regrets. A small cumulative regret entails a small simple regret but too small a cumulative regret prevents the simple regret from decreasing exponentially towards zero, its optimal distribution-dependent rate. We therefore introduce specific strategies, for which we prove both distribution-dependent and distribution-free bounds. A concluding experimental study puts these theoretical bounds in perspective and shows the interest of nonuniform exploration of the arms.

In recent years deep reinforcement learning (RL) systems have attained superhuman performance in a number of challenging task domains. However, a major limitation of such applications is their demand for massive amounts of training data. A critical present objective is thus to develop deep RL methods that can adapt rapidly to new tasks. In the present work we introduce a novel approach to this challenge, which we refer to as deep meta-reinforcement learning. Previous work has shown that recurrent networks can support meta-learning in a fully supervised context. We extend this approach to the RL setting. What emerges is a system that is trained using one RL algorithm, but whose recurrent dynamics implement a second, quite separate RL procedure. This second, learned RL algorithm can differ from the original one in arbitrary ways. Importantly, because it is learned, it is configured to exploit structure in the training domain. We unpack these points in a series of seven proof-of-concept experiments, each of which examines a key aspect of deep meta-RL. We consider prospects for extending and scaling up the approach, and also point out some potentially important implications for neuroscience.