Motivated by the success of reinforcement learning (RL) for discrete-time tasks such as AlphaGo and Atari games, there has been a recent surge of interest in using RL for continuous-time control of physical systems (cf. many challenging tasks in OpenAI Gym and DeepMind Control Suite). Since discretization of time is susceptible to error, it is methodologically more desirable to handle the system dynamics directly in continuous time. However, very few techniques exist for continuous-time RL and they lack flexibility in value function approximation. In this paper, we propose a novel framework for model-based continuous-time value function approximation in reproducing kernel Hilbert spaces. The resulting framework is so flexible that it can accommodate any kind of kernel-based approach, such as Gaussian processes and kernel adaptive filters, and it allows us to handle uncertainties and nonstationarity without prior knowledge about the environment or what basis functions to employ. We demonstrate the validity of the presented framework through experiments.

A generative recurrent neural network is quickly trained in an unsupervised manner to model popular reinforcement learning environments through compressed spatio-temporal representations. The world model's extracted features are fed into compact and simple policies trained by evolution, achieving state of the art results in various environments. We also train our agent entirely inside of an environment generated by its own internal world model, and transfer this policy back into the actual environment. Interactive version of this paper is available at https://worldmodels.github.io

The goal of reinforcement learning algorithms is to estimate and/or optimise the value function. However, unlike supervised learning, no teacher or oracle is available to provide the true value function. Instead, the majority of reinforcement learning algorithms estimate and/or optimise a proxy for the value function. This proxy is typically based on a sampled and bootstrapped approximation to the true value function, known as a return. The particular choice of return is one of the chief components determining the nature of the algorithm: the rate at which future rewards are discounted; when and how values should be bootstrapped; or even the nature of the rewards themselves. It is well-known that these decisions are crucial to the overall success of RL algorithms. We discuss a gradient-based meta-learning algorithm that is able to adapt the nature of the return, online, whilst interacting and learning from the environment. When applied to 57 games on the Atari 2600 environment over 200 million frames, our algorithm achieved a new state-of-the-art performance.

We identify a fundamental source of error in Q-learning and other forms of dynamic programming with function approximation. Delusional bias arises when the approximation architecture limits the class of expressible greedy policies. Since standard Q-updates make globally uncoordinated action choices with respect to the expressible policy class, inconsistent or even conflicting Q-value estimates can result, leading to pathological behaviour such as over/under-estimation, instability and even divergence. To solve this problem, we introduce a new notion of policy consistency and define a local backup process that ensures global consistency through the use of information sets---sets that record constraints on policies consistent with backed-up Q-values. We prove that both the model-based and model-free algorithms using this backup remove delusional bias, yielding the first known algorithms that guarantee optimal results under general conditions. These algorithms furthermore only require polynomially many information sets (from a potentially exponential support). Finally, we suggest other practical heuristics for value-iteration and Q-learning that attempt to reduce delusional bias.

The design of a reward function often poses a major practical challenge to real-world applications of reinforcement learning. Approaches such as inverse reinforcement learning attempt to overcome this challenge, but require expert demonstrations, which can be difficult or expensive to obtain in practice. We propose inverse event-based control, which generalizes inverse reinforcement learning methods to cases where full demonstrations are not needed, such as when only samples of desired goal states are available. Our method is grounded in an alternative perspective on control and reinforcement learning, where an agent's goal is to maximize the probability that one or more events will happen at some point in the future, rather than maximizing cumulative rewards. We demonstrate the effectiveness of our methods on continuous control tasks, with a focus on high-dimensional observations like images where rewards are hard or even impossible to specify.

We study a safe reinforcement learning problem in which the constraints are defined as the expected cost over finite-length trajectories. We propose a constrained cross-entropy-based method to solve this problem. The method explicitly tracks its performance with respect to constraint satisfaction and thus is well-suited for safety-critical applications. We show that the asymptotic behavior of the proposed algorithm can be almost-surely described by that of an ordinary differential equation. Then we give sufficient conditions on the properties of this differential equation to guarantee the convergence of the proposed algorithm. At last, we show with simulation experiments that the proposed algorithm can effectively learn feasible policies without assumptions on the feasibility of initial policies, even with non-Markovian objective functions and constraint functions.

Learning to cooperate with friends and compete with foes is a key component of multi-agent reinforcement learning. Typically to do so, one requires access to either a model of or interaction with the other agent(s). Here we show how to learn effective strategies for cooperation and competition in an asymmetric information game with no such model or interaction. Our approach is to encourage an agent to reveal or hide their intentions using an information-theoretic regularizer. We consider both the mutual information between goal and action given state, as well as the mutual information between goal and state. We show how to stochastically optimize these regularizers in a way that is easy to integrate with policy gradient reinforcement learning. Finally, we demonstrate that cooperative (competitive) policies learned with our approach lead to more (less) reward for a second agent in two simple asymmetric information games.

Groups of humans are often able to find ways to cooperate with one another in complex, temporally extended social dilemmas. Models based on behavioral economics are only able to explain this phenomenon for unrealistic stateless matrix games. Recently, multi-agent reinforcement learning has been applied to generalize social dilemma problems to temporally and spatially extended Markov games. However, this has not yet generated an agent that learns to cooperate in social dilemmas as humans do. A key insight is that many, but not all, human individuals have inequity averse social preferences. This promotes a particular resolution of the matrix game social dilemma wherein inequity-averse individuals are personally pro-social and punish defectors. Here we extend this idea to Markov games and show that it promotes cooperation in several types of sequential social dilemma, via a profitable interaction with policy learnability. In particular, we find that inequity aversion improves temporal credit assignment for the important class of intertemporal social dilemmas. These results help explain how large-scale cooperation may emerge and persist.

Variational inference with α-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using α-divergences (with positive α values) is their mass-covering property. However, estimating and optimizing α-divergences require to use importance sampling, which could have extremely large or infinite variances due to heavy tails of importance weights. In this paper, we propose a new class of tail-adaptive f-divergences that adaptively change the convex function f with the tail of the importance weights, in a way that theoretically guarantee finite moments, while simultaneously achieving mass-covering properties. We test our methods on Bayesian neural networks, as well as deep reinforcement learning in which our method is applied to improve a recent soft actor-critic (SAC) algorithm (Haarnoja et al., 2018). Our results show that our approach yields significant advantages compared with existing methods based on classical KL and α-divergences.

We consider the off-policy estimation problem of estimating the expected reward of a target policy using samples collected by a different behavior policy. Importance sampling (IS) has been a key technique to derive (nearly) unbiased estimators, but is known to suffer from an excessively high variance in long-horizon problems. In the extreme case of in infinite-horizon problems, the variance of an IS-based estimator may even be unbounded. In this paper, we propose a new off-policy estimation method that applies IS directly on the stationary state-visitation distributions to avoid the exploding variance issue faced by existing estimators.Our key contribution is a novel approach to estimating the density ratio of two stationary distributions, with trajectories sampled from only the behavior distribution. We develop a mini-max loss function for the estimation problem, and derive a closed-form solution for the case of RKHS. We support our method with both theoretical and empirical analyses.