Intelligent behaviour in the physical world exhibits structure at multiple spatial and temporal scales. Although movements are ultimately executed at the level of instantaneous muscle tensions or joint torques, they must be selected to serve goals de
fined on much longer timescales, and in terms of relations that extend far beyond the body itself, ultimately involving coordination with other agents. Recent research in artificial intelligence has shown the promise of learning-based approaches to the respective problems of complex movement, longer-term planning and multi-agent coordination. However, there is limited research aimed at their integration. We study this problem by training teams of physically simulated humanoid avatars to play football in a realistic virtual environment. We develop a method that combines imitation learning, single- and multi-agent reinforcement learning and population-based training, and makes use of transferable representations of behaviour for decision making at different levels of abstraction. In a sequence of stages, players first learn to control a fully articulated body to perform realistic, human-like movements such as running and turning; they then acquire mid-level football skills such as dribbling and shooting; finally, they develop awareness of others and play as a team, bridging the gap between low-level motor control at a timescale of milliseconds, and coordinated goal-directed behaviour as a team at the timescale of tens of seconds. We investigate the emergence of behaviours at different levels of abstraction, as well as the representations that underlie these behaviours using several analysis techniques, including statistics from real-world sports analytics. Our work constitutes a complete demonstration of integrated decision-making at multiple scales in a physically embodied multi-agent setting. See project video at https://youtu.be/KHMwq9pv7mg.
We study the problem of emergent communication, in which language arises because speakers and listeners must communicate information in order to solve tasks. In temporally extended reinforcement learning domains, it has proved hard to learn such comm
unication without centralized training of agents, due in part to a difficult joint exploration problem. We introduce inductive biases for positive signalling and positive listening, which ease this problem. In a simple one-step environment, we demonstrate how these biases ease the learning problem. We also apply our methods to a more extended environment, showing that agents with these inductive biases achieve better performance, and analyse the resulting communication protocols.
We study the emergence of cooperative behaviors in reinforcement learning agents by introducing a challenging competitive multi-agent soccer environment with continuous simulated physics. We demonstrate that decentralized, population-based training w
ith co-play can lead to a progression in agents behaviors: from random, to simple ball chasing, and finally showing evidence of cooperation. Our study highlights several of the challenges encountered in large scale multi-agent training in continuous control. In particular, we demonstrate that the automatic optimization of simple shaping rewards, not themselves conducive to co-operative behavior, can lead to long-horizon team behavior. We further apply an evaluation scheme, grounded by game theoretic principals, that can assess agent performance in the absence of pre-defined evaluation tasks or human baselines.
We study the problem of cooperative multi-agent reinforcement learning with a single joint reward signal. This class of learning problems is difficult because of the often large combined action and observation spaces. In the fully centralized and dec
entralized approaches, we find the problem of spurious rewards and a phenomenon we call the lazy agent problem, which arises due to partial observability. We address these problems by training individual agents with a novel value decomposition network architecture, which learns to decompose the team value function into agent-wise value functions. We perform an experimental evaluation across a range of partially-observable multi-agent domains and show that learning such value-decompositions leads to superior results, in particular when combined with weight sharing, role information and information channels.
We present a unifying framework for adapting the update direction in gradient-based iterative optimization methods. As natural special cases we re-derive classical momentum and Nesterovs accelerated gradient method, lending a new intuitive interpreta
tion to the latter algorithm. We show that a new algorithm, which we term Regularised Gradient Descent, can converge more quickly than either Nesterovs algorithm or the classical momentum algorithm.
Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newtons method, such as a fast rate of convergence, whilst alleviating its drawbacks, such as computationally expensive calculation or estimation of the
inverse Hessian. In this work we investigate approximate Newton methods for policy optimization in Markov Decision Processes (MDPs). We first analyse the structure of the Hessian of the objective function for MDPs. We show that, like the gradient, the Hessian exhibits useful structure in the context of MDPs and we use this analysis to motivate two Gauss-Newton Methods for MDPs. Like the Gauss-Newton method for non-linear least squares, these methods involve approximating the Hessian by ignoring certain terms in the Hessian which are difficult to estimate. The approximate Hessians possess desirable properties, such as negative definiteness, and we demonstrate several important performance guarantees including guaranteed ascent directions, invariance to affine transformation of the parameter space, and convergence guarantees. We finally provide a unifying perspective of key policy search algorithms, demonstrating that our second Gauss-Newton algorithm is closely related to both the EM-algorithm and natural gradient ascent applied to MDPs, but performs significantly better in practice on a range of challenging domains.
Recently two approximate Newton methods were proposed for the optimisation of Markov Decision Processes. While these methods were shown to have desirable properties, such as a guarantee that the preconditioner is negative-semidefinite when the policy
is $log$-concave with respect to the policy parameters, and were demonstrated to have strong empirical performance in challenging domains, such as the game of Tetris, no convergence analysis was provided. The purpose of this paper is to provide such an analysis. We start by providing a detailed analysis of the Hessian of a Markov Decision Process, which is formed of a negative-semidefinite component, a positive-semidefinite component and a remainder term. The first part of our analysis details how the negative-semidefinite and positive-semidefinite components relate to each other, and how these two terms contribute to the Hessian. The next part of our analysis shows that under certain conditions, relating to the richness of the policy class, the remainder term in the Hessian vanishes in the vicinity of a local optimum. Finally, we bound the behaviour of this remainder term in terms of the mixing time of the Markov chain induced by the policy parameters, where this part of the analysis is applicable over the entire parameter space. Given this analysis of the Hessian we then provide our local convergence analysis of the approximate Newton framework.
We propose a new, nonparametric approach to learning and representing transition dynamics in Markov decision processes (MDPs), which can be combined easily with dynamic programming methods for policy optimisation and value estimation. This approach m
akes use of a recently developed representation of conditional distributions as emph{embeddings} in a reproducing kernel Hilbert space (RKHS). Such representations bypass the need for estimating transition probabilities or densities, and apply to any domain on which kernels can be defined. This avoids the need to calculate intractable integrals, since expectations are represented as RKHS inner products whose computation has linear complexity in the number of points used to represent the embedding. We provide guarantees for the proposed applications in MDPs: in the context of a value iteration algorithm, we prove convergence to either the optimal policy, or to the closest projection of the optimal policy in our model class (an RKHS), under reasonable assumptions. In experiments, we investigate a learning task in a typical classical control setting (the under-actuated pendulum), and on a navigation problem where only images from a sensor are observed. For policy optimisation we compare with least-squares policy iteration where a Gaussian process is used for value function estimation. For value estimation we also compare to the NPDP method. Our approach achieves better performance in all experiments.
We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings minimise, pro
viding an intuitive understanding of the embeddings and a justification for their use. Furthermore, the equivalence allows the application of vector-valued regression methods and results to the problem of learning conditional distributions. Using this link we derive a sparse version of the embedding by considering alternative formulations. Further, by applying convergence results for vector-valued regression to the embedding problem we derive minimax convergence rates which are O(log(n)/n) -- compared to current state of the art rates of O(n^{-1/4}) -- and are valid under milder and more intuitive assumptions. These minimax upper rates coincide with lower rates up to a logarithmic factor, showing that the embedding method achieves nearly optimal rates. We study our sparse embedding algorithm in a reinforcement learning task where the algorithm shows significant improvement in sparsity over an incomplete Cholesky decomposition.
