Guy Lever

Tuomas Haarnoja, Ben Moran, Guy Lever et al. · deepmind

We investigate whether Deep Reinforcement Learning (Deep RL) is able to synthesize sophisticated and safe movement skills for a low-cost, miniature humanoid robot that can be composed into complex behavioral strategies in dynamic environments. We used Deep RL to train a humanoid robot with 20 actuated joints to play a simplified one-versus-one (1v1) soccer game. The resulting agent exhibits robust and dynamic movement skills such as rapid fall recovery, walking, turning, kicking and more; and it transitions between them in a smooth, stable, and efficient manner. The agent's locomotion and tactical behavior adapts to specific game contexts in a way that would be impractical to manually design. The agent also developed a basic strategic understanding of the game, and learned, for instance, to anticipate ball movements and to block opponent shots. Our agent was trained in simulation and transferred to real robots zero-shot. We found that a combination of sufficiently high-frequency control, targeted dynamics randomization, and perturbations during training in simulation enabled good-quality transfer. Although the robots are inherently fragile, basic regularization of the behavior during training led the robots to learn safe and effective movements while still performing in a dynamic and agile way -- well beyond what is intuitively expected from the robot. Indeed, in experiments, they walked 181% faster, turned 302% faster, took 63% less time to get up, and kicked a ball 34% faster than a scripted baseline, while efficiently combining the skills to achieve the longer term objectives.

Dhruva Tirumala, Thomas Lampe, Jose Enrique Chen et al. · deepmind

Replaying data is a principal mechanism underlying the stability and data efficiency of off-policy reinforcement learning (RL). We present an effective yet simple framework to extend the use of replays across multiple experiments, minimally adapting the RL workflow for sizeable improvements in controller performance and research iteration times. At its core, Replay Across Experiments (RaE) involves reusing experience from previous experiments to improve exploration and bootstrap learning while reducing required changes to a minimum in comparison to prior work. We empirically show benefits across a number of RL algorithms and challenging control domains spanning both locomotion and manipulation, including hard exploration tasks from egocentric vision. Through comprehensive ablations, we demonstrate robustness to the quality and amount of data available and various hyperparameter choices. Finally, we discuss how our approach can be applied more broadly across research life cycles and can increase resilience by reloading data across random seeds or hyperparameter variations.

Ian Gemp, Thomas Anthony, Yoram Bachrach et al. · deepmind

The Game Theory & Multi-Agent team at DeepMind studies several aspects of multi-agent learning ranging from computing approximations to fundamental concepts in game theory to simulating social dilemmas in rich spatial environments and training 3-d humanoids in difficult team coordination tasks. A signature aim of our group is to use the resources and expertise made available to us at DeepMind in deep reinforcement learning to explore multi-agent systems in complex environments and use these benchmarks to advance our understanding. Here, we summarise the recent work of our team and present a taxonomy that we feel highlights many important open challenges in multi-agent research.

Dhruva Tirumala, Markus Wulfmeier, Ben Moran et al. · deepmind

We apply multi-agent deep reinforcement learning (RL) to train end-to-end robot soccer policies with fully onboard computation and sensing via egocentric RGB vision. This setting reflects many challenges of real-world robotics, including active perception, agile full-body control, and long-horizon planning in a dynamic, partially-observable, multi-agent domain. We rely on large-scale, simulation-based data generation to obtain complex behaviors from egocentric vision which can be successfully transferred to physical robots using low-cost sensors. To achieve adequate visual realism, our simulation combines rigid-body physics with learned, realistic rendering via multiple Neural Radiance Fields (NeRFs). We combine teacher-based multi-agent RL and cross-experiment data reuse to enable the discovery of sophisticated soccer strategies. We analyze active-perception behaviors including object tracking and ball seeking that emerge when simply optimizing perception-agnostic soccer play. The agents display equivalent levels of performance and agility as policies with access to privileged, ground-truth state. To our knowledge, this paper constitutes a first demonstration of end-to-end training for multi-agent robot soccer, mapping raw pixel observations to joint-level actions, that can be deployed in the real world. Videos of the game-play and analyses can be seen on our website https://sites.google.com/view/vision-soccer .

Siqi Liu, Guy Lever, Zhe Wang et al.

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 defined 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.

Tom Eccles, Yoram Bachrach, Guy Lever et al.

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 communication 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.

Paul Muller, Shayegan Omidshafiei, Mark Rowland et al.

This paper investigates a population-based training regime based on game-theoretic principles called Policy-Spaced Response Oracles (PSRO). PSRO is general in the sense that it (1) encompasses well-known algorithms such as fictitious play and double oracle as special cases, and (2) in principle applies to general-sum, many-player games. Despite this, prior studies of PSRO have been focused on two-player zero-sum games, a regime wherein Nash equilibria are tractably computable. In moving from two-player zero-sum games to more general settings, computation of Nash equilibria quickly becomes infeasible. Here, we extend the theoretical underpinnings of PSRO by considering an alternative solution concept, $α$-Rank, which is unique (thus faces no equilibrium selection issues, unlike Nash) and applies readily to general-sum, many-player settings. We establish convergence guarantees in several games classes, and identify links between Nash equilibria and $α$-Rank. We demonstrate the competitive performance of $α$-Rank-based PSRO against an exact Nash solver-based PSRO in 2-player Kuhn and Leduc Poker. We then go beyond the reach of prior PSRO applications by considering 3- to 5-player poker games, yielding instances where $α$-Rank achieves faster convergence than approximate Nash solvers, thus establishing it as a favorable general games solver. We also carry out an initial empirical validation in MuJoCo soccer, illustrating the feasibility of the proposed approach in another complex domain.

Siqi Liu, Guy Lever, Josh Merel et al.

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 with 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.

Max Jaderberg, Wojciech M. Czarnecki, Iain Dunning et al.

Recent progress in artificial intelligence through reinforcement learning (RL) has shown great success on increasingly complex single-agent environments and two-player turn-based games. However, the real-world contains multiple agents, each learning and acting independently to cooperate and compete with other agents, and environments reflecting this degree of complexity remain an open challenge. In this work, we demonstrate for the first time that an agent can achieve human-level in a popular 3D multiplayer first-person video game, Quake III Arena Capture the Flag, using only pixels and game points as input. These results were achieved by a novel two-tier optimisation process in which a population of independent RL agents are trained concurrently from thousands of parallel matches with agents playing in teams together and against each other on randomly generated environments. Each agent in the population learns its own internal reward signal to complement the sparse delayed reward from winning, and selects actions using a novel temporally hierarchical representation that enables the agent to reason at multiple timescales. During game-play, these agents display human-like behaviours such as navigating, following, and defending based on a rich learned representation that is shown to encode high-level game knowledge. In an extensive tournament-style evaluation the trained agents exceeded the win-rate of strong human players both as teammates and opponents, and proved far stronger than existing state-of-the-art agents. These results demonstrate a significant jump in the capabilities of artificial agents, bringing us closer to the goal of human-level intelligence.

Peter Sunehag, Guy Lever, Audrunas Gruslys et al.

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 decentralized 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.

Aleksandar Botev, Guy Lever, David Barber

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 Nesterov's accelerated gradient method, lending a new intuitive interpretation to the latter algorithm. We show that a new algorithm, which we term Regularised Gradient Descent, can converge more quickly than either Nesterov's algorithm or the classical momentum algorithm.

Thomas Furmston, Guy Lever

Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newton's 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.

Steffen Grunewalder, Guy Lever, Luca Baldassarre et al.

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 makes 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.

Steffen Grünewälder, Guy Lever, Luca Baldassarre et al.

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, providing 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.