Gregory Farquhar

Matthew Thomas Jackson, Minqi Jiang, Jack Parker-Holder et al. · oxford

The past decade has seen vast progress in deep reinforcement learning (RL) on the back of algorithms manually designed by human researchers. Recently, it has been shown that it is possible to meta-learn update rules, with the hope of discovering algorithms that can perform well on a wide range of RL tasks. Despite impressive initial results from algorithms such as Learned Policy Gradient (LPG), there remains a generalization gap when these algorithms are applied to unseen environments. In this work, we examine how characteristics of the meta-training distribution impact the generalization performance of these algorithms. Motivated by this analysis and building on ideas from Unsupervised Environment Design (UED), we propose a novel approach for automatically generating curricula to maximize the regret of a meta-learned optimizer, in addition to a novel approximation of regret, which we name algorithmic regret (AR). The result is our method, General RL Optimizers Obtained Via Environment Design (GROOVE). In a series of experiments, we show that GROOVE achieves superior generalization to LPG, and evaluate AR against baseline metrics from UED, identifying it as a critical component of environment design in this setting. We believe this approach is a step towards the discovery of truly general RL algorithms, capable of solving a wide range of real-world environments.

Risto Vuorio, Jacob Beck, Shimon Whiteson et al.

Meta-gradients provide a general approach for optimizing the meta-parameters of reinforcement learning (RL) algorithms. Estimation of meta-gradients is central to the performance of these meta-algorithms, and has been studied in the setting of MAML-style short-horizon meta-RL problems. In this context, prior work has investigated the estimation of the Hessian of the RL objective, as well as tackling the problem of credit assignment to pre-adaptation behavior by making a sampling correction. However, we show that Hessian estimation, implemented for example by DiCE and its variants, always adds bias and can also add variance to meta-gradient estimation. Meanwhile, meta-gradient estimation has been studied less in the important long-horizon setting, where backpropagation through the full inner optimization trajectories is not feasible. We study the bias and variance tradeoff arising from truncated backpropagation and sampling correction, and additionally compare to evolution strategies, which is a recently popular alternative strategy to long-horizon meta-learning. While prior work implicitly chooses points in this bias-variance space, we disentangle the sources of bias and variance and present an empirical study that relates existing estimators to each other.

Mikayel Samvelyan, Tabish Rashid, Christian Schroeder de Witt et al.

In the last few years, deep multi-agent reinforcement learning (RL) has become a highly active area of research. A particularly challenging class of problems in this area is partially observable, cooperative, multi-agent learning, in which teams of agents must learn to coordinate their behaviour while conditioning only on their private observations. This is an attractive research area since such problems are relevant to a large number of real-world systems and are also more amenable to evaluation than general-sum problems. Standardised environments such as the ALE and MuJoCo have allowed single-agent RL to move beyond toy domains, such as grid worlds. However, there is no comparable benchmark for cooperative multi-agent RL. As a result, most papers in this field use one-off toy problems, making it difficult to measure real progress. In this paper, we propose the StarCraft Multi-Agent Challenge (SMAC) as a benchmark problem to fill this gap. SMAC is based on the popular real-time strategy game StarCraft II and focuses on micromanagement challenges where each unit is controlled by an independent agent that must act based on local observations. We offer a diverse set of challenge maps and recommendations for best practices in benchmarking and evaluations. We also open-source a deep multi-agent RL learning framework including state-of-the-art algorithms. We believe that SMAC can provide a standard benchmark environment for years to come. Videos of our best agents for several SMAC scenarios are available at: https://youtu.be/VZ7zmQ_obZ0.

Jakob Foerster, Gregory Farquhar, Maruan Al-Shedivat et al.

The score function estimator is widely used for estimating gradients of stochastic objectives in stochastic computation graphs (SCG), eg, in reinforcement learning and meta-learning. While deriving the first-order gradient estimators by differentiating a surrogate loss (SL) objective is computationally and conceptually simple, using the same approach for higher-order derivatives is more challenging. Firstly, analytically deriving and implementing such estimators is laborious and not compliant with automatic differentiation. Secondly, repeatedly applying SL to construct new objectives for each order derivative involves increasingly cumbersome graph manipulations. Lastly, to match the first-order gradient under differentiation, SL treats part of the cost as a fixed sample, which we show leads to missing and wrong terms for estimators of higher-order derivatives. To address all these shortcomings in a unified way, we introduce DiCE, which provides a single objective that can be differentiated repeatedly, generating correct estimators of derivatives of any order in SCGs. Unlike SL, DiCE relies on automatic differentiation for performing the requisite graph manipulations. We verify the correctness of DiCE both through a proof and numerical evaluation of the DiCE derivative estimates. We also use DiCE to propose and evaluate a novel approach for multi-agent learning. Our code is available at https://www.github.com/alshedivat/lola.

Dan A. Calian, Gregory Farquhar, Iurii Kemaev et al.

The quality of foundation models depends heavily on their training data. Consequently, great efforts have been put into dataset curation. Yet most approaches rely on manual tuning of coarse-grained mixtures of large buckets of data, or filtering by hand-crafted heuristics. An approach that is ultimately more scalable (let alone more satisfying) is to \emph{learn} which data is actually valuable for training. This type of meta-learning could allow more sophisticated, fine-grained, and effective curation. Our proposed \emph{DataRater} is an instance of this idea. It estimates the value of training on any particular data point. This is done by meta-learning using `meta-gradients', with the objective of improving training efficiency on held out data. In extensive experiments across a range of model scales and datasets, we find that using our DataRater to filter data is highly effective, resulting in significantly improved compute efficiency.

Iurii Kemaev, Dan A Calian, Luisa M Zintgraf et al.

Gradient-based bilevel optimisation is a powerful technique with applications in hyperparameter optimisation, task adaptation, algorithm discovery, meta-learning more broadly, and beyond. It often requires differentiating through the gradient-based optimisation itself, leading to "gradient-of-a-gradient" calculations with computationally expensive second-order and mixed derivatives. While modern automatic differentiation libraries provide a convenient way to write programs for calculating these derivatives, they oftentimes cannot fully exploit the specific structure of these problems out-of-the-box, leading to suboptimal performance. In this paper, we analyse such cases and propose Mixed-Flow Meta-Gradients, or MixFlow-MG -- a practical algorithm that uses mixed-mode differentiation to construct more efficient and scalable computational graphs yielding over 10x memory and up to 25% wall-clock time improvements over standard implementations in modern meta-learning setups.

Angelos Filos, Eszter Vértes, Zita Marinho et al.

Using a model of the environment and a value function, an agent can construct many estimates of a state's value, by unrolling the model for different lengths and bootstrapping with its value function. Our key insight is that one can treat this set of value estimates as a type of ensemble, which we call an \emph{implicit value ensemble} (IVE). Consequently, the discrepancy between these estimates can be used as a proxy for the agent's epistemic uncertainty; we term this signal \emph{model-value inconsistency} or \emph{self-inconsistency} for short. Unlike prior work which estimates uncertainty by training an ensemble of many models and/or value functions, this approach requires only the single model and value function which are already being learned in most model-based reinforcement learning algorithms. We provide empirical evidence in both tabular and function approximation settings from pixels that self-inconsistency is useful (i) as a signal for exploration, (ii) for acting safely under distribution shifts, and (iii) for robustifying value-based planning with a learned model.

Gregory Farquhar, Kate Baumli, Zita Marinho et al.

Learned models of the environment provide reinforcement learning (RL) agents with flexible ways of making predictions about the environment. In particular, models enable planning, i.e. using more computation to improve value functions or policies, without requiring additional environment interactions. In this work, we investigate a way of augmenting model-based RL, by additionally encouraging a learned model and value function to be jointly \emph{self-consistent}. Our approach differs from classic planning methods such as Dyna, which only update values to be consistent with the model. We propose multiple self-consistency updates, evaluate these in both tabular and function approximation settings, and find that, with appropriate choices, self-consistency helps both policy evaluation and control.

Christopher Grimm, André Barreto, Gregory Farquhar et al.

One of the main challenges in model-based reinforcement learning (RL) is to decide which aspects of the environment should be modeled. The value-equivalence (VE) principle proposes a simple answer to this question: a model should capture the aspects of the environment that are relevant for value-based planning. Technically, VE distinguishes models based on a set of policies and a set of functions: a model is said to be VE to the environment if the Bellman operators it induces for the policies yield the correct result when applied to the functions. As the number of policies and functions increase, the set of VE models shrinks, eventually collapsing to a single point corresponding to a perfect model. A fundamental question underlying the VE principle is thus how to select the smallest sets of policies and functions that are sufficient for planning. In this paper we take an important step towards answering this question. We start by generalizing the concept of VE to order-$k$ counterparts defined with respect to $k$ applications of the Bellman operator. This leads to a family of VE classes that increase in size as $k \rightarrow \infty$. In the limit, all functions become value functions, and we have a special instantiation of VE which we call proper VE or simply PVE. Unlike VE, the PVE class may contain multiple models even in the limit when all value functions are used. Crucially, all these models are sufficient for planning, meaning that they will yield an optimal policy despite the fact that they may ignore many aspects of the environment. We construct a loss function for learning PVE models and argue that popular algorithms such as MuZero can be understood as minimizing an upper bound for this loss. We leverage this connection to propose a modification to MuZero and show that it can lead to improved performance in practice.

Angelos Filos, Clare Lyle, Yarin Gal et al.

We study reinforcement learning (RL) with no-reward demonstrations, a setting in which an RL agent has access to additional data from the interaction of other agents with the same environment. However, it has no access to the rewards or goals of these agents, and their objectives and levels of expertise may vary widely. These assumptions are common in multi-agent settings, such as autonomous driving. To effectively use this data, we turn to the framework of successor features. This allows us to disentangle shared features and dynamics of the environment from agent-specific rewards and policies. We propose a multi-task inverse reinforcement learning (IRL) algorithm, called \emph{inverse temporal difference learning} (ITD), that learns shared state features, alongside per-agent successor features and preference vectors, purely from demonstrations without reward labels. We further show how to seamlessly integrate ITD with learning from online environment interactions, arriving at a novel algorithm for reinforcement learning with demonstrations, called $ΨΦ$-learning (pronounced `Sci-Fi'). We provide empirical evidence for the effectiveness of $ΨΦ$-learning as a method for improving RL, IRL, imitation, and few-shot transfer, and derive worst-case bounds for its performance in zero-shot transfer to new tasks.

Tabish Rashid, Gregory Farquhar, Bei Peng et al.

QMIX is a popular $Q$-learning algorithm for cooperative MARL in the centralised training and decentralised execution paradigm. In order to enable easy decentralisation, QMIX restricts the joint action $Q$-values it can represent to be a monotonic mixing of each agent's utilities. However, this restriction prevents it from representing value functions in which an agent's ordering over its actions can depend on other agents' actions. To analyse this representational limitation, we first formalise the objective QMIX optimises, which allows us to view QMIX as an operator that first computes the $Q$-learning targets and then projects them into the space representable by QMIX. This projection returns a representable $Q$-value that minimises the unweighted squared error across all joint actions. We show in particular that this projection can fail to recover the optimal policy even with access to $Q^*$, which primarily stems from the equal weighting placed on each joint action. We rectify this by introducing a weighting into the projection, in order to place more importance on the better joint actions. We propose two weighting schemes and prove that they recover the correct maximal action for any joint action $Q$-values, and therefore for $Q^*$ as well. Based on our analysis and results in the tabular setting, we introduce two scalable versions of our algorithm, Centrally-Weighted (CW) QMIX and Optimistically-Weighted (OW) QMIX and demonstrate improved performance on both predator-prey and challenging multi-agent StarCraft benchmark tasks.

Maximilian Igl, Gregory Farquhar, Jelena Luketina et al.

Non-stationarity can arise in Reinforcement Learning (RL) even in stationary environments. For example, most RL algorithms collect new data throughout training, using a non-stationary behaviour policy. Due to the transience of this non-stationarity, it is often not explicitly addressed in deep RL and a single neural network is continually updated. However, we find evidence that neural networks exhibit a memory effect where these transient non-stationarities can permanently impact the latent representation and adversely affect generalisation performance. Consequently, to improve generalisation of deep RL agents, we propose Iterated Relearning (ITER). ITER augments standard RL training by repeated knowledge transfer of the current policy into a freshly initialised network, which thereby experiences less non-stationarity during training. Experimentally, we show that ITER improves performance on the challenging generalisation benchmarks ProcGen and Multiroom.

Tabish Rashid, Mikayel Samvelyan, Christian Schroeder de Witt et al.

In many real-world settings, a team of agents must coordinate its behaviour while acting in a decentralised fashion. At the same time, it is often possible to train the agents in a centralised fashion where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a mixing network that estimates joint action-values as a monotonic combination of per-agent values. We structurally enforce that the joint-action value is monotonic in the per-agent values, through the use of non-negative weights in the mixing network, which guarantees consistency between the centralised and decentralised policies. To evaluate the performance of QMIX, we propose the StarCraft Multi-Agent Challenge (SMAC) as a new benchmark for deep multi-agent reinforcement learning. We evaluate QMIX on a challenging set of SMAC scenarios and show that it significantly outperforms existing multi-agent reinforcement learning methods.

Gregory Farquhar, Shimon Whiteson, Jakob Foerster

Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance unbiased estimators of derivatives at any order. Our objective is compatible with arbitrary advantage estimators, which allows the control of the bias and variance of any-order derivatives when using function approximation. Furthermore, we propose a method to trade off bias and variance of higher order derivatives by discounting the impact of more distant causal dependencies. We demonstrate the correctness and utility of our objective in analytically tractable MDPs and in meta-reinforcement-learning for continuous control.

Gregory Farquhar, Laura Gustafson, Zeming Lin et al.

In complex tasks, such as those with large combinatorial action spaces, random exploration may be too inefficient to achieve meaningful learning progress. In this work, we use a curriculum of progressively growing action spaces to accelerate learning. We assume the environment is out of our control, but that the agent may set an internal curriculum by initially restricting its action space. Our approach uses off-policy reinforcement learning to estimate optimal value functions for multiple action spaces simultaneously and efficiently transfers data, value estimates, and state representations from restricted action spaces to the full task. We show the efficacy of our approach in proof-of-concept control tasks and on challenging large-scale StarCraft micromanagement tasks with large, multi-agent action spaces.

Jelena Luketina, Nantas Nardelli, Gregory Farquhar et al.

To be successful in real-world tasks, Reinforcement Learning (RL) needs to exploit the compositional, relational, and hierarchical structure of the world, and learn to transfer it to the task at hand. Recent advances in representation learning for language make it possible to build models that acquire world knowledge from text corpora and integrate this knowledge into downstream decision making problems. We thus argue that the time is right to investigate a tight integration of natural language understanding into RL in particular. We survey the state of the field, including work on instruction following, text games, and learning from textual domain knowledge. Finally, we call for the development of new environments as well as further investigation into the potential uses of recent Natural Language Processing (NLP) techniques for such tasks.

Christian A. Schroeder de Witt, Jakob N. Foerster, Gregory Farquhar et al.

Cooperative multi-agent reinforcement learning often requires decentralised policies, which severely limit the agents' ability to coordinate their behaviour. In this paper, we show that common knowledge between agents allows for complex decentralised coordination. Common knowledge arises naturally in a large number of decentralised cooperative multi-agent tasks, for example, when agents can reconstruct parts of each others' observations. Since agents an independently agree on their common knowledge, they can execute complex coordinated policies that condition on this knowledge in a fully decentralised fashion. We propose multi-agent common knowledge reinforcement learning (MACKRL), a novel stochastic actor-critic algorithm that learns a hierarchical policy tree. Higher levels in the hierarchy coordinate groups of agents by conditioning on their common knowledge, or delegate to lower levels with smaller subgroups but potentially richer common knowledge. The entire policy tree can be executed in a fully decentralised fashion. As the lowest policy tree level consists of independent policies for each agent, MACKRL reduces to independently learnt decentralised policies as a special case. We demonstrate that our method can exploit common knowledge for superior performance on complex decentralised coordination tasks, including a stochastic matrix game and challenging problems in StarCraft II unit micromanagement.

Tabish Rashid, Mikayel Samvelyan, Christian Schroeder de Witt et al.

In many real-world settings, a team of agents must coordinate their behaviour while acting in a decentralised way. At the same time, it is often possible to train the agents in a centralised fashion in a simulated or laboratory setting, where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a network that estimates joint action-values as a complex non-linear combination of per-agent values that condition only on local observations. We structurally enforce that the joint-action value is monotonic in the per-agent values, which allows tractable maximisation of the joint action-value in off-policy learning, and guarantees consistency between the centralised and decentralised policies. We evaluate QMIX on a challenging set of StarCraft II micromanagement tasks, and show that QMIX significantly outperforms existing value-based multi-agent reinforcement learning methods.

Gregory Farquhar, Tim Rocktäschel, Maximilian Igl et al.

Combining deep model-free reinforcement learning with on-line planning is a promising approach to building on the successes of deep RL. On-line planning with look-ahead trees has proven successful in environments where transition models are known a priori. However, in complex environments where transition models need to be learned from data, the deficiencies of learned models have limited their utility for planning. To address these challenges, we propose TreeQN, a differentiable, recursive, tree-structured model that serves as a drop-in replacement for any value function network in deep RL with discrete actions. TreeQN dynamically constructs a tree by recursively applying a transition model in a learned abstract state space and then aggregating predicted rewards and state-values using a tree backup to estimate Q-values. We also propose ATreeC, an actor-critic variant that augments TreeQN with a softmax layer to form a stochastic policy network. Both approaches are trained end-to-end, such that the learned model is optimised for its actual use in the tree. We show that TreeQN and ATreeC outperform n-step DQN and A2C on a box-pushing task, as well as n-step DQN and value prediction networks (Oh et al. 2017) on multiple Atari games. Furthermore, we present ablation studies that demonstrate the effect of different auxiliary losses on learning transition models.

Jakob Foerster, Gregory Farquhar, Triantafyllos Afouras et al.

Cooperative multi-agent systems can be naturally used to model many real world problems, such as network packet routing and the coordination of autonomous vehicles. There is a great need for new reinforcement learning methods that can efficiently learn decentralised policies for such systems. To this end, we propose a new multi-agent actor-critic method called counterfactual multi-agent (COMA) policy gradients. COMA uses a centralised critic to estimate the Q-function and decentralised actors to optimise the agents' policies. In addition, to address the challenges of multi-agent credit assignment, it uses a counterfactual baseline that marginalises out a single agent's action, while keeping the other agents' actions fixed. COMA also uses a critic representation that allows the counterfactual baseline to be computed efficiently in a single forward pass. We evaluate COMA in the testbed of StarCraft unit micromanagement, using a decentralised variant with significant partial observability. COMA significantly improves average performance over other multi-agent actor-critic methods in this setting, and the best performing agents are competitive with state-of-the-art centralised controllers that get access to the full state.

Jakob Foerster, Nantas Nardelli, Gregory Farquhar et al.

Many real-world problems, such as network packet routing and urban traffic control, are naturally modeled as multi-agent reinforcement learning (RL) problems. However, existing multi-agent RL methods typically scale poorly in the problem size. Therefore, a key challenge is to translate the success of deep learning on single-agent RL to the multi-agent setting. A major stumbling block is that independent Q-learning, the most popular multi-agent RL method, introduces nonstationarity that makes it incompatible with the experience replay memory on which deep Q-learning relies. This paper proposes two methods that address this problem: 1) using a multi-agent variant of importance sampling to naturally decay obsolete data and 2) conditioning each agent's value function on a fingerprint that disambiguates the age of the data sampled from the replay memory. Results on a challenging decentralised variant of StarCraft unit micromanagement confirm that these methods enable the successful combination of experience replay with multi-agent RL.