Théophane Weber

Nan Rosemary Ke, Silvia Chiappa, Jane Wang et al. · deepmind, mila

The fundamental challenge in causal induction is to infer the underlying graph structure given observational and/or interventional data. Most existing causal induction algorithms operate by generating candidate graphs and evaluating them using either score-based methods (including continuous optimization) or independence tests. In our work, we instead treat the inference process as a black box and design a neural network architecture that learns the mapping from both observational and interventional data to graph structures via supervised training on synthetic graphs. The learned model generalizes to new synthetic graphs, is robust to train-test distribution shifts, and achieves state-of-the-art performance on naturalistic graphs for low sample complexity.

Nan Rosemary Ke, Sara-Jane Dunn, Jorg Bornschein et al. · deepmind, mila

Accurately inferring Gene Regulatory Networks (GRNs) is a critical and challenging task in biology. GRNs model the activatory and inhibitory interactions between genes and are inherently causal in nature. To accurately identify GRNs, perturbational data is required. However, most GRN discovery methods only operate on observational data. Recent advances in neural network-based causal discovery methods have significantly improved causal discovery, including handling interventional data, improvements in performance and scalability. However, applying state-of-the-art (SOTA) causal discovery methods in biology poses challenges, such as noisy data and a large number of samples. Thus, adapting the causal discovery methods is necessary to handle these challenges. In this paper, we introduce DiscoGen, a neural network-based GRN discovery method that can denoise gene expression measurements and handle interventional data. We demonstrate that our model outperforms SOTA neural network-based causal discovery methods.

Pol Moreno, Adam R. Kosiorek, Heiko Strathmann et al. · deepmind

NeRF provides unparalleled fidelity of novel view synthesis: rendering a 3D scene from an arbitrary viewpoint. NeRF requires training on a large number of views that fully cover a scene, which limits its applicability. While these issues can be addressed by learning a prior over scenes in various forms, previous approaches have been either applied to overly simple scenes or struggling to render unobserved parts. We introduce Laser-NV: a generative model which achieves high modelling capacity, and which is based on a set-valued latent representation modelled by normalizing flows. Similarly to previous amortized approaches, Laser-NV learns structure from multiple scenes and is capable of fast, feed-forward inference from few views. To encourage higher rendering fidelity and consistency with observed views, Laser-NV further incorporates a geometry-informed attention mechanism over the observed views. Laser-NV further produces diverse and plausible completions of occluded parts of a scene while remaining consistent with observations. Laser-NV shows state-of-the-art novel-view synthesis quality when evaluated on ShapeNet and on a novel simulated City dataset, which features high uncertainty in the unobserved regions of the scene.

Peter C. Humphreys, Arthur Guez, Olivier Tieleman et al.

Effective decision making involves flexibly relating past experiences and relevant contextual information to a novel situation. In deep reinforcement learning (RL), the dominant paradigm is for an agent to amortise information that helps decision making into its network weights via gradient descent on training losses. Here, we pursue an alternative approach in which agents can utilise large-scale context sensitive database lookups to support their parametric computations. This allows agents to directly learn in an end-to-end manner to utilise relevant information to inform their outputs. In addition, new information can be attended to by the agent, without retraining, by simply augmenting the retrieval dataset. We study this approach for offline RL in 9x9 Go, a challenging game for which the vast combinatorial state space privileges generalisation over direct matching to past experiences. We leverage fast, approximate nearest neighbor techniques in order to retrieve relevant data from a set of tens of millions of expert demonstration states. Attending to this information provides a significant boost to prediction accuracy and game-play performance over simply using these demonstrations as training trajectories, providing a compelling demonstration of the value of large-scale retrieval in offline RL agents.

Jacob Walker, Eszter Vértes, Yazhe Li et al. · mila

State of the art reinforcement learning has enabled training agents on tasks of ever increasing complexity. However, the current paradigm tends to favor training agents from scratch on every new task or on collections of tasks with a view towards generalizing to novel task configurations. The former suffers from poor data efficiency while the latter is difficult when test tasks are out-of-distribution. Agents that can effectively transfer their knowledge about the world pose a potential solution to these issues. In this paper, we investigate transfer learning in the context of model-based agents. Specifically, we aim to understand when exactly environment models have an advantage and why. We find that a model-based approach outperforms controlled model-free baselines for transfer learning. Through ablations, we show that both the policy and dynamics model learnt through exploration matter for successful transfer. We demonstrate our results across three domains which vary in their requirements for transfer: in-distribution procedural (Crafter), in-distribution identical (RoboDesk), and out-of-distribution (Meta-World). Our results show that intrinsic exploration combined with environment models present a viable direction towards agents that are self-supervised and able to generalize to novel reward functions.

Andreea Deac, Théophane Weber, George Papamakarios

Deep reinforcement learning repeatedly succeeds in closed, well-defined domains such as games (Chess, Go, StarCraft). The next frontier is real-world scenarios, where setups are numerous and varied. For this, agents need to learn the underlying rules governing the environment, so as to robustly generalise to conditions that differ from those they were trained on. Model-based reinforcement learning algorithms, such as the highly successful MuZero, aim to accomplish this by learning a world model. However, leveraging a world model has not consistently shown greater generalisation capabilities compared to model-free alternatives. In this work, we propose improving the data efficiency and generalisation capabilities of MuZero by explicitly incorporating the symmetries of the environment in its world-model architecture. We prove that, so long as the neural networks used by MuZero are equivariant to a particular symmetry group acting on the environment, the entirety of MuZero's action-selection algorithm will also be equivariant to that group. We evaluate Equivariant MuZero on procedurally-generated MiniPacman and on Chaser from the ProcGen suite: training on a set of mazes, and then testing on unseen rotated versions, demonstrating the benefits of equivariance. Further, we verify that our performance improvements hold even when only some of the components of Equivariant MuZero obey strict equivariance, which highlights the robustness of our construction.

Ankesh Anand, Jacob Walker, Yazhe Li et al.

One of the key promises of model-based reinforcement learning is the ability to generalize using an internal model of the world to make predictions in novel environments and tasks. However, the generalization ability of model-based agents is not well understood because existing work has focused on model-free agents when benchmarking generalization. Here, we explicitly measure the generalization ability of model-based agents in comparison to their model-free counterparts. We focus our analysis on MuZero (Schrittwieser et al., 2020), a powerful model-based agent, and evaluate its performance on both procedural and task generalization. We identify three factors of procedural generalization -- planning, self-supervised representation learning, and procedural data diversity -- and show that by combining these techniques, we achieve state-of-the art generalization performance and data efficiency on Procgen (Cobbe et al., 2019). However, we find that these factors do not always provide the same benefits for the task generalization benchmarks in Meta-World (Yu et al., 2019), indicating that transfer remains a challenge and may require different approaches than procedural generalization. Overall, we suggest that building generalizable agents requires moving beyond the single-task, model-free paradigm and towards self-supervised model-based agents that are trained in rich, procedural, multi-task environments.

Matteo Hessel, Ivo Danihelka, Fabio Viola et al.

We propose a novel policy update that combines regularized policy optimization with model learning as an auxiliary loss. The update (henceforth Muesli) matches MuZero's state-of-the-art performance on Atari. Notably, Muesli does so without using deep search: it acts directly with a policy network and has computation speed comparable to model-free baselines. The Atari results are complemented by extensive ablations, and by additional results on continuous control and 9x9 Go.

David Raposo, Sam Ritter, Adam Santoro et al.

Since the earliest days of reinforcement learning, the workhorse method for assigning credit to actions over time has been temporal-difference (TD) learning, which propagates credit backward timestep-by-timestep. This approach suffers when delays between actions and rewards are long and when intervening unrelated events contribute variance to long-term returns. We propose state-associative (SA) learning, where the agent learns associations between states and arbitrarily distant future rewards, then propagates credit directly between the two. In this work, we use SA-learning to model the contribution of past states to the current reward. With this model we can predict each state's contribution to the far future, a quantity we call "synthetic returns". TD-learning can then be applied to select actions that maximize these synthetic returns (SRs). We demonstrate the effectiveness of augmenting agents with SRs across a range of tasks on which TD-learning alone fails. We show that the learned SRs are interpretable: they spike for states that occur after critical actions are taken. Finally, we show that our IMPALA-based SR agent solves Atari Skiing -- a game with a lengthy reward delay that posed a major hurdle to deep-RL agents -- 25 times faster than the published state-of-the-art.

Pol Moreno, Edward Hughes, Kevin R. McKee et al.

In multi-agent reinforcement learning, the problem of learning to act is particularly difficult because the policies of co-players may be heavily conditioned on information only observed by them. On the other hand, humans readily form beliefs about the knowledge possessed by their peers and leverage beliefs to inform decision-making. Such abilities underlie individual success in a wide range of Markov games, from bluffing in Poker to conditional cooperation in the Prisoner's Dilemma, to convention-building in Bridge. Classical methods are usually not applicable to complex domains due to the intractable nature of hierarchical beliefs (i.e. beliefs of other agents' beliefs). We propose a scalable method to approximate these belief structures using recursive deep generative models, and to use the belief models to obtain representations useful to acting in complex tasks. Our agents trained with belief models outperform model-free baselines with equivalent representational capacity using common training paradigms. We also show that higher-order belief models outperform agents with lower-order models.

Mihaela Rosca, Theophane Weber, Arthur Gretton et al.

How sensitive should machine learning models be to input changes? We tackle the question of model smoothness and show that it is a useful inductive bias which aids generalization, adversarial robustness, generative modeling and reinforcement learning. We explore current methods of imposing smoothness constraints and observe they lack the flexibility to adapt to new tasks, they don't account for data modalities, they interact with losses, architectures and optimization in ways not yet fully understood. We conclude that new advances in the field are hinging on finding ways to incorporate data, tasks and learning into our definitions of smoothness.

Thomas Mesnard, Théophane Weber, Fabio Viola et al.

Credit assignment in reinforcement learning is the problem of measuring an action's influence on future rewards. In particular, this requires separating skill from luck, i.e. disentangling the effect of an action on rewards from that of external factors and subsequent actions. To achieve this, we adapt the notion of counterfactuals from causality theory to a model-free RL setup. The key idea is to condition value functions on future events, by learning to extract relevant information from a trajectory. We formulate a family of policy gradient algorithms that use these future-conditional value functions as baselines or critics, and show that they are provably low variance. To avoid the potential bias from conditioning on future information, we constrain the hindsight information to not contain information about the agent's actions. We demonstrate the efficacy and validity of our algorithm on a number of illustrative and challenging problems.

Jessica B. Hamrick, Abram L. Friesen, Feryal Behbahani et al.

Model-based planning is often thought to be necessary for deep, careful reasoning and generalization in artificial agents. While recent successes of model-based reinforcement learning (MBRL) with deep function approximation have strengthened this hypothesis, the resulting diversity of model-based methods has also made it difficult to track which components drive success and why. In this paper, we seek to disentangle the contributions of recent methods by focusing on three questions: (1) How does planning benefit MBRL agents? (2) Within planning, what choices drive performance? (3) To what extent does planning improve generalization? To answer these questions, we study the performance of MuZero (Schrittwieser et al., 2019), a state-of-the-art MBRL algorithm with strong connections and overlapping components with many other MBRL algorithms. We perform a number of interventions and ablations of MuZero across a wide range of environments, including control tasks, Atari, and 9x9 Go. Our results suggest the following: (1) Planning is most useful in the learning process, both for policy updates and for providing a more useful data distribution. (2) Using shallow trees with simple Monte-Carlo rollouts is as performant as more complex methods, except in the most difficult reasoning tasks. (3) Planning alone is insufficient to drive strong generalization. These results indicate where and how to utilize planning in reinforcement learning settings, and highlight a number of open questions for future MBRL research.

Peter Karkus, Mehdi Mirza, Arthur Guez et al.

Intelligent robots need to achieve abstract objectives using concrete, spatiotemporally complex sensory information and motor control. Tabula rasa deep reinforcement learning (RL) has tackled demanding tasks in terms of either visual, abstract, or physical reasoning, but solving these jointly remains a formidable challenge. One recent, unsolved benchmark task that integrates these challenges is Mujoban, where a robot needs to arrange 3D warehouses generated from 2D Sokoban puzzles. We explore whether integrated tasks like Mujoban can be solved by composing RL modules together in a sense-plan-act hierarchy, where modules have well-defined roles similarly to classic robot architectures. Unlike classic architectures that are typically model-based, we use only model-free modules trained with RL or supervised learning. We find that our modular RL approach dramatically outperforms the state-of-the-art monolithic RL agent on Mujoban. Further, learned modules can be reused when, e.g., using a different robot platform to solve the same task. Together our results give strong evidence for the importance of research into modular RL designs. Project website: https://sites.google.com/view/modular-rl/

Mehdi Mirza, Andrew Jaegle, Jonathan J. Hunt et al.

Recent work in deep reinforcement learning (RL) has produced algorithms capable of mastering challenging games such as Go, chess, or shogi. In these works the RL agent directly observes the natural state of the game and controls that state directly with its actions. However, when humans play such games, they do not just reason about the moves but also interact with their physical environment. They understand the state of the game by looking at the physical board in front of them and modify it by manipulating pieces using touch and fine-grained motor control. Mastering complicated physical systems with abstract goals is a central challenge for artificial intelligence, but it remains out of reach for existing RL algorithms. To encourage progress towards this goal we introduce a set of physically embedded planning problems and make them publicly available. We embed challenging symbolic tasks (Sokoban, tic-tac-toe, and Go) in a physics engine to produce a set of tasks that require perception, reasoning, and motor control over long time horizons. Although existing RL algorithms can tackle the symbolic versions of these tasks, we find that they struggle to master even the simplest of their physically embedded counterparts. As a first step towards characterizing the space of solution to these tasks, we introduce a strong baseline that uses a pre-trained expert game player to provide hints in the abstract space to an RL agent's policy while training it on the full sensorimotor control task. The resulting agent solves many of the tasks, underlining the need for methods that bridge the gap between abstract planning and embodied control. See illustrating video at https://youtu.be/RwHiHlym_1k.

Giambattista Parascandolo, Lars Buesing, Josh Merel et al.

Standard planners for sequential decision making (including Monte Carlo planning, tree search, dynamic programming, etc.) are constrained by an implicit sequential planning assumption: The order in which a plan is constructed is the same in which it is executed. We consider alternatives to this assumption for the class of goal-directed Reinforcement Learning (RL) problems. Instead of an environment transition model, we assume an imperfect, goal-directed policy. This low-level policy can be improved by a plan, consisting of an appropriate sequence of sub-goals that guide it from the start to the goal state. We propose a planning algorithm, Divide-and-Conquer Monte Carlo Tree Search (DC-MCTS), for approximating the optimal plan by means of proposing intermediate sub-goals which hierarchically partition the initial tasks into simpler ones that are then solved independently and recursively. The algorithm critically makes use of a learned sub-goal proposal for finding appropriate partitions trees of new tasks based on prior experience. Different strategies for learning sub-goal proposals give rise to different planning strategies that strictly generalize sequential planning. We show that this algorithmic flexibility over planning order leads to improved results in navigation tasks in grid-worlds as well as in challenging continuous control environments.

Arthur Guez, Fabio Viola, Théophane Weber et al.

Value estimation is a critical component of the reinforcement learning (RL) paradigm. The question of how to effectively learn value predictors from data is one of the major problems studied by the RL community, and different approaches exploit structure in the problem domain in different ways. Model learning can make use of the rich transition structure present in sequences of observations, but this approach is usually not sensitive to the reward function. In contrast, model-free methods directly leverage the quantity of interest from the future, but receive a potentially weak scalar signal (an estimate of the return). We develop an approach for representation learning in RL that sits in between these two extremes: we propose to learn what to model in a way that can directly help value prediction. To this end, we determine which features of the future trajectory provide useful information to predict the associated return. This provides tractable prediction targets that are directly relevant for a task, and can thus accelerate learning the value function. The idea can be understood as reasoning, in hindsight, about which aspects of the future observations could help past value prediction. We show how this can help dramatically even in simple policy evaluation settings. We then test our approach at scale in challenging domains, including on 57 Atari 2600 games.

Danilo J. Rezende, Ivo Danihelka, George Papamakarios et al.

In reinforcement learning, we can learn a model of future observations and rewards, and use it to plan the agent's next actions. However, jointly modeling future observations can be computationally expensive or even intractable if the observations are high-dimensional (e.g. images). For this reason, previous works have considered partial models, which model only part of the observation. In this paper, we show that partial models can be causally incorrect: they are confounded by the observations they don't model, and can therefore lead to incorrect planning. To address this, we introduce a general family of partial models that are provably causally correct, yet remain fast because they do not need to fully model future observations.

Jessica B. Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez et al.

We introduce "Search with Amortized Value Estimates" (SAVE), an approach for combining model-free Q-learning with model-based Monte-Carlo Tree Search (MCTS). In SAVE, a learned prior over state-action values is used to guide MCTS, which estimates an improved set of state-action values. The new Q-estimates are then used in combination with real experience to update the prior. This effectively amortizes the value computation performed by MCTS, resulting in a cooperative relationship between model-free learning and model-based search. SAVE can be implemented on top of any Q-learning agent with access to a model, which we demonstrate by incorporating it into agents that perform challenging physical reasoning tasks and Atari. SAVE consistently achieves higher rewards with fewer training steps, and---in contrast to typical model-based search approaches---yields strong performance with very small search budgets. By combining real experience with information computed during search, SAVE demonstrates that it is possible to improve on both the performance of model-free learning and the computational cost of planning.

Lars Buesing, Nicolas Heess, Theophane Weber

A plethora of problems in AI, engineering and the sciences are naturally formalized as inference in discrete probabilistic models. Exact inference is often prohibitively expensive, as it may require evaluating the (unnormalized) target density on its entire domain. Here we consider the setting where only a limited budget of calls to the unnormalized density oracle is available, raising the challenge of where in the domain to allocate these function calls in order to construct a good approximate solution. We formulate this problem as an instance of sequential decision-making under uncertainty and leverage methods from reinforcement learning for probabilistic inference with budget constraints. In particular, we propose the TreeSample algorithm, an adaptation of Monte Carlo Tree Search to approximate inference. This algorithm caches all previous queries to the density oracle in an explicit search tree, and dynamically allocates new queries based on a "best-first" heuristic for exploration, using existing upper confidence bound methods. Our non-parametric inference method can be effectively combined with neural networks that compile approximate conditionals of the target, which are then used to guide the inference search and enable generalization across multiple target distributions. We show empirically that TreeSample outperforms standard approximate inference methods on synthetic factor graphs.

John F. J. Mellor, Eunbyung Park, Yaroslav Ganin et al.

We investigate using reinforcement learning agents as generative models of images (extending arXiv:1804.01118). A generative agent controls a simulated painting environment, and is trained with rewards provided by a discriminator network simultaneously trained to assess the realism of the agent's samples, either unconditional or reconstructions. Compared to prior work, we make a number of improvements to the architectures of the agents and discriminators that lead to intriguing and at times surprising results. We find that when sufficiently constrained, generative agents can learn to produce images with a degree of visual abstraction, despite having only ever seen real photographs (no human brush strokes). And given enough time with the painting environment, they can produce images with considerable realism. These results show that, under the right circumstances, some aspects of human drawing can emerge from simulated embodiment, without the need for external supervision, imitation or social cues. Finally, we note the framework's potential for use in creative applications.

Arthur Guez, Mehdi Mirza, Karol Gregor et al.

The field of reinforcement learning (RL) is facing increasingly challenging domains with combinatorial complexity. For an RL agent to address these challenges, it is essential that it can plan effectively. Prior work has typically utilized an explicit model of the environment, combined with a specific planning algorithm (such as tree search). More recently, a new family of methods have been proposed that learn how to plan, by providing the structure for planning via an inductive bias in the function approximator (such as a tree structured neural network), trained end-to-end by a model-free RL algorithm. In this paper, we go even further, and demonstrate empirically that an entirely model-free approach, without special structure beyond standard neural network components such as convolutional networks and LSTMs, can learn to exhibit many of the characteristics typically associated with a model-based planner. We measure our agent's effectiveness at planning in terms of its ability to generalize across a combinatorial and irreversible state space, its data efficiency, and its ability to utilize additional thinking time. We find that our agent has many of the characteristics that one might expect to find in a planning algorithm. Furthermore, it exceeds the state-of-the-art in challenging combinatorial domains such as Sokoban and outperforms other model-free approaches that utilize strong inductive biases toward planning.

Théophane Weber, Nicolas Heess, Lars Buesing et al.

Stochastic computation graphs (SCGs) provide a formalism to represent structured optimization problems arising in artificial intelligence, including supervised, unsupervised, and reinforcement learning. Previous work has shown that an unbiased estimator of the gradient of the expected loss of SCGs can be derived from a single principle. However, this estimator often has high variance and requires a full model evaluation per data point, making this algorithm costly in large graphs. In this work, we address these problems by generalizing concepts from the reinforcement learning literature. We introduce the concepts of value functions, baselines and critics for arbitrary SCGs, and show how to use them to derive lower-variance gradient estimates from partial model evaluations, paving the way towards general and efficient credit assignment for gradient-based optimization. In doing so, we demonstrate how our results unify recent advances in the probabilistic inference and reinforcement learning literature.

Laurent Orseau, Levi H. S. Lelis, Tor Lattimore et al.

We introduce two novel tree search algorithms that use a policy to guide search. The first algorithm is a best-first enumeration that uses a cost function that allows us to prove an upper bound on the number of nodes to be expanded before reaching a goal state. We show that this best-first algorithm is particularly well suited for `needle-in-a-haystack' problems. The second algorithm is based on sampling and we prove an upper bound on the expected number of nodes it expands before reaching a set of goal states. We show that this algorithm is better suited for problems where many paths lead to a goal. We validate these tree search algorithms on 1,000 computer-generated levels of Sokoban, where the policy used to guide the search comes from a neural network trained using A3C. Our results show that the policy tree search algorithms we introduce are competitive with a state-of-the-art domain-independent planner that uses heuristic search.

Lars Buesing, Theophane Weber, Yori Zwols et al.

Learning policies on data synthesized by models can in principle quench the thirst of reinforcement learning algorithms for large amounts of real experience, which is often costly to acquire. However, simulating plausible experience de novo is a hard problem for many complex environments, often resulting in biases for model-based policy evaluation and search. Instead of de novo synthesis of data, here we assume logged, real experience and model alternative outcomes of this experience under counterfactual actions, actions that were not actually taken. Based on this, we propose the Counterfactually-Guided Policy Search (CF-GPS) algorithm for learning policies in POMDPs from off-policy experience. It leverages structural causal models for counterfactual evaluation of arbitrary policies on individual off-policy episodes. CF-GPS can improve on vanilla model-based RL algorithms by making use of available logged data to de-bias model predictions. In contrast to off-policy algorithms based on Importance Sampling which re-weight data, CF-GPS leverages a model to explicitly consider alternative outcomes, allowing the algorithm to make better use of experience data. We find empirically that these advantages translate into improved policy evaluation and search results on a non-trivial grid-world task. Finally, we show that CF-GPS generalizes the previously proposed Guided Policy Search and that reparameterization-based algorithms such Stochastic Value Gradient can be interpreted as counterfactual methods.

Karol Gregor, George Papamakarios, Frederic Besse et al.

To act and plan in complex environments, we posit that agents should have a mental simulator of the world with three characteristics: (a) it should build an abstract state representing the condition of the world; (b) it should form a belief which represents uncertainty on the world; (c) it should go beyond simple step-by-step simulation, and exhibit temporal abstraction. Motivated by the absence of a model satisfying all these requirements, we propose TD-VAE, a generative sequence model that learns representations containing explicit beliefs about states several steps into the future, and that can be rolled out directly without single-step transitions. TD-VAE is trained on pairs of temporally separated time points, using an analogue of temporal difference learning used in reinforcement learning.

Adam Santoro, Ryan Faulkner, David Raposo et al.

Memory-based neural networks model temporal data by leveraging an ability to remember information for long periods. It is unclear, however, whether they also have an ability to perform complex relational reasoning with the information they remember. Here, we first confirm our intuitions that standard memory architectures may struggle at tasks that heavily involve an understanding of the ways in which entities are connected -- i.e., tasks involving relational reasoning. We then improve upon these deficits by using a new memory module -- a \textit{Relational Memory Core} (RMC) -- which employs multi-head dot product attention to allow memories to interact. Finally, we test the RMC on a suite of tasks that may profit from more capable relational reasoning across sequential information, and show large gains in RL domains (e.g. Mini PacMan), program evaluation, and language modeling, achieving state-of-the-art results on the WikiText-103, Project Gutenberg, and GigaWord datasets.

Arthur Guez, Théophane Weber, Ioannis Antonoglou et al.

Planning problems are among the most important and well-studied problems in artificial intelligence. They are most typically solved by tree search algorithms that simulate ahead into the future, evaluate future states, and back-up those evaluations to the root of a search tree. Among these algorithms, Monte-Carlo tree search (MCTS) is one of the most general, powerful and widely used. A typical implementation of MCTS uses cleverly designed rules, optimized to the particular characteristics of the domain. These rules control where the simulation traverses, what to evaluate in the states that are reached, and how to back-up those evaluations. In this paper we instead learn where, what and how to search. Our architecture, which we call an MCTSnet, incorporates simulation-based search inside a neural network, by expanding, evaluating and backing-up a vector embedding. The parameters of the network are trained end-to-end using gradient-based optimisation. When applied to small searches in the well known planning problem Sokoban, the learned search algorithm significantly outperformed MCTS baselines.

Lars Buesing, Theophane Weber, Sebastien Racaniere et al.

A key challenge in model-based reinforcement learning (RL) is to synthesize computationally efficient and accurate environment models. We show that carefully designed generative models that learn and operate on compact state representations, so-called state-space models, substantially reduce the computational costs for predicting outcomes of sequences of actions. Extensive experiments establish that state-space models accurately capture the dynamics of Atari games from the Arcade Learning Environment from raw pixels. The computational speed-up of state-space models while maintaining high accuracy makes their application in RL feasible: We demonstrate that agents which query these models for decision making outperform strong model-free baselines on the game MSPACMAN, demonstrating the potential of using learned environment models for planning.

M. Botvinick, D. G. T. Barrett, P. Battaglia et al.

We agree with Lake and colleagues on their list of key ingredients for building humanlike intelligence, including the idea that model-based reasoning is essential. However, we favor an approach that centers on one additional ingredient: autonomy. In particular, we aim toward agents that can both build and exploit their own internal models, with minimal human hand-engineering. We believe an approach centered on autonomous learning has the greatest chance of success as we scale toward real-world complexity, tackling domains for which ready-made formal models are not available. Here we survey several important examples of the progress that has been made toward building autonomous agents with humanlike abilities, and highlight some outstanding challenges.

Théophane Weber, Sébastien Racanière, David P. Reichert et al.

We introduce Imagination-Augmented Agents (I2As), a novel architecture for deep reinforcement learning combining model-free and model-based aspects. In contrast to most existing model-based reinforcement learning and planning methods, which prescribe how a model should be used to arrive at a policy, I2As learn to interpret predictions from a learned environment model to construct implicit plans in arbitrary ways, by using the predictions as additional context in deep policy networks. I2As show improved data efficiency, performance, and robustness to model misspecification compared to several baselines.

Razvan Pascanu, Yujia Li, Oriol Vinyals et al.

Conventional wisdom holds that model-based planning is a powerful approach to sequential decision-making. It is often very challenging in practice, however, because while a model can be used to evaluate a plan, it does not prescribe how to construct a plan. Here we introduce the "Imagination-based Planner", the first model-based, sequential decision-making agent that can learn to construct, evaluate, and execute plans. Before any action, it can perform a variable number of imagination steps, which involve proposing an imagined action and evaluating it with its model-based imagination. All imagined actions and outcomes are aggregated, iteratively, into a "plan context" which conditions future real and imagined actions. The agent can even decide how to imagine: testing out alternative imagined actions, chaining sequences of actions together, or building a more complex "imagination tree" by navigating flexibly among the previously imagined states using a learned policy. And our agent can learn to plan economically, jointly optimizing for external rewards and computational costs associated with using its imagination. We show that our architecture can learn to solve a challenging continuous control problem, and also learn elaborate planning strategies in a discrete maze-solving task. Our work opens a new direction toward learning the components of a model-based planning system and how to use them.

Nicholas Watters, Andrea Tacchetti, Theophane Weber et al.

From just a glance, humans can make rich predictions about the future state of a wide range of physical systems. On the other hand, modern approaches from engineering, robotics, and graphics are often restricted to narrow domains and require direct measurements of the underlying states. We introduce the Visual Interaction Network, a general-purpose model for learning the dynamics of a physical system from raw visual observations. Our model consists of a perceptual front-end based on convolutional neural networks and a dynamics predictor based on interaction networks. Through joint training, the perceptual front-end learns to parse a dynamic visual scene into a set of factored latent object representations. The dynamics predictor learns to roll these states forward in time by computing their interactions and dynamics, producing a predicted physical trajectory of arbitrary length. We found that from just six input video frames the Visual Interaction Network can generate accurate future trajectories of hundreds of time steps on a wide range of physical systems. Our model can also be applied to scenes with invisible objects, inferring their future states from their effects on the visible objects, and can implicitly infer the unknown mass of objects. Our results demonstrate that the perceptual module and the object-based dynamics predictor module can induce factored latent representations that support accurate dynamical predictions. This work opens new opportunities for model-based decision-making and planning from raw sensory observations in complex physical environments.

S. M. Ali Eslami, Nicolas Heess, Theophane Weber et al.

We present a framework for efficient inference in structured image models that explicitly reason about objects. We achieve this by performing probabilistic inference using a recurrent neural network that attends to scene elements and processes them one at a time. Crucially, the model itself learns to choose the appropriate number of inference steps. We use this scheme to learn to perform inference in partially specified 2D models (variable-sized variational auto-encoders) and fully specified 3D models (probabilistic renderers). We show that such models learn to identify multiple objects - counting, locating and classifying the elements of a scene - without any supervision, e.g., decomposing 3D images with various numbers of objects in a single forward pass of a neural network. We further show that the networks produce accurate inferences when compared to supervised counterparts, and that their structure leads to improved generalization.

Gabriel Dulac-Arnold, Richard Evans, Hado van Hasselt et al.

Being able to reason in an environment with a large number of discrete actions is essential to bringing reinforcement learning to a larger class of problems. Recommender systems, industrial plants and language models are only some of the many real-world tasks involving large numbers of discrete actions for which current methods are difficult or even often impossible to apply. An ability to generalize over the set of actions as well as sub-linear complexity relative to the size of the set are both necessary to handle such tasks. Current approaches are not able to provide both of these, which motivates the work in this paper. Our proposed approach leverages prior information about the actions to embed them in a continuous space upon which it can generalize. Additionally, approximate nearest-neighbor methods allow for logarithmic-time lookup complexity relative to the number of actions, which is necessary for time-wise tractable training. This combined approach allows reinforcement learning methods to be applied to large-scale learning problems previously intractable with current methods. We demonstrate our algorithm's abilities on a series of tasks having up to one million actions.

John Schulman, Nicolas Heess, Theophane Weber et al.

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external world. Estimating the gradient of this loss function, using samples, lies at the core of gradient-based learning algorithms for these problems. We introduce the formalism of stochastic computation graphs---directed acyclic graphs that include both deterministic functions and conditional probability distributions---and describe how to easily and automatically derive an unbiased estimator of the loss function's gradient. The resulting algorithm for computing the gradient estimator is a simple modification of the standard backpropagation algorithm. The generic scheme we propose unifies estimators derived in variety of prior work, along with variance-reduction techniques therein. It could assist researchers in developing intricate models involving a combination of stochastic and deterministic operations, enabling, for example, attention, memory, and control actions.

David Wingate, Theophane Weber

We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly practical for distributions which are not analytically tractable, including highly structured distributions that arise in probabilistic programs. We show how to automatically derive mean-field probabilistic programs and optimize them, and demonstrate that our perspective improves inference efficiency over other algorithms.