Transformers have revolutionized machine learning with their simple yet effective architecture. Pre-training Transformers on massive text datasets from the Internet has led to unmatched generalization for natural language understanding (NLU) tasks. However, such language models remain fragile when tasked with algorithmic forms of reasoning, where computations must be precise and robust. To address this limitation, we propose a novel approach that combines the Transformer's language understanding with the robustness of graph neural network (GNN)-based neural algorithmic reasoners (NARs). Such NARs proved effective as generic solvers for algorithmic tasks, when specified in graph form. To make their embeddings accessible to a Transformer, we propose a hybrid architecture with a two-phase training procedure, allowing the tokens in the language model to cross-attend to the node embeddings from the NAR. We evaluate our resulting TransNAR model on CLRS-Text, the text-based version of the CLRS-30 benchmark, and demonstrate significant gains over Transformer-only models for algorithmic reasoning, both in and out of distribution.

Recent work in machine learning and cognitive science has suggested that understanding causal information is essential to the development of intelligence. The extensive literature in cognitive science using the ``blicket detector'' environment shows that children are adept at many kinds of causal inference and learning. We propose to adapt that environment for machine learning agents. One of the key challenges for current machine learning algorithms is modeling and understanding causal overhypotheses: transferable abstract hypotheses about sets of causal relationships. In contrast, even young children spontaneously learn and use causal overhypotheses. In this work, we present a new benchmark -- a flexible environment which allows for the evaluation of existing techniques under variable causal overhypotheses -- and demonstrate that many existing state-of-the-art methods have trouble generalizing in this environment. The code and resources for this benchmark are available at https://github.com/CannyLab/casual_overhypotheses.

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.

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.

Despite recent progress in reinforcement learning (RL), RL algorithms for exploration still remain an active area of research. Existing methods often focus on state-based metrics, which do not consider the underlying causal structures of the environment, and while recent research has begun to explore RL environments for causal learning, these environments primarily leverage causal information through causal inference or induction rather than exploration. In contrast, human children - some of the most proficient explorers - have been shown to use causal information to great benefit. In this work, we introduce a novel RL environment designed with a controllable causal structure, which allows us to evaluate exploration strategies used by both agents and children in a unified environment. In addition, through experimentation on both computation models and children, we demonstrate that there are significant differences between information-gain optimal RL exploration in causal environments and the exploration of children in the same environments. We conclude with a discussion of how these findings may inspire new directions of research into efficient exploration and disambiguation of causal structures for RL algorithms.

Designing physical artifacts that serve a purpose—such as tools and other functional structures—is central to engineering as well as everyday human behavior. Though automating design using machine learning has tremendous promise, existing methods are often limited by the task-dependent distributions they were exposed to during training. Here we showcase a task-agnostic approach to inverse design, by combining general-purpose graph network simulators with gradient-based design optimization. This constitutes a simple, fast, and reusable approach that solves high-dimensional problems with complex physical dynamics, including designing surfaces and tools to manipulate fluid flows and optimizing the shape of an airfoil to minimize drag. This framework produces high-quality designs by propagating gradients through trajectories of hundreds of steps, even when using models that were pre-trained for single-step predictions on data substantially different from the design tasks. In our fluid manipulation tasks, the resulting designs outperformed those found by sampling-based optimization techniques. In airfoil design, they matched the quality of those obtained with a specialized solver. Our results suggest that despite some remaining challenges, machine learning-based simulators are maturing to the point where they can support general-purpose design optimization across a variety of fluid-structure interaction domains.

Designing physical artifacts that serve a purpose - such as tools and other functional structures - is central to engineering as well as everyday human behavior. Though automating design has tremendous promise, general-purpose methods do not yet exist. Here we explore a simple, fast, and robust approach to inverse design which combines learned forward simulators based on graph neural networks with gradient-based design optimization. Our approach solves high-dimensional problems with complex physical dynamics, including designing surfaces and tools to manipulate fluid flows and optimizing the shape of an airfoil to minimize drag. This framework produces high-quality designs by propagating gradients through trajectories of hundreds of steps, even when using models that were pre-trained for single-step predictions on data substantially different from the design tasks. In our fluid manipulation tasks, the resulting designs outperformed those found by sampling-based optimization techniques. In airfoil design, they matched the quality of those obtained with a specialized solver. Our results suggest that despite some remaining challenges, machine learning-based simulators are maturing to the point where they can support general-purpose design optimization across a variety of domains.

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.

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.

Machine learning is currently involved in some of the most vigorous debates it has ever seen. Such debates often seem to go around in circles, reaching no conclusion or resolution. This is perhaps unsurprising given that researchers in machine learning come to these discussions with very different frames of reference, making it challenging for them to align perspectives and find common ground. As a remedy for this dilemma, we advocate for the adoption of a common conceptual framework which can be used to understand, analyze, and discuss research. We present one such framework which is popular in cognitive science and neuroscience and which we believe has great utility in machine learning as well: Marr's levels of analysis. Through a series of case studies, we demonstrate how the levels facilitate an understanding and dissection of several methods from machine learning. By adopting the levels of analysis in one's own work, we argue that researchers can be better equipped to engage in the debates necessary to drive forward progress in our field.

Research in developmental psychology consistently shows that children explore the world thoroughly and efficiently and that this exploration allows them to learn. In turn, this early learning supports more robust generalization and intelligent behavior later in life. While much work has gone into developing methods for exploration in machine learning, artificial agents have not yet reached the high standard set by their human counterparts. In this work we propose using DeepMind Lab (Beattie et al., 2016) as a platform to directly compare child and agent behaviors and to develop new exploration techniques. We outline two ongoing experiments to demonstrate the effectiveness of a direct comparison, and outline a number of open research questions that we believe can be tested using this methodology.

Research in developmental psychology consistently shows that children explore the world thoroughly and efficiently and that this exploration allows them to learn. In turn, this early learning supports more robust generalization and intelligent behavior later in life. While much work has gone into developing methods for exploration in machine learning, artificial agents have not yet reached the high standard set by their human counterparts. In this work we propose using DeepMind Lab (Beattie et al., 2016) as a platform to directly compare child and agent behaviors and to develop new exploration techniques. We outline two ongoing experiments to demonstrate the effectiveness of a direct comparison, and outline a number of open research questions that we believe can be tested using this methodology. 1 THE PROBLEM OF EXPLORATION The problem of exploration is one of the most fundamental issues in reinforcement learning (RL): how should an agent gather enough experience from different parts of the world in order to later produce approximately optimal behavior? Questions surrounding exploration have been investigated for as long as the field has existed (Thompson, 1933; Robbins, 1952; Gittins & Jones, 1979), and it continues to be a major focus of research today, with recent approaches estimating various quantities to guide exploration, such as visit counts (Bellemare et al., 2013; Ostrovski et al., 2017; Martin et al., 2017; Tang et al., 2017; Machado et al., 2018), uncertainty (Osband et al., 2016; Burda et al., 2018), surprise (Schmidhuber, 1991; Pathak et al., 2017), learning progress (Kaplan & Oudeyer, 2004; Baranes & Oudeyer, 2013), disagreement (Pathak et al., 2019), or other forms of novelty (Fu et al., 2017); see François-Lavet et al. (2018) for a recent review. Yet, despite these efforts, the problem of exploration remains far from solved. Indeed, algorithms which achieve state-of-the-art performance on benchmarks such as Atari often still rely on simple exploration strategies like -greedy combined with huge amounts of computation (Kapturowski et al., 2018). As with artificial agents, exploration is a key feature of human behavior. Dating back to Piaget (1933), developmental researchers have conceived of children as active and curious learners who are intrinsically motivated to explore the world in systematic and rational ways (Schulz & Bonawitz, 2007; Cook et al., 2011; Legare, 2012; Schulz, 2012; Schulz et al., 2019a); see Schulz (2012) for a review. The simplest example of this exploration may be in the way that active movement through space informs both object understanding and navigation. For example, when infants become mobile and begin to crawl this exploration appears to allow them to learn both about space and objects (Campos et al., 2000). Even 11-month old infants choose to physically explore objects that violate expectations of object solidity or object support instead of a novel distractor object (Stahl & Feigenson, 2015). Older children also explore in more complex ways, both when evidence does not conform to their expectations (Bonawitz et al., 2012; Legare, 2012) and when evidence is causally confounded (Schulz & Bonawitz, 2007; Schulz et al., 2007; Cook et al., 2011; Schulz, 2012). The simple fact that children know less than adults may make them more open to new kinds of learning and exploration (Lucas et al., 2014; Gopnik, 2017). Recent evidence suggests that children do indeed explore more than adults, and that this translates into higher amounts of learning, even when exploration comes at a cost (Liquin & Gopnik, 2019; Schulz et al., 2019b; Sumner et al., 2019; ∗Corresponding author: eko@berkeley.edu

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.

As intelligent systems gain autonomy and capability, it becomes vital to ensure that their objectives match those of their human users; this is known as the value-alignment problem. In robotics, value alignment is key to the design of collaborative robots that can integrate into human workflows, successfully inferring and adapting to their users’ objectives as they go. We argue that a meaningful solution to value alignment must combine multi-agent decision theory with rich mathematical models of human cognition, enabling robots to tap into people’s natural collaborative capabilities. We present a solution to the cooperative inverse reinforcement learning (CIRL) dynamic game based on well-established cognitive models of decision making and theory of mind. The solution captures a key reciprocity relation: the human will not plan her actions in isolation, but rather reason pedagogically about how the robot might learn from them; the robot, in turn, can anticipate this and interpret the human’s actions pragmatically. To our knowledge, this work constitutes the first formal analysis of value alignment grounded in empirically validated cognitive models.

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.

nbgrader is a flexible tool for creating and grading assignments in the Jupyter Notebook (Kluyver et al., 2016). nbgrader allows instructors to create a single, master copy of an assignment, including tests and canonical solutions. From the master copy, a student version is generated without the solutions, thus obviating the need to maintain two separate versions. nbgrader also automatically grades submitted assignments by executing the notebooks and storing the results of the tests in a database. After auto-grading, instructors can manually grade free responses and provide partial credit using the formgrader Jupyter Notebook extension. Finally, instructors can use nbgrader to leave personalized feedback for each student’s submission, including comments as well as detailed error information.

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.

Physical construction-the ability to compose objects, subject to physical dynamics, to serve some function-is fundamental to human intelligence. We introduce a suite of challenging physical construction tasks inspired by how children play with blocks, such as matching a target configuration, stacking blocks to connect objects together, and creating shelter-like structures over target objects. We examine how a range of deep reinforcement learning agents fare on these challenges, and introduce several new approaches which provide superior performance. Our results show that agents which use structured representations (e.g., objects and scene graphs) and structured policies (e.g., object-centric actions) outperform those which use less structured representations, and generalize better beyond their training when asked to reason about larger scenes. Model-based agents which use Monte-Carlo Tree Search also outperform strictly model-free agents in our most challenging construction problems. We conclude that approaches which combine structured representations and reasoning with powerful learning are a key path toward agents that possess rich intuitive physics, scene understanding, and planning.