We introduce Codex, a GPT language model finetuned on publicly available code from GitHub, and study its Python code-writing capabilities. A distinct production version of Codex powers GitHub Copilot. On HumanEval, a new evaluation set we release to measure functional correctness for synthesizing programs from docstrings, our model solves 28.8% of the problems, while GPT-3 solves 0% and GPT-J solves 11.4%. Furthermore, we find that repeated sampling from the model is a surprisingly effective strategy for producing working solutions to difficult prompts. Using this method, we solve 70.2% of our problems with 100 samples per problem. Careful investigation of our model reveals its limitations, including difficulty with docstrings describing long chains of operations and with binding operations to variables. Finally, we discuss the potential broader impacts of deploying powerful code generation technologies, covering safety, security, and economics.

The sample inefficiency of standard deep reinforcement learning methods precludes their application to many real-world problems. Methods which leverage human demonstrations require fewer samples but have been researched less. As demonstrated in the computer vision and natural language processing communities, large-scale datasets have the capacity to facilitate research by serving as an experimental and benchmarking platform for new methods. However, existing datasets compatible with reinforcement learning simulators do not have sufficient scale, structure, and quality to enable the further development and evaluation of methods focused on using human examples. Therefore, we introduce a comprehensive, large-scale, simulatorpaired dataset of human demonstrations: MineRL. The dataset consists of over 60 million automatically annotated state-action pairs across a variety of related tasks in Minecraft, a dynamic, 3D, openworld environment. We present a novel data collection scheme which allows for the ongoing introduction of new tasks and the gathering of complete state information suitable for a variety of methods. We demonstrate the hierarchality, diversity, and scale of the MineRL dataset. Further, we show the difficulty of the Minecraft domain along with the potential of MineRL in developing techniques to solve key research challenges within it.

No abstract

The study of universal approximation of arbitrary functions f : X → Y by neural networks has a rich and thorough history dating back to Kolmogorov (1957). In the case of learning finite dimensional maps, many authors have shown various forms of the universality of both fixed depth and fixed width neural networks. However, in many cases, these classical results fail to extend to the recent use of approximations of neural networks with infinitely many units for functional data analysis, dynamical systems identification, and other applications where either X or Y become infinite dimensional. Two questions naturally arise: which infinite dimensional analogues of neural networks are sufficient to approximate any map f : X → Y, and when do the finite approximations to these analogues used in practice approximate f uniformly over its infinite dimensional domain X ?In this paper, we answer the open question of universal approximation of nonlinear operators when X and Y are both infinite dimensional. We show that for a large class of different infinite analogues of neural networks, any continuous map can be approximated arbitrarily closely with some mild topological conditions on X . Additionally, we provide the first lower-bound on the minimal number of input and output units required by a finite approximation to an infinite neural network to guarantee that it can uniformly approximate any nonlinear operator using samples from its inputs and outputs.

Reinforcement learning competitions have formed the basis for standard research benchmarks, galvanized advances in the state-of-the-art, and shaped the direction of the field. Despite this, a majority of challenges suffer from the same fundamental problems: participant solutions to the posed challenge are usually domain-specific, biased to maximally exploit compute resources, and not guaranteed to be reproducible. In this paper, we present a new framework of competition design that promotes the development of algorithms that overcome these barriers. We propose four central mechanisms for achieving this end: submission retraining, domain randomization, desemantization through domain obfuscation, and the © W.H. Guss et al.