The general approach taken when training deep learning classifiers is to save the parameters after every few iterations, train until either a human observer or a simple metric-based heuristic decides the network isn't learning anymore, and then backtrack and pick the saved parameters with the best validation accuracy. Simple methods are used to determine if a neural network isn't learning anymore because, as long as it's well after the optimal values are found, the condition doesn't impact the final accuracy of the model. However from a runtime perspective, this is of great significance to the many cases where numerous neural networks are trained simultaneously (e.g. hyper-parameter tuning). Motivated by this, we introduce a statistical significance test to determine if a neural network has stopped learning. This stopping criterion appears to represent a happy medium compared to other popular stopping criterions, achieving comparable accuracy to the criterions that achieve the highest final accuracies in 77% or fewer epochs, while the criterions which stop sooner do so with an appreciable loss to final accuracy. Additionally, we use this as the basis of a new learning rate scheduler, removing the need to manually choose learning rate schedules and acting as a quasi-line search, achieving superior or comparable empirical performance to existing methods.

This paper introduces PettingZoo, a library of diverse sets of multi-agent environments under a single elegant Python API. PettingZoo was developed with the goal of accelerating research in multi-agent reinforcement learning, by creating a set of benchmark environments easily accessible to all researchers and a standardized API for the field. This goal is inspired by what OpenAI's Gym library did for accelerating research in single-agent reinforcement learning, and PettingZoo draws heavily from Gym in terms of API and user experience. PettingZoo is unique from other multi-agent environment libraries in that it's API is based on the model of Agent Environment Cycle ("AEC") games, which allows for the sensible representation of all varieties of games under one API for the first time. While retaining a very simple and Gym-like API, PettingZoo still allows access to low-level environment properties required by nontraditional learning methods. Reinforcement Learning ("RL") considers learning a policy -- a function that takes in an observation from an environment and emits an action -- that achieves the maximum expected discounted reward when acting in an environment, and it's capabilities have been one of the great success of modern machine learning. Multi-Agent Reinforcement Learning (MARL) in particular has been behind many of the most publicized achievements of modern machine learning -- AlphaGo Zero (Silver et al., 2017), OpenAI Five (OpenAI, 2018), AlphaStar (Vinyals et al., 2019) -- and has seen a boom in recent years.