In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Ex Input:
The reproducibility of reinforcement-learning research has been highlighted as a key challenge area in the field. In this paper, we present a case study in reproducing the results of one groundbreaking algorithm, AlphaZero, a reinforcement learning system that learns how to play Go at a superhuman level given only the rules of the game. We describe Minigo, a reproduction of the AlphaZero system using publicly available Google Cloud Platform infrastructure and Google Cloud TPUs. The Minigo system includes both the central reinforcement learning loop as well as auxiliary monitoring and evaluation infrastructure. With ten days of training from scratch on 800 Cloud TPUs, Minigo can play evenly against LeelaZero and ELF OpenGo, two of the strongest publicly available Go AIs. We discuss the difficulties of scaling a reinforcement learning system and the monitoring systems required to understand the complex interplay of hyperparameter configurations.

Ex Output:
We reproduced AlphaZero on Google Cloud Platform


Ex Input:
Deep neural networks use deeper and broader structures to achieve better performance and consequently, use increasingly more GPU memory as well. However, limited GPU memory restricts many potential designs of neural networks. In this paper, we propose a reinforcement learning based variable swapping and recomputation algorithm to reduce the memory cost, without sacrificing the accuracy of models. Variable swapping can transfer variables between CPU and GPU memory to reduce variables stored in GPU memory. Recomputation can trade time for space by removing some feature maps during forward propagation. Forward functions are executed once again to get the feature maps before reuse. However, how to automatically decide which variables to be swapped or recomputed remains a challenging problem. To address this issue, we propose to use a deep Q-network(DQN) to make plans. By combining variable swapping and recomputation, our results outperform several well-known benchmarks.

Ex Output:
We propose a reinforcement learning based variable swapping and recomputation algorithm to reduce the memory cost.


Ex Input:
Humans are capable of attributing latent mental contents such as beliefs, or intentions to others. The social skill is critical in everyday life to reason about the potential consequences of their behaviors so as to plan ahead. It is known that humans use this reasoning ability recursively, i.e. considering what others believe about their own beliefs.   In this paper, we start  from level-$1$ recursion and introduce a probabilistic recursive reasoning (PR2) framework for multi-agent reinforcement learning. Our hypothesis is that it is beneficial for each agent to account for how the opponents would react to its future behaviors. Under the PR2 framework, we adopt variational Bayes methods to approximate the opponents' conditional policy, to which each agent finds the  best response and then improve their own policy. We develop  decentralized-training-decentralized-execution  algorithms, PR2-Q and PR2-Actor-Critic, that are proved to converge in the self-play scenario when there is one Nash equilibrium. Our methods are tested on both the matrix game and the differential game, which have a non-trivial equilibrium where common gradient-based methods fail to converge. Our experiments show that it is critical to reason about how the opponents believe about what the agent believes. We expect our work to contribute a new idea of modeling the opponents to the multi-agent reinforcement learning community.  


Ex Output:

We proposed a novel probabilisitic recursive reasoning (PR2) framework for multi-agent deep reinforcement learning tasks.