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arXiv 2102.09161cs.LGcs.SYeess.SY
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稳定性约束模仿学习的样本复杂度

On the Sample Complexity of Stability Constrained Imitation Learning

Google Brain Robotics(谷歌大脑机器人);University of Pennsylvania(宾夕法尼亚大学)

Stephen Tu, Alexander Robey, Tingnan Zhang, Nikolai Matni

摘要:

我们研究以下问题的背景下,连续控制的模仿学习:如何反映在样本复杂性的模仿学习任务的专家政策的潜在稳定性?我们提供的第一个结果表明,一个令人惊讶的粒度之间的连接可以底层专家系统的增量增益稳定性,一种新的措施之间的鲁棒收敛对系统轨迹,并依赖于任务范围$T$的泛化界限。特别是,我们提出并分析了增量增益稳定性约束版本的行为克隆和Dagger算法,并表明所得到的样本复杂性界自然反映了潜在的稳定性属性的专家系统。作为一个特殊的情况下,我们描绘了一类系统的数量需要实现$\varepsilon$ -次优是次线性的任务范围$T$,这样做,而不需要(强)凸的损失函数的政策参数。最后,我们进行了数值实验,证明了我们的见解的有效性,一个简单的非线性系统,其基本的稳定性可以很容易地调整,并在一个高维四足机器人模拟。

英文摘要:

We study the following question in the context of imitation learning for continuous control: how are the underlying stability properties of an expert policy reflected in the sample-complexity of an imitation learning task? We provide the first results showing that a surprisingly granular connection can be made between the underlying expert system's incremental gain stability, a novel measure of robust convergence between pairs of system trajectories, and the dependency on the task horizon $T$ of the resulting generalization bounds. In particular, we propose and analyze incremental gain stability constrained versions of behavior cloning and a DAgger-like algorithm, and show that the resulting sample-complexity bounds naturally reflect the underlying stability properties of the expert system. As a special case, we delineate a class of systems for which the number of trajectories needed to achieve $\varepsilon$-suboptimality is sublinear in the task horizon $T$, and do so without requiring (strong) convexity of the loss function in the policy parameters. Finally, we conduct numerical experiments demonstrating the validity of our insights on both a simple nonlinear system for which the underlying stability properties can be easily tuned, and on a high-dimensional quadrupedal robotic simulation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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