arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.04622cs.LGcs.AImath.OCmath.STstat.MLstat.TH
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关于强化学习中的函数逼近:面对大状态空间的乐观主义

On Function Approximation in Reinforcement Learning: Optimism in the Face of Large State Spaces

Princeton University(普林斯顿大学);Northwestern University(西北大学);University of California, Berkeley(加州大学伯克利分校)

Zhuoran Yang, Chi Jin, Zhaoran Wang, Mengdi Wang, Michael I. Jordan

摘要:

强化学习(RL)的经典理论集中于价值函数的表格和线性表示。进一步的进展取决于将RL与核函数和深度神经网络等现代函数逼近器相结合,事实上,在大规模应用中利用这种组合已经取得了许多经验性的成功。然而,在开发一种理论来支持这一企业方面存在着深刻的挑战,最值得注意的是需要考虑RL核心的探索-利用权衡,以及现代基于函数近似的学习系统中出现的计算和统计权衡。我们通过研究最小二乘值迭代算法的乐观修改来接近这些挑战,在由核函数或过参数化神经网络表示的动作价值函数的上下文中。我们建立多项式运行时复杂度和多项式样本复杂度的算法,没有额外的假设的数据生成模型。特别是,我们证明了该算法招致的$\tilde{\mathcal{O}}(δ_{\mathcal{F}} H^2 \sqrt{T})$遗憾,其中$δ_{\mathcal{F}}$的特点是内在的复杂性的功能类$\mathcal{F}$,$H$是每个情节的长度,和$T$是情节的总数。我们的遗憾界是独立的状态的数量,这一结果清楚地表现出在RL函数逼近的好处。

英文摘要:

The classical theory of reinforcement learning (RL) has focused on tabular and linear representations of value functions. Further progress hinges on combining RL with modern function approximators such as kernel functions and deep neural networks, and indeed there have been many empirical successes that have exploited such combinations in large-scale applications. There are profound challenges, however, in developing a theory to support this enterprise, most notably the need to take into consideration the exploration-exploitation tradeoff at the core of RL in conjunction with the computational and statistical tradeoffs that arise in modern function-approximation-based learning systems. We approach these challenges by studying an optimistic modification of the least-squares value iteration algorithm, in the context of the action-value function represented by a kernel function or an overparameterized neural network. We establish both polynomial runtime complexity and polynomial sample complexity for this algorithm, without additional assumptions on the data-generating model. In particular, we prove that the algorithm incurs an $\tilde{\mathcal{O}}(δ_{\mathcal{F}} H^2 \sqrt{T})$ regret, where $δ_{\mathcal{F}}$ characterizes the intrinsic complexity of the function class $\mathcal{F}$, $H$ is the length of each episode, and $T$ is the total number of episodes. Our regret bounds are independent of the number of states, a result which exhibits clearly the benefit of function approximation in RL.

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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