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arXiv 2403.14432eess.SYcs.AIcs.SY
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关于强化学习与最优控制中价值函数的连续性与平滑性

On the continuity and smoothness of the value function in reinforcement learning and optimal control

Paderborn University(帕德博恩大学)

Hans Harder, Sebastian Peitz

AI总结:

本文研究强化学习与最优控制中价值函数的连续性,通过提供并验证连续性模的上界,证明在较弱假设下价值函数始终Hölder连续,且轻微扰动系统可使不可微价值函数变得可微。

摘要:

价值函数在强化学习和最优控制中作为衡量智能体所获累积未来奖励的指标发挥着关键作用。因此,研究相邻状态的值有多相似,即考察价值函数的连续性,具有重要意义。我们通过提供并验证价值函数连续性模的上界来实现这一点。此外,我们证明,在对底层系统施加相对较弱的假设下,价值函数始终是Hölder连续的,并且不可微的价值函数可以通过对系统进行轻微的“扰动”来使其变得可微。

英文摘要:

The value function plays a crucial role as a measure for the cumulative future reward an agent receives in both reinforcement learning and optimal control. It is therefore of interest to study how similar the values of neighboring states are, i.e., to investigate the continuity of the value function. We do so by providing and verifying upper bounds on the value function's modulus of continuity. Additionally, we show that the value function is always Hölder continuous under relatively weak assumptions on the underlying system and that non-differentiable value functions can be made differentiable by slightly "disturbing" the system.

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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