April 2022
Intermediate to advanced
376 pages
4h 55m
Japanese
Content preview from ゼロから作るDeep Learning ❹ ―強化学習編
![\nabla_\theta J(\theta) =\mathbb{E}_{\tau \sim \pi_{\theta}}\left[\sum^T_{t=0} G(\tau) \nabla_\theta \log \pi_{\theta}(A_t| S_t)\right]\tag{9.1}](/api/v2/epubs/urn:orm:book:9784873119755/files/images/_review_math/_gen_71de416228f0422847f73082306e826a116d2ad633942e14ff3977cbc5f60ea7.svg)
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付録D方策勾配法の証明
ここでは「9章 方策勾配法」で使用した数式の証明を行います。
D.1 方策勾配法の導出
「9.1 最も単純な方策勾配法」で説明したとおり、![J(\theta) = \mathbb{E}_{\tau \sim \pi_{\theta}}[G(\tau)]](/api/v2/epubs/urn:orm:book:9784873119755/files/images/_review_math/_gen_b034fa9efbe7469b7a0468eef9ed1ff008a8caba76e62279ea67ea983d6e68a2.svg)
としたとき、その勾配は次の式(9.1)で表されます。
ここでは、式(9.1)の導出を行います。
まずは記号の確認です。ここでは方策を
としたとき、軌道
が得られる確率を
で表すことにします。それでは、を数式で順に展開していきます。
数式の右側にあるコメントを参考に1つずつ追ってみましょう。微分についての知識があれば、特に難しい点はないと思います。ここでは1点「 ...
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