Bellman expectation equation

Reinforcement learning · Formula · Appears in 1 lesson

Vπ(s)=Eπ ⁣[r+γVπ(s′)∣s]V^{\pi}(s) = \mathbb{E}_{\pi}\!\left[r + \gamma V^{\pi}(s') \mid s\right]

Value defined in terms of itself one step later: a reward now, plus the discounted value of wherever you land. Every value-based algorithm is some way of solving this fixed point.

Symbols

s′s'
The next state.
rr
The immediate reward.
γ\gamma
The discount factor.
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