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Equation 1 · Part 6 · Comparing the Main Approaches to Robotics and Embodied AI

Symbol gamma

Q(s,a)←Q(s,a)+α[r+γmax⁡a′Q(s′,a′)−Q(s,a)]Q(s,a) \leftarrow Q(s,a) + \alpha \left[ r + \gamma \max_{a'} Q(s',a') - Q(s,a) \right]
γ\gamma

What this part means

gamma is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

gamma is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

A model-free update never references a transition model. A canonical form, temporal-difference learning, updates a value estimate purely from sampled transitions: Q(s,a)←Q(s,a)+α[r+γmax⁡a′Q(s′,a′)−Q(s,a)]Q(s,a) \leftarrow Q(s,a) + \alpha \left[ r + \gamma \max_{a'} Q(s',a') - Q(s,a) \right]. Nothing in this update requires knowing or estimating p(s' ∣\mid s, a) ; it only requires having experienced (s, a, r, s') . A model-based approach instead fits an explicit dynamics model p^θ(s′∣s,a)\hat{p}_\theta(s' \mid s, a) — a “world model” — and plans against it directly:

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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