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Equation 1 · Part 9 · Comparing the Main Approaches to Robotics and Embodied AI

subscript

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]
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.