Equation 5 · Part 14 · Comparing the Main Approaches to Robotics and Embodied AI

Ending index or upper bound: H

a^{*}_{1:H} = \arg\max_{a_{1:H}} \; \mathbb{E}_{\hat{p}_\theta} \left[ \sum_{t=1}^{H} \gamma^{t} \, r(s_t, a_t) \right]

H

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

H appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionEnding index or upper bound: HArticle meaning

The passage around this formula

…queried and its predictions checked against reality independent of the policy it supports; the cost is that policy quality is now bounded by model accuracy, and errors in $\hat{p}_\theta$ compound over the planning horizon H in ways that are hard to detect from the outside [ 6 ] . Classical robotics has practiced a version of this for decades without calling it “model-based reinforcement learning”: model-predictive control on the MIT Cheetah 3 solves a convex optimization over ground reaction forces against a…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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