irrational numbers are real numbers that are not rational numbers.

Formally:

\begin{equation} \mathbb{C} = \mathbb{R} \backslash \mathbb{Q} \end{equation}

where, \(\backslash\) is subtracting two sets.

Motivation

Large crowd navigation with sudden changes: unlikely events are out of likely sample. So, we want to bring in another distribution based on importance and not likelyness.

Goals

• retains DESPOT garantees
• outperforms DESPOT and POMCP

DESPOT with Importance Sampling

1. take our initial belief
2. sample trajectories according to Importance Sampling distribution
3. calculate values of those states
4. obtain value estimate based on weighted average of the values

Importance Sampling of trajectories

We define an importance distribution of some trajectory \(\xi\):

An isomorphism is an invertable Linear Map. Two vector spaces are called isomorphic if there is an isomorphism from one to another.

“A linear map that maintain the correct structure of the structure.”

This makes the vector spaces that are isomorphic “equivalent”, because the isomorphism is the equivalence relationship. Of course, they are still not equal.

Generally, isomorphisms can only be built between vector spaces over the same field.

additional information

matrices

We know we can represent Linear Maps as matricies.

So, given some \(A\), we have an inverse \(A^{-1}\).