The oxidation states of iodine in the given compounds are as follows:
- In \( \text{HI} \), iodine has an oxidation state of \(-1\).
- In \( \text{ICl} \), iodine has an oxidation state of \(-1\).
- In \( \text{HIO}_3 \), iodine has an oxidation state of \(+5\).
- In \( \text{HIO}_2 \), iodine has an oxidation state of \(+3\).
- In \( \text{KIO}_3 \), iodine has an oxidation state of \(+5\).
Thus, the correct order of increasing oxidation states of iodine is:
\[
\text{HI}<\text{ICl}<\text{HIO}_2<\text{KIO}_3
\]