---
title: "best-action worst-state"
type: concept
related: [Alpha Vector, Worst Possible State]
source: https://www.jemoka.com/posts/kbhworst_possible_state/
confidence: high
status: active
---

best-action worst-state is a lower bound for alpha vectors:
\begin{equation} r_{baws} = \max_{a} \sum_{k=1}^{\infty} \gamma^{k-1} \min_{s}R(s,a) \end{equation}
The alpha vector corresponding to this system would be the same \(r_{baws}\) at each slot.
which should give us the highest possible reward possible given we always pick the most optimal actions while being stuck in the worst state
