Definition. Named reward channel [ftip-00DZ]

For a fixed task \(x\), let \(\mathcal Y_x\) be a finite response set and let a named reward channel be a map \(r:\mathcal Y_x\to \mathbb R\). A utility map \(u:\mathcal Y_x\to \mathbb R\) is a separate evaluation quantity.

If an interaction has state space \(\mathcal S\), action space \(\mathcal A\), and transition kernel \(K(\mathord {\cdot }\mid s,a)\), then \(K\) is a third object: changing \(K\) can change consequences without changing \(r\).