  A Random Walk in Changing Environment (RWCE) is a weighted random walk on a
locally finite, connected graph $G$ with random, time-dependent edge-weights.
This includes self-interacting random walks, where the edge-weights depend on
the history of the process. In general, even the basic question of recurrence
or transience for RWCEs is difficult, especially when the underlying graph
contains cycles. In this note, we derive a condition for recurrence or
transience that is too restrictive for classical RWCEs but instead works for
any graph $G.$ Namely, we show that any bounded RWCE on $G$ with "slowly"
changing edge-weights inherits the recurrence or transience of the initial
weighted graph.
