We introduce the notion of LImited Memory Influence Diagram (LIMID) to desc
ribe multistage decision problems in which the traditional assumption of no
forgetting is relaxed. This can be relevant in situations with multiple de
cision makers or when decisions must be prescribed under memory constraints
, such as in partially observed Markov decision processes (POMDPs). We give
an algorithm for improving any given strategy by local computation of sing
le policy updates and investigate conditions for the resulting strategy to
be optimal.