  We consider the problem of finding good finite-horizon policies for POMDPs
under the expected reward metric. The policies considered are {em free
finite-memory policies with limited memory}; a policy is a mapping from the
space of observation-memory pairs to the space of action-memeory pairs (the
policy updates the memory as it goes), and the number of possible memory states
is a parameter of the input to the policy-finding algorithms. The algorithms
considered here are preliminary implementations of three search heuristics:
local search, simulated annealing, and genetic algorithms. We compare their
outcomes to each other and to the optimal policies for each instance. We
compare run times of each policy and of a dynamic programming algorithm for
POMDPs developed by Hansen that iteratively improves a finite-state controller
--- the previous state of the art for finite memory policies. The value of the
best policy can only improve as the amount of memory increases, up to the
amount needed for an optimal finite-memory policy. Our most surprising finding
is that more memory helps in another way: given more memory than is needed for
an optimal policy, the algorithms are more likely to converge to optimal-valued
policies.
