Fix division by zero in ValueIteration._boundIter
#32
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mdp.ValueIterationusesValueIteration._boundIterto setself.max_iterfor discounted MDPs. This is based on the span: the difference between the minimum and maximum values after one step of the Bellman operator.The problem is for some MDPs the value can be identical for all states after a single application of the Bellman operator. This happens when$R(s,a)$ is equal to $Q(s,a)$ -- not common, but it does happen (e.g. any MDP with an all-zero reward is a degenerate example). In this case,
spanis0andmax_iterbecomes negative infinity.If my understanding of the bound is correct, in this case we actually don't need to perform any iterations of value iteration -- the all-zero initialisation is OK. So I've added an explicit check that sets
max_iter = 0in this case avoiding the division by zero. I've also added a regression test for the all-zero MDP.Some doctests are failing but they were failing before. All other tests are passing on my machine.