Bouajjani, A.
; Holík, L.
; Wu, Z.
(Ed.)

When omega-regular objectives were first proposed in model-free reinforcement learning (RL) for controlling MDPs, deterministic Rabin automata were used in an attempt to provide a direct translation from their transitions to scalar values. While these translations failed, it has turned out that it is possible to repair them by using good-for-MDPs (GFM) Buechi automata instead. These are nondeterministic Buechi automata with a restricted type of nondeterminism, albeit not as restricted as in good-for-games automata. Indeed, deterministic Rabin automata have a pretty straightforward translation to such GFM automata, which is bi-linear in the number of states and pairs. Interestingly, the same cannot be said for deterministic Streett automata: a translation to nondeterministic Rabin or Buechi automata comes at an exponential cost, even without requiring the target automaton to be good-for-MDPs. Do we have to pay more than that to obtain a good-for-MDPs automaton? The surprising answer is that we have to pay significantly less when we instead expand the good-for-MDPs property to alternating automata: like the nondeterministic GFM automata obtained from deterministic Rabin automata, the alternating good-for-MDPs automata we produce from deterministic Streett automata are bi-linear in the size of the deterministic automaton and its index. They can therefore be exponentially more succinct than the minimal nondeterministic Buechi automaton.

more »
« less