Alternating Good-for-MDP Automata
This provides a more efficient method for handling omega-regular objectives in reinforcement learning, addressing a specific bottleneck in automata theory.
The paper tackles the problem of translating deterministic Streett automata to good-for-MDP automata for model-free reinforcement learning, showing that using alternating automata yields a bi-linear size increase, which is exponentially more succinct than previous nondeterministic approaches.
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) Büchi automata instead. These are nondeterministic Büchi 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 Büchi 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-MDP automaton? The surprising answer is that we have to pay significantly less when we instead expand the good-for-MDP property to alternating automata: like the nondeterministic GFM automata obtained from deterministic Rabin automata, the alternating good-for-MDP automata we produce from deterministic Streett automata are bi-linear in the the size of the deterministic automaton and its index, and can therefore be exponentially more succinct than minimal nondeterministic Büchi automata.