Stochastic Fairness and Language-Theoretic Fairness in Planning on Nondeterministic Domains
This clarifies a confusion in planning literature for researchers, offering corrected algorithms and proofs, though it is incremental in addressing specific fairness definitions.
The paper addresses two fairness notions in nondeterministic planning, showing they diverge for temporal goals and that existing algorithms incorrectly applied state-action fairness reductions. It provides a sound and complete algorithm for state-action fair planning with LTL/LTLf goals and proves a lower bound, demonstrating stochastic fairness is more well-behaved.
We address two central notions of fairness in the literature of planning on nondeterministic fully observable domains. The first, which we call stochastic fairness, is classical, and assumes an environment which operates probabilistically using possibly unknown probabilities. The second, which is language-theoretic, assumes that if an action is taken from a given state infinitely often then all its possible outcomes should appear infinitely often (we call this state-action fairness). While the two notions coincide for standard reachability goals, they diverge for temporally extended goals. This important difference has been overlooked in the planning literature, and we argue has led to confusion in a number of published algorithms which use reductions that were stated for state-action fairness, for which they are incorrect, while being correct for stochastic fairness. We remedy this and provide an optimal sound and complete algorithm for solving state-action fair planning for LTL/LTLf goals, as well as a correct proof of the lower bound of the goal-complexity (our proof is general enough that it provides new proofs also for the no-fairness and stochastic-fairness cases). Overall, we show that stochastic fairness is better behaved than state-action fairness.