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We consider the problem of learning an inner approximation of the region ofattraction (ROA) of an asymptotically stable equilibrium point without anexplicit model of the dynamics. Rather than leveraging approximate models withbounded uncertainty to find a (robust) invariant set contained in the ROA, wepropose to learn sets that satisfy a more relaxed notion of containment knownas recurrence. We define a set to be $\tau$-recurrent (resp. $k$-recurrent) ifevery trajectory that starts within the set, returns to it after at most $\tau$seconds (resp. $k$ steps). We show that under mild assumptions a$\tau$-recurrent set containing a stable equilibrium must be a subset of itsROA. We then leverage this property to develop algorithms that compute innerapproximations of the ROA using counter-examples of recurrence that areobtained by sampling finite-length trajectories. Our algorithms process samplessequentially, which allow them to continue being executed even after an initialoffline training stage. We further provide an upper bound on the number ofcounter-examples used by the algorithm, and almost sure convergence guarantees.

Model-free Learning of Regions of Attraction via Recurrent Sets