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Limit-average automata are weighted automata on infinite words that use average to aggregate the weights seen in infinite runs. We study approximate learning problems for limit-average automata in two settings: passive and active. In the passive learning case, we show that limit-average automata are not PAC-learnable as samples must be of exponential-size to provide (with good probability) enough details to learn an automaton. We also show that the problem of finding an automaton that fits adoi:10.4230/lipics.concur.2019.17 dblp:conf/concur/MichaliszynO19 fatcat:2wfyl3juwnagndmiibp34qdl4q