Learning Quantitative Automata Modulo Theories

We introduce QUINTIC, a general algorithm for actively learning quantitative automata from preferences. Quantitative automata evaluate input sequences by applying a valuation function---such as sum, product, or average---to the output labels of the states visited. Such models naturally arise in use cases ranging from probabilistic verification, sequence classification, and sequential decision making. However, existing learning approaches, such as variants of L*, weighted‐automata learning algorithms, and active learning preference‐driven methods, either assume finite output alphabets or restrict the valuation function to particular forms. QUINTIC utilizes a symbolic observation table and applies deductive reasoning with the assistance of an SMT solver to identify the correct minimal state, transition, and state label combination of the quantitative automaton. The deductive reasoning relies on the minimal combination of theories determined by the valuation function and output alphabet. Consequently, QUINTIC has completeness, minimalism, and query complexity guarantees, and learns quantitative automata across finite, integer, and rational outputs. Our extensive experiments show how QUINTIC scales under weak or strong feedback, and alternative MaxSMT objectives.