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In many synthesis problems, it can be essential to generate implementationswhich not only satisfy functional constraints but are also randomized toimprove variety, robustness, or unpredictability. The recently-proposedframework of control improvisation (CI) provides techniques for thecorrect-by-construction synthesis of randomized systems subject to hard andsoft constraints. However, prior work on CI has focused on qualitativespecifications, whereas in robotic planning and other areas we often havequantitative quality metrics which can be traded against each other. Forexample, a designer of a patrolling security robot might want to know by howmuch the average patrol time needs to be increased in order to ensure that aparticular aspect of the robot's route is sufficiently diverse and henceunpredictable. In this paper, we enable this type of application bygeneralizing the CI problem to support quantitative soft constraints whichbound the expected value of a given cost function, and randomness constraintswhich enforce diversity of the generated traces with respect to a given labelfunction. We establish the basic theory of labelled quantitative CI problems,and develop efficient algorithms for solving them when the specifications areencoded by finite automata. We also provide an approximate improvisationalgorithm based on constraint solving for any specifications encodable asBoolean formulas. We demonstrate the utility of our problem formulation andalgorithms with experiments applying them to generate diverse near-optimalplans for robotic planning problems.

Randomized Synthesis for Diversity and Cost Constraints with Control Improvisation