Multi-objective controller synthesis concerns the problem of computing an optimal controller subject to multiple (possibly conflicting) objective properties. The relative importance of objectives is often specified by human decision-makers. However, there is inherent uncertainty in human preferences (e.g., due to different preference elicitation methods). In this paper, we formalize the notion of uncertain human preferences and present a novel approach that accounts for uncertain human preferences in the multi-objective controller synthesis for Markov decision processes (MDPs). Our approach is based on mixed-integer linear programming (MILP) and synthesizes a sound, optimally permissive multi-strategy with respect to a multi-objective property and an uncertain set of human preferences. Experimental results on a range of large case studies show that our MILP-based approach is feasible and scalable to synthesize sound, optimally permissive multi-strategies with varying MDP model sizes and uncertainty levels of human preferences. Evaluation via an online user study also demonstrates the quality and benefits of synthesized (multi-)strategies.
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