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This paper aims to introduce an adaptive preference elicitation method for interactive decision support in sequential decision problems. The Decision Maker's preferences are assumed to be representable by an additive utility, initially unknown or imperfectly known. We first study the determination of possibly optimal policies when admissible utilities are imprecisely defined by some linear constraints derived from observed preferences. Then, we introduce a new approach interleaving elicitation of utilities and backward induction to incrementally determine an optimal or near-optimal policy. We propose an interactive algorithm with performance guarantees and describe numerical experiments demonstrating the practical efficiency of our approach.