text: In this paper, we present a link between preference-based and multiobjective sequential decision-making. While transforming a multiobjective problem to a preference-based one is quite natural, the other direction is a bit less obvious. We present how this transformation (from preference-based to multiobjective) can be done under the classic condition that preferences over histories can be represented by additively decomposable utilities and that the decision criterion to evaluate policies in a state is based on expectation. This link yields a new source of multiobjective sequential decision-making problems (i.e., when reward values are unknown) and justifies the use of solving methods developed in one setting in the other one.
  @cite_25: The procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted Tchebycheff metric. Using ‘filtering’ techniques, maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration. The procedure has the advantage that it can converge to non-extreme final solutions. Especially suitable for multiple objective linear programming, the procedure is also applicable to integer and nonlinear multiple objective programs.
  @cite_12: Specifying the reward function of a Markov decision process (MDP) can be demanding, requiring human assessment of the precise quality of, and tradeoffs among, various states and actions. However, reward functions often possess considerable structure which can be leveraged to streamline their specification. We develop new, decision-theoretically sound heuristics for eliciting rewards for factored MDPs whose reward functions exhibit additive independence. Since we can often find good policies without complete reward specification, we also develop new (exact and approximate) algorithms for robust optimization of imprecise-reward MDPs with such additive reward. Our methods are evaluated in two domains: autonomic computing and assistive technology.
summary: A final approach to multiobjective problem assumes an interactive setting where a human expert is present and can provide additional preferential information (i.e., how to trade-off between different objectives). This approach loops between the following two steps until a certain criterion is satisfied (e.g., the expert is satisfied with a proposed solution or there is only one solution left): show potential solutions or ask query to the expert receive a feedback answer from the expert The feedback answer from the expert allows to guide the search for a preferred solution among all Pareto-optimal ones @cite_25 , or elicit unknown parameters of user preference model @cite_12 .