Imprecise-reward Markov decision processes (IRMDPs) are MDPs in which the reward function is only partially specified (e.g., by some elicitation process). Recent work using minimax regret to solve IRMDPs has shown, despite theoretical intractability, how the set of policies that are nondom- inated w.r.t. reward uncertainty can be exploited to accelerate regret computation. However, the number of nondominated policies is generally so large as to undermine this leverage. In this paper, we show how the quality of the approximation can be improved online by pruning/adding nondominated policies during reward elicitation, while maintain- ing computational tractability. Drawing insights from the POMDP literature, we also develop a new anytime algorithm for constructing the set of nondominated policies with provable (anytime) error bounds.

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.

The precise specification of reward functions for Markov decision processes (MDPs) is often extremely difficult, motivating research into both reward elicitation and the robust solution of MDPs with imprecisely specified reward (IRMDPs). We develop new techniques for the robust optimization of IRMDPs, using the minimax regret decision criterion, that exploit the set of nondominated policies, i.e., policies that are optimal for some instantiation of the imprecise reward function. Drawing parallels to POMDP value functions, we devise a Witness-style algorithm for identifying nondominated policies. We also examine several new algorithms for computing minimax regret using the nondominated set, and examine both practically and theoretically the impact of approximating this set. Our results suggest that a small subset of the nondominated set can greatly speed up computation, yet yield very tight approximations to minimax regret.

Most models of utility elicitation in decision support and interactive optimization assume a predefined set of "catalog" features over which user preferences are expressed. However, users may differ in the features over which they are most comfortable expressing their preferences. In this work we consider the problem of feature elicitation: a user's utility function is expressed using features whose definitions (in terms of "catalog" features) are unknown. We cast this as a problem of concept learning, but whose goal is to identify only enough about the concept to enable a good decision to be recommended. We describe computational procedures for identifying optimal alternatives w.r.t. minimax regret in the presence of concept uncertainty; and describe several heuristic query strategies that focus on reduction of relevant concept uncertainty.