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_3: From the Publisher: The past decade has seen considerable theoretical and applied research on Markov decision processes, as well as the growing use of these models in ecology, economics, communications engineering, and other fields where outcomes are uncertain and sequential decision-making processes are needed. A timely response to this increased activity, Martin L. Puterman's new work provides a uniquely up-to-date, unified, and rigorous treatment of the theoretical, computational, and applied research on Markov decision process models. It discusses all major research directions in the field, highlights many significant applications of Markov decision processes models, and explores numerous important topics that have previously been neglected or given cursory coverage in the literature. Markov Decision Processes focuses primarily on infinite horizon discrete time models and models with discrete time spaces while also examining models with arbitrary state spaces, finite horizon models, and continuous-time discrete state models. The book is organized around optimality criteria, using a common framework centered on the optimality (Bellman) equation for presenting results. The results are presented in a "theorem-proof" format and elaborated on through both discussion and examples, including results that are not available in any other book. A two-state Markov decision process model, presented in Chapter 3, is analyzed repeatedly throughout the book and demonstrates many results and algorithms. Markov Decision Processes covers recent research advances in such areas as countable state space models with average reward criterion, constrained models, and models with risk sensitive optimality criteria. It also explores several topics that have received little or no attention in other books, including modified policy iteration, multichain models with average reward criterion, and sensitive optimality. In addition, a Bibliographic Remarks section in each chapter comments on relevant historic
summary: A reinforcement learning problem is usually defined using the Markov Decision Process (MDP) model. A standard MDP @cite_3 is defined as a tuple @math where: @math is a finite set of states, @math is a finite set of actions, @math is a transition function with @math being the probability of reaching state @math after executing action @math in state @math , @math is a reward function with @math being the immediate numerical environmental feedback received by the agent after performing action @math in state @math . In this framework, a @math -step history @math is a sequence of state-action: where @math and @math . The value of such a history @math is defined as: where @math is a discount factor. A policy specifies how to choose an action in every state. A deterministic policy @math is a function from the set of states to the set of actions, while a randomized policy @math states the probability @math of choosing an action @math in a state @math .