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.
Classically, in reinforcement learning (RL), it is assumed that the agent does not know the transition and reward functions. In that case, an optimal policy has to be learned by interacting with the environment. Two main approaches can be distinguished here @cite_28 . The first (called indirect or model-based method), tries to first estimate the transition and reward functions and then use an MDP solving method on the learned environment model (e.g., @cite_13 ). The second (called direct or model-free method), searches for an optimal policy without trying to learn a model of the environment.
@cite_28 @cite_13
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The goal of reinforcement learning (RL) is to let an agent learn an optimal control policy in an unknown environment so that future expected rewards are maximized. The model-free RL approach directly learns the policy based on data samples. Although using many samples tends to improve the accuracy of policy learning, collecting a large number of samples is often expensive in practice. On the other hand, the model-based RL approach first estimates the transition model of the environment and then learns the policy based on the estimated transition model. Thus, if the transition model is accurately learned from a small amount of data, the model-based approach is a promising alternative to the model-free approach. In this paper, we propose a novel model-based RL method by combining a recently proposed model-free policy search method called policy gradients with parameter-based exploration and the state-of-the-art transition model estimator called least-squares conditional density estimation. Through experiments, we demonstrate the practical usefulness of the proposed method. Consider the problem of approximating the optimal policy of a Markov decision process (MDP) by sampling state transitions. In contrast to existing reinforcement learning methods that are based on successive approximations to the nonlinear Bellman equation, we propose a Primal-Dual @math Learning method in light of the linear duality between the value and policy. The @math learning method is model-free and makes primal-dual updates to the policy and value vectors as new data are revealed. For infinite-horizon undiscounted Markov decision process with finite state space @math and finite action space @math , the @math learning method finds an @math -optimal policy using the following number of sample transitions @math where @math is an upper bound of mixing times across all policies and @math is a parameter characterizing the range of stationary distributions across policies. The @math learning method also applies to the computational problem of MDP where the transition probabilities and rewards are explicitly given as the input. In the case where each state transition can be sampled in @math time, the @math learning method gives a sublinear-time algorithm for solving the averaged-reward MDP.