In this paper, we propose a novel policy optimization framework that maximizes Return on Investment (ROI) of a policy using a fixed dataset within a Markov Decision Process (MDP) equipped with a cost function. ROI, defined as the ratio between the return and the accumulated cost of a policy, serves as a measure of efficiency of the policy. Despite the importance of maximizing ROI in various applications, it remains a challenging problem due to its nature as a ratio of two long-term values: return and accumulated cost. To address this, we formulate the ROI maximizing reinforcement learning problem as a linear fractional programming. We then incorporate the stationary distribution correction (DICE) framework to develop a practical offline ROI maximization algorithm.Our proposed algorithm, ROIDICE, yields an efficient policy that offers a superior trade-off between return and accumulated cost compared to policies trained using existing frameworks.

In economics, Return on Investment (ROI) is a financial metric used to evaluate the profitability of an investment relative to its cost. The concept of ROI originates from the work of [5] and is widelyregardedasavaluable metricbythemajority ofmarketingmanagers [4].

Decision Process (MDP) equipped with a cost function.

In this paper, we propose a novel policy optimization framework that maximizes Return on Investment (ROI) of a policy using a fixed dataset within a Markov Decision Process (MDP) equipped with a cost function. ROI, defined as the ratio between the return and the accumulated cost of a policy, serves as a measure of efficiency of the policy. Despite the importance of maximizing ROI in various applications, it remains a challenging problem due to its nature as a ratio of two long-term values: return and accumulated cost. To address this, we formulate the ROI maximizing reinforcement learning problem as a linear fractional programming. We then incorporate the stationary distribution correction (DICE) framework to develop a practical offline ROI maximization algorithm.Our proposed algorithm, ROIDICE, yields an efficient policy that offers a superior trade-off between return and accumulated cost compared to policies trained using existing frameworks.