Tackling Decision Processes with Non-Cumulative Objectives using Reinforcement Learning
This work addresses a limitation in reinforcement learning for problems with non-cumulative objectives, offering a general solution that is incremental but broadens applicability across domains.
The paper tackles the problem of non-cumulative Markov decision processes (NCMDPs), where objectives like maximum reward or mean divided by standard deviation are used instead of cumulative sums, by introducing a general mapping to standard MDPs, enabling the use of existing techniques like reinforcement learning and showing improvements in performance and training time across tasks such as control, finance, and optimization.
Markov decision processes (MDPs) are used to model a wide variety of applications ranging from game playing over robotics to finance. Their optimal policy typically maximizes the expected sum of rewards given at each step of the decision process. However, a large class of problems does not fit straightforwardly into this framework: Non-cumulative Markov decision processes (NCMDPs), where instead of the expected sum of rewards, the expected value of an arbitrary function of the rewards is maximized. Example functions include the maximum of the rewards or their mean divided by their standard deviation. In this work, we introduce a general mapping of NCMDPs to standard MDPs. This allows all techniques developed to find optimal policies for MDPs, such as reinforcement learning or dynamic programming, to be directly applied to the larger class of NCMDPs. Focusing on reinforcement learning, we show applications in a diverse set of tasks, including classical control, portfolio optimization in finance, and discrete optimization problems. Given our approach, we can improve both final performance and training time compared to relying on standard MDPs.