Analyzing and Bridging the Gap between Maximizing Total Reward and Discounted Reward in Deep Reinforcement Learning

The optimal objective is a fundamental aspect of reinforcement learning (RL), as it determines how policies are evaluated and optimized. While total return maximization is the ideal objective in RL, discounted return maximization is the practical objective due to its stability. This can lead to a misalignment of objectives. To better understand the problem, we theoretically analyze the performance gap between the policy maximizes the total return and the policy maximizes the discounted return. Our analysis reveals that increasing the discount factor can be ineffective at eliminating this gap when environment contains cyclic states,a frequent scenario. To address this issue, we propose two alternative approaches to align the objectives. The first approach achieves alignment by modifying the terminal state value, treating it as a tunable hyper-parameter with its suitable range defined through theoretical analysis. The second approach focuses on calibrating the reward data in trajectories, enabling alignment in practical Deep RL applications using off-policy algorithms. This method enhances robustness to the discount factor and improve performance when the trajectory length is large. Our proposed methods demonstrate that adjusting reward data can achieve alignment, providing an insight that can be leveraged to design new optimization objectives to fundamentally enhance the performance of RL algorithms.