In Reinforcement Learning (RL), it is commonly assumed that an immediate reward signal is generated for each action taken by the agent, helping the agent maximize cumulative rewards to obtain the optimal policy. However, in many real-world scenarios, immediate reward signals are not obtainable; instead, agents receive a single reward that is contingent upon a partial sequence or a complete trajectory. In this work, we define this challenging problem as Reinforcement Learning from Bagged Reward (RLBR), where sequences of data are treated as bags with non-Markovian bagged rewards. We provide a theoretical study to establish the connection between RLBR and standard RL in Markov Decision Processes (MDPs). To effectively explore the reward distributions within these bags and enhance policy training, we propose a Transformer-based reward model, the Reward Bag Transformer, which employs a bidirectional attention mechanism to interpret contextual nuances and temporal dependencies within each bag. Our empirical evaluations reveal that the challenge intensifies as the bag length increases, leading to the performance degradation due to reduced informational granularity. Nevertheless, our approach consistently outperforms existing methods, demonstrating the least decline in efficacy across varying bag lengths and excelling in approximating the original MDP's reward distribution.
View on arXiv