Recursive Reward Aggregation

Yuting Tang, Yivan Zhang, Johannes Ackermann, Yu-Jie Zhang, Soichiro Nishimori, Masashi Sugiyama

Keywords: Markov decision process, reward aggregation, policy preference, Bellman equation, algebraic data type, dynamic programming, recursion scheme, algebra fusion, bidirectional process

Abstract: In reinforcement learning (RL), aligning agent behavior with specific objectives typically requires careful design of the reward function, which can be challenging when the desired objectives are complex. In this work, we propose an alternative approach for flexible behavior alignment that eliminates the need to modify the reward function by selecting appropriate reward aggregation functions. By introducing an algebraic perspective on Markov decision processes, we show that the Bellman equations naturally emerge from the recursive generation and aggregation of rewards, allowing for the generalization of the standard discounted sum to other recursive aggregations, such as discounted max and variance-regularized mean. Our approach applies to both deterministic and stochastic settings and integrates seamlessly with value-based and policy-based RL algorithms. Experimental results demonstrate that our approach effectively optimizes diverse objectives, highlighting its versatility and potential for real-world applications.

Submission Number: 106