Recursive Reward Aggregation

TL;DR

This paper introduces a recursive reward aggregation framework in reinforcement learning that generalizes reward functions through algebraic methods, enabling flexible behavior alignment without redesigning rewards.

Contribution

It presents an algebraic perspective on MDPs that derives Bellman equations from recursive reward aggregations, broadening the scope of reward functions in RL.

Findings

Effective optimization of diverse objectives demonstrated

Seamless integration with value-based and actor-critic algorithms

Applicable to both deterministic and stochastic environments

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 (MDPs), 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 Sharpe ratio. Our approach applies to both deterministic and stochastic settings and integrates seamlessly with value-based and actor-critic algorithms. Experimental results demonstrate that our approach effectively optimizes diverse objectives, highlighting its versatility and potential for real-world applications.