Global Reinforcement Learning: Beyond Linear and Convex Rewards via Submodular Semi-gradient Methods
This addresses a foundational problem in RL for applications like experiment design and risk-averse RL by enabling modeling of state interactions, though it is incremental as it builds on submodular optimization.
The paper tackles the limitation of classic Reinforcement Learning (RL) in modeling real-world applications with additive objectives by introducing Global RL (GRL), which defines rewards over trajectories to capture state interactions, and proposes an algorithm that converts GRL problems to classic RL with curvature-dependent approximation guarantees, demonstrating effectiveness empirically.
In classic Reinforcement Learning (RL), the agent maximizes an additive objective of the visited states, e.g., a value function. Unfortunately, objectives of this type cannot model many real-world applications such as experiment design, exploration, imitation learning, and risk-averse RL to name a few. This is due to the fact that additive objectives disregard interactions between states that are crucial for certain tasks. To tackle this problem, we introduce Global RL (GRL), where rewards are globally defined over trajectories instead of locally over states. Global rewards can capture negative interactions among states, e.g., in exploration, via submodularity, positive interactions, e.g., synergetic effects, via supermodularity, while mixed interactions via combinations of them. By exploiting ideas from submodular optimization, we propose a novel algorithmic scheme that converts any GRL problem to a sequence of classic RL problems and solves it efficiently with curvature-dependent approximation guarantees. We also provide hardness of approximation results and empirically demonstrate the effectiveness of our method on several GRL instances.