Generalization in Monitored Markov Decision Processes (Mon-MDPs)

Abstract: Reinforcement learning (RL) typically models the interaction between the agent and environment as a Markov decision process (MDP), where the rewards that guide the agent's behavior are always observable. However, in many real-world scenarios, rewards are not always observable, which can be modeled as a monitored Markov decision process (Mon-MDP). Prior work on Mon-MDPs have been limited to simple, tabular cases, restricting their applicability to real-world problems. This work explores Mon-MDPs using function approximation (FA) and investigates the challenges involved. We show that combining function approximation with a learned reward model enables agents to generalize from monitored states with observable rewards, to unmonitored environment states with unobservable rewards. Therefore, we demonstrate that such generalization with a reward model achieves near-optimal policies in environments formally defined as unsolvable. However, we identify a critical limitation of such function approximation, where agents incorrectly extrapolate rewards due to overgeneralization, resulting in undesirable behaviors. To mitigate overgeneralization, we propose a cautious police optimization method leveraging reward uncertainty. This work serves as a step towards bridging this gap between Mon-MDP theory and real-world applications.

Generalization in Monitored Markov Decision Processes (Mon-MDPs)

The paper "Generalization in Monitored Markov Decision Processes (Mon-MDPs)" addresses a compelling challenge in reinforcement learning (RL): how to model environments where reward signals are not always observable. Traditional RL models, which treat these as Markov decision processes (MDPs), rely on consistently observable rewards, a condition often violated in real-world applications. This work explores the Monitored Markov Decision Processes (Mon-MDPs) framework as a novel solution to this problem, in which rewards are sometimes unobservable.

Overview

The Mon-MDP framework expands the MDP formulation by introducing a separate monitor MDP that dictates when rewards are observable. The authors' key contribution is extending Mon-MDPs to non-tabular settings using function approximation (FA), as previous research has been constrained to simple, tabular cases. The paper demonstrates that integrating FA with a learned reward model enables agents to generalize from monitored states, where rewards are observable, to unmonitored states, where rewards are not directly accessible. This approach permits the derivation of near-optimal policies in certain scenarios defined as unsolvable in prior literature.

Methodology

The authors employ a function approximator for the reward model, utilizing neural network architectures that include two convolutional layers followed by fully connected layers. These networks learn both the reward function and the Q-values. The central observation is that this setup allows for effective generalization in Mon-MDPs – agents can infer appropriate actions in states without observable rewards by leveraging learned representations from states with observable rewards.

Key Findings

1. The paper empirically substantiates that reward models in combination with FA facilitate better policy learning compared to treating unobservable rewards as zero or discarding them, notably demonstrated in a plant-watering robot simulation.
2. Generalization from monitored states with observable rewards to unmonitored states is feasible, even achieving optimal outcomes in environments previously deemed unsolvable under tabular assumptions.
3. There is a notable risk of overgeneralization with FA; agents might incorrectly extrapolate reward estimations to novel states, potentially resulting in suboptimal or unsafe behaviors.

Limitations and Mitigation Strategies

A critical limitation identified is the overgeneralization inherent in function approximation, which can lead to incorrect reward predictions in states not well represented during training. The authors propose a novel cautious policy optimization approach that incorporates reward uncertainty, leveraging $k$-of-$N$ counterfactual regret minimization (CFR) to ensure robust policy learning. This method effectively mitigates overgeneralization issues, steering the agent towards safer behavior in the presence of uncertainty.

Implications and Future Work

This research extends the applicability of Mon-MDPs to more complex, real-world scenarios, emphasizing the need for adaptability when rewards are inconsistently observable. Practically, it signifies a potential breakthrough for robotics, autonomous systems, and industrial automation domains where occasional feedback is unavailable or impractical.

Further research directions include adapting Mon-MDPs to continuous action spaces, developing computationally efficient methods for capturing epistemic uncertainty, and understanding plasticity loss phenomena when utilizing deep learning in Mon-MDPs. Moreover, the exploration of Mon-MDPs in real-world applications would provide valuable insights into their practical utility and robustness.

Overall, this paper represents a thoughtful advancement in the modeling of complex decision processes where observable feedback is intermittently available, paving the way for further innovations in the field of RL and AI.