Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processes with Confounded Data

Core Concepts

This work proposes the Proxy variable Pessimistic Policy Optimization (P3O) algorithm, which provably addresses the challenges of confounding bias and distributional shift in offline reinforcement learning for partially observable Markov decision processes.

Abstract

The content discusses the problem of offline reinforcement learning (RL) in partially observable Markov decision processes (POMDPs), where the dataset only contains partial observations of the states. The key challenges are the confounding bias caused by the latent states simultaneously affecting the actions and observations, and the distributional shift between the behavior policy and the target policies.
To address these challenges, the authors propose the Proxy variable Pessimistic Policy Optimization (P3O) algorithm, which leverages tools from proximal causal inference to identify the value of each policy. Specifically:

P3O identifies the policy value using confounding bridge functions that satisfy a sequence of backward conditional moment equations, similar to the Bellman equations in classical RL.
P3O estimates these bridge functions via minimax estimation, and constructs a sequence of novel confidence regions to handle the distributional shift.
P3O then applies the pessimism principle to learn the optimal policy within the confidence regions.

Under a partial coverage assumption on the confounded dataset, the authors prove that P3O achieves a $\tilde{O}(n^{-1/2})$ suboptimality, where $n$ is the number of trajectories in the dataset. This establishes the first provably efficient offline RL algorithm for POMDPs with confounded data.

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Key Insights Distilled From

Pessimism in the Face of Confounders

by Miao Lu,Yife... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2205.13589.pdf

Deeper Inquiries

How can the proposed approach be extended to handle more general forms of confounding beyond the proxy variable assumption

To extend the proposed approach to handle more general forms of confounding beyond the proxy variable assumption, we can explore the use of more advanced causal inference techniques. One potential approach is to incorporate instrumental variables, which are variables that are correlated with the confounder but not directly with the outcome. By leveraging instrumental variables, we can disentangle the effects of the confounder on the action and observation variables more effectively. Additionally, we can consider using more complex causal inference models, such as structural equation modeling or Bayesian networks, to capture the intricate relationships between the latent variables and the observed variables in a more nuanced manner. These advanced techniques can help address more complex forms of confounding and improve the robustness of the algorithm in handling real-world scenarios with intricate causal structures.

What are the potential limitations of the partial coverage assumption, and how can it be further relaxed

The partial coverage assumption in the context of the proposed algorithm can have certain limitations that may impact the generalizability and effectiveness of the approach. One potential limitation is that the assumption may not hold in all real-world scenarios, leading to potential biases in the learned policy. To address this limitation, one approach is to relax the partial coverage assumption by incorporating techniques from transfer learning or domain adaptation. By leveraging knowledge from related domains or datasets with different coverage patterns, we can improve the generalizability of the learned policy and mitigate the impact of the partial coverage assumption. Additionally, ensemble learning techniques can be employed to combine multiple models trained on different subsets of the data to account for variations in coverage and improve the overall performance of the algorithm.

Can the ideas of P3O be applied to other reinforcement learning settings beyond offline POMDP, such as online RL or multi-agent RL

The ideas and principles of the P3O algorithm can be applied to other reinforcement learning settings beyond offline POMDP, such as online RL or multi-agent RL, with appropriate modifications and adaptations. In the context of online RL, the pessimism principle and minimax estimation techniques can be utilized to address the challenges of distributional shift and confounding bias in real-time decision-making scenarios. By incorporating online data collection and updating the policy iteratively, the algorithm can adapt to changing environments and improve decision-making performance over time. In the case of multi-agent RL, the concepts of proximal causal inference and confounding bridge functions can be extended to model complex interactions between multiple agents and infer optimal policies in a collaborative or competitive setting. By considering the interplay of latent variables and observed actions across multiple agents, the algorithm can facilitate more effective coordination and decision-making in multi-agent environments.