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Embed to Control Partially Observed Systems: Representation Learning with Provable Sample Efficiency


Core Concepts
The core message of this article is that by exploiting the low-rank structure in the state transition of POMDPs, it is possible to learn a minimal but sufficient representation of the observation and state histories, enabling sample-efficient reinforcement learning in POMDPs with infinite observation and state spaces.
Abstract
The article proposes a reinforcement learning algorithm called Embed to Control (ETC) that learns the representation at two levels: For each step, ETC learns to represent the state with a low-dimensional feature, which factorizes the transition kernel. Across multiple steps, ETC learns to represent the full history with a low-dimensional embedding, which assembles the per-step feature. The key insights are: The low-rank structure in the state transition allows for efficient representation learning and reinforcement learning. The future and past sufficiency assumptions ensure that the density of the state can be identified from the density of the future and past observations, respectively. ETC balances exploitation and exploration by constructing a confidence set of embeddings and conducting optimistic planning. ETC achieves an O(1/ε^2) sample complexity that scales polynomially with the horizon and the intrinsic dimension (the rank of the transition), bypassing the exponential dependence on the sizes of the observation and state spaces.
Stats
The article does not provide any specific numerical data or metrics. It focuses on the theoretical analysis of the proposed algorithm.
Quotes
None.

Key Insights Distilled From

by Lingxiao Wan... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2205.13476.pdf
Embed to Control Partially Observed Systems

Deeper Inquiries

What are some potential real-world applications of the low-rank POMDP model and the ETC algorithm

The low-rank POMDP model and the ETC algorithm have various potential real-world applications. One application could be in autonomous driving systems, where the model can help in decision-making processes based on partial observations and continuous state spaces. Another application could be in robotics, where the algorithm can assist in navigating complex environments with limited information. Additionally, the model and algorithm could be used in healthcare settings for personalized treatment recommendations based on patient data.

How would the performance of ETC compare to other POMDP solution methods, such as belief-based approaches or deep reinforcement learning techniques, in practical scenarios

The performance of ETC compared to other POMDP solution methods would depend on the specific characteristics of the problem at hand. In scenarios where the POMDP has a low-rank structure in the transition kernel, ETC may outperform belief-based approaches by efficiently learning representations and optimizing policies. However, in cases where the POMDP is more complex and does not exhibit a low-rank structure, deep reinforcement learning techniques may perform better due to their ability to handle high-dimensional and continuous state spaces.

Are there any limitations or assumptions of the low-rank POMDP model that may restrict its applicability in certain domains

One limitation of the low-rank POMDP model is that it assumes a specific structure in the transition kernel, which may not always hold true in real-world scenarios. This assumption could restrict the applicability of the model to POMDPs that do not exhibit a low-rank structure, limiting its effectiveness in more general settings. Additionally, the model's reliance on the future and past sufficiency assumptions may not always be feasible in practice, especially in dynamic environments where the information available may not fully capture the state of the system.
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