Why Linear Recurrent Memory Works in Partially Observable Reinforcement Learning
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| Authors | Yike Zhao et al. |
| Year | 2026 |
| Field | Machine Learning |
| arXiv | 2605.31261 |
| Download | |
| Categories | cs.LG, cs.AI, stat.ML |
Abstract
The family of linear recurrent neural networks has shown strong performance as recurrent memory units in partially observable reinforcement learning. We provide a theoretical justification for their empirical effectiveness by constructing and studying two linear filters: (i) the first exactly reproduces the pre-softmax logits of the belief vector in a hidden Markov model (HMM) under a deterministic transition matrix, thereby serving as a sufficient statistic for optimal policy learning, (ii) the second achieves vanishing state-decoding error under a nearly deterministic transition matrix, thus reducing state ambiguity to near zero. The results extend to action-controlled HMMs, where the corresponding linear filters become time-varying with action-dependent dynamics. We illustrate our main results through numerical experiments and further show that the constructed linear filter serves as a strong feature extractor in a small reinforcement learning game.
Engineering Breakdown
The Problem
The family of linear recurrent neural networks has shown strong performance as recurrent memory units in partially observable reinforcement learning.
The Approach
We provide a theoretical justification for their empirical effectiveness by constructing and studying two linear filters: (i) the first exactly reproduces the pre-softmax logits of the belief vector in a hidden Markov model (HMM) under a deterministic transition matrix, thereby serving as a sufficient statistic for optimal policy learning, (ii) the second achieves vanishing state-decoding error under a nearly deterministic transition matrix, thus reducing state ambiguity to near zero.
Key Results
We illustrate our main results through numerical experiments and further show that the constructed linear filter serves as a strong feature extractor in a small reinforcement learning game.
Research Areas
This paper contributes to the following areas of AI/ML engineering:
- Model training
- Generalization
- Optimization
- Supervised learning
- Deep learning
- Recurrent
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