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Title: Learning Finite State Representations of Recurrent Policy Networks

Paper content:
Recurrent neural networks (RNNs) are an effective representation of control policies for a wide range of reinforcement and imitation learning problems.
RNN policies, however, are particularly difficult to explain, understand, and analyze due to their use of continuous-valued memory vectors and observation features.
In this paper, we introduce a new technique, Quantized Bottleneck Insertion, to learn finite representations of these vectors and features.
The result is a quantized representation of the RNN that can be analyzed to improve our understanding of memory use and general behavior.
We present results of this approach on synthetic environments and six Atari games.
The resulting finite representations are surprisingly small in some cases, using as few as 3 discrete memory states and 10 observations for a perfect Pong policy.
We also show that these finite policy representations lead to improved interpretability.
Deep reinforcement learning (RL) and imitation learning (IL) have demonstrated impressive performance across a wide range of applications.
Unfortunately, the learned policies are difficult to understand and explain, which limits the degree that they can be trusted and used in high-stakes applications.
Such explanations are particularly problematic for policies represented as recurrent neural networks (RNNs) BID16 BID14 , which are increasingly used to achieve state-of-the-art performance BID15 BID21 .
This is because RNN policies use internal memory to encode features of the observation history, which are critical to their decision making, but extremely difficult to interpret.
In this paper, we take a step towards comprehending and explaining RNN policies by learning more compact memory representations.Explaining RNN memory is challenging due to the typical use of high-dimensional continuous memory vectors that are updated through complex gating networks (e.g. LSTMs, GRUs BID10 BID5 ).
We hypothesize that, in many cases, the continuous memory is capturing and updating one or more discrete concepts.
If exposed, such concepts could significantly aid explainability.
This motivates attempting to quantize the memory and observation representation used by an RNN to more directly capture those concepts.
In this case, understanding the memory use can be approached by manipulating and analyzing the quantized system.
Of course, not all RNN policies will have compact quantized representations, but many powerful forms of memory usage can be captured in this way.Our main contribution is to introduce an approach for transforming an RNN policy with continuous memory and continuous observations to a finite-state representation known as a Moore Machine.
To accomplish this we introduce the idea of Quantized Bottleneck Network (QBN) insertion.
QBNs are simply auto-encoders, where the latent representation is quantized.
Given a trained RNN, we train QBNs to encode the memory states and observation vectors that are encountered during the RNN operation.
We then insert the QBNs into the trained RNN policy in place of the "wires" that propagated the memory and observation vectors.
The combination of the RNN and QBN results in a policy represented as a Moore Machine Network (MMN) with quantized memory and observations that is nearly equivalent to the original RNN.
The MMN can be used directly or fine-tuned to improve on inaccuracies introduced by QBN insertion.While training quantized networks is often considered to be quite challenging, we show that a simple approach works well in the case of QBNs.
In particular, we demonstrate that "straight through" gradient estimators as in BID1 BID6 are quite effective.We present experiments in synthetic domains designed to exercise different types of memory use as well as benchmark grammar learning problems.
Our approach is able to accurately extract the ground-truth MMNs, providing insight into the RNN memory use.
We also did experiments on 6 Atari games using RNNs that achieve state-of-the-art performance.
We show that in most cases it is possible to extract near-equivalent MMNs and that the MMNs can be surprisingly small.
Further, the extracted MMNs give insights into the memory usage that are not obvious based on just observing the RNN policy in action.
For example, we identify games where the RNNs do not use memory in a meaningful way, indicating the RNN is implementing purely reactive control.
In contrast, in other games, the RNN does not use observations in a meaningful way, which indicates that the RNN is implementing an open-loop controller.

assistant: text: Extracting a finite state machine from a recurrent neural network via quantization for the purpose of interpretability with experiments on Atari.