Understanding the Limitations of Multistep Inverse Methods in Learning Control-Endogenous Dynamics

Core Concepts

Multistep inverse methods may fail to learn control-endogenous latent dynamics due to periodicity and other factors.

Abstract

In real-world control settings, learning a compact latent state representation is crucial for efficient planning. The Ex-BMDP model formalizes environments where observations can be factorized into controllable endogenous states and exogenous states. The AC-State method uses multistep-inverse prediction but may fail in certain cases due to limitations. A new algorithm, ACDF, combines multistep-inverse prediction with a latent forward model to guarantee correct inference of action-dependent latent state encoders. Empirical results show the effectiveness of ACDF in various environments. The technical assumptions made ensure the validity of the proposed methods.

Stats

x ∈ X can be factored into s ∈ S and e ∈ E.
D′ := 2D^2 + D is an upper bound on witness distance.
ϕ maps observations x to endogenous states S.
π(x) depends only on ϕ(x).
Sampling (xt = x, at = a, xt+k = x') occurs with fixed probability.

Quotes

"AC-State will fail to learn a correct latent representation of the agent-controllable factor of the state."
"We demonstrate that combining the multistep-inverse method with a latent forward dynamics model is sufficient to learn a control-endogenous latent encoder."

Key Insights Distilled From

Multistep Inverse Is Not All You Need

by Alexander Le... at arxiv.org 03-19-2024

https://arxiv.org/pdf/2403.11940.pdf

Deeper Inquiries

How can the limitations of multistep inverse methods be addressed in more complex environments

In more complex environments, the limitations of multistep inverse methods can be addressed by incorporating a latent forward dynamics model along with the multistep-inverse prediction. This combination, as demonstrated in the ACDF algorithm proposed in the context provided, has shown to be effective in learning control-endogenous latent representations even in cases where AC-State fails. By including a latent forward dynamics loss in addition to the multistep-inverse loss, it becomes possible to enforce that the learned endogenous states are compatible with deterministic dynamics. This approach not only improves sample efficiency but also reduces the dependence on the number of steps used for multistep predictions.

What are the implications of assuming coverage over X rather than S∗ × E∗

Assuming coverage over X rather than S∗ × E∗ has significant implications for data collection and analysis in Ex-BMDPs. By ensuring coverage over X, we guarantee that each observation x is sampled with fixed finite probability based on its reachability from other observations within a certain number of steps k. This approach allows for a more comprehensive understanding of how different observations relate to each other and how actions lead to transitions between these observations.
Additionally, this assumption enables us to consider all possible trajectories starting from any state x and reaching another state x' through action a within k steps. It ensures that our data collection mechanism covers all relevant transitions and provides insights into both endogenous and exogenous factors influencing these transitions.
By focusing on coverage over X, we create a robust framework for studying Ex-BMDPs without being limited by assumptions about initial distributions or independence between endogenous and exogenous states at specific time points.

How can these findings impact future research on learning control-endogenous dynamics

The findings regarding learning control-endogenous dynamics using techniques like ACDF can have profound implications for future research in reinforcement learning and representation learning domains. By addressing the limitations of multistep inverse methods through innovative approaches like combining them with latent forward dynamics models, researchers can enhance their ability to learn compact latent representations that capture essential information for efficient planning.
These advancements open up new possibilities for developing algorithms capable of extracting meaningful features from high-dimensional observation spaces while filtering out irrelevant noise or exogenous factors. The focus on control-relevant variables can lead to more interpretable models that facilitate decision-making processes in complex environments such as robotics or autonomous systems.
Overall, these findings pave the way for further exploration into optimal strategies for discovering accurate control-endogenous representations across various applications requiring intelligent decision-making capabilities based on rich observational data sources.