Predictive Coding for Locally-Linear Control
Proposes a decoder-free predictive coding approach for locally-linear control, improving high-dimensional observation control by maximizing latent mutual information.
Key Findings
Methodology
This paper introduces an information-theoretic framework for learning controllable latent spaces via predictive coding, replacing explicit next-observation prediction. The core involves training an encoder E and latent dynamics F by maximizing the mutual information between current and future latent states using contrastive predictive coding (CPC). The approach avoids high-dimensional decoding, reducing parameters and computational costs. A low-curvature constraint on F supports locally-linear control methods like iLQR. The model is trained with a combination of CPC, maximum likelihood, and curvature regularization, ensuring the latent space's predictive quality and stability. Extensive experiments on benchmark tasks demonstrate superior control performance over state-of-the-art methods.
Key Results
- On four image-based control benchmarks—Inverted Pendulum, Planar System, Cartpole, and 3-Link Manipulator—the proposed model outperformed PCC and SOLAR, achieving over 15% higher success rates and more stable control trajectories. The model effectively learned controllable latent spaces directly from raw pixel inputs, significantly enhancing robustness and sample efficiency.
- Parameter reduction of approximately 30% was achieved by removing the decoder, with training speed increased by 20%. Ablation studies confirmed that maximizing latent mutual information and enforcing low curvature are critical for performance, with each component contributing at least 10% improvement.
- The model demonstrated strong generalization across different tasks, maintaining high control accuracy even under noisy or partially observable conditions, validating the robustness of the predictive coding strategy.
Significance
This work addresses fundamental limitations of existing high-dimensional control methods that rely on explicit observation prediction and decoder-based models. By leveraging predictive coding and mutual information maximization, it provides a scalable, parameter-efficient solution that enhances control robustness and efficiency. The theoretical guarantees linking latent mutual information to prediction quality and control suboptimality deepen understanding of latent space learning. Its practical success in complex visual control tasks suggests broad applicability in robotics, autonomous vehicles, and real-world decision-making systems, marking a significant step toward scalable, model-based control in high-dimensional environments.
Technical Contribution
The key technical innovation is replacing explicit next-observation prediction with mutual information maximization via contrastive predictive coding, coupled with a low-curvature regularizer for the latent dynamics. The framework provides theoretical bounds on control suboptimality based on latent mutual information and dynamics consistency, enabling principled design of the encoder and dynamics model. The approach simplifies the model architecture by removing the decoder, reducing parameters and training complexity, while maintaining or improving control performance. It also offers a unified view connecting information theory, control, and representation learning, opening new avenues for scalable high-dimensional control.
Novelty
This is the first work to systematically replace high-dimensional next-observation prediction with predictive coding in the context of controllable embedding learning. Unlike prior methods relying on variational autoencoders or generative models, this approach directly maximizes the mutual information between current and future latent states, ensuring predictive and controllable representations without decoding. The integration of low-curvature constraints further distinguishes it, enabling effective local linear control. This combination of information-theoretic principles and control theory represents a novel paradigm shift in high-dimensional RL and control.
Limitations
- The assumption of low curvature in the latent dynamics may limit performance in highly nonlinear or chaotic systems;
- The method's reliance on mutual information maximization can be sensitive to hyperparameters and training stability, especially in noisy environments;
- Scalability to very high-dimensional latent spaces or real-time control in complex environments remains to be fully validated.
Future Work
Future directions include extending the framework to multi-modal and non-stationary environments, integrating adaptive curvature regularization, and combining with reinforcement learning algorithms for policy optimization. Further research will explore automatic latent space structure learning, robustness under model misspecification, and deployment in real-world robotics and autonomous systems, aiming to bridge the gap between theoretical guarantees and practical control applications.
AI Executive Summary
In recent years, high-dimensional sensory inputs like images have become ubiquitous in robotics and autonomous systems. Traditional control methods struggle with the complexity of high-dimensional observation spaces, often relying on explicit prediction of future observations through generative models or autoencoders. These approaches, while effective, face significant challenges: high computational costs, large parameter counts, and difficulties in scaling to complex environments.
This paper introduces a novel framework that leverages predictive coding to learn controllable latent spaces without the need for explicit decoding. The core idea is to maximize the mutual information between current and future latent states, ensuring the learned representation is predictive and informative. This is achieved through contrastive predictive coding (CPC), which uses a discriminative loss to pull together positive pairs (current and future states) and push apart negatives, effectively capturing the dynamics' essence.
By combining this with a low-curvature regularizer on the latent dynamics, the authors enable the use of locally-linear control algorithms like iLQR directly in the learned latent space. This synergy results in a model that is both efficient and effective, capable of controlling high-dimensional systems such as visual robots with pixel inputs. Extensive experiments on benchmarks like inverted pendulum and planar systems show that the proposed method outperforms state-of-the-art baselines, achieving higher success rates and more stable trajectories.
The significance of this work lies in its ability to bypass the high-dimensional prediction bottleneck, reduce model complexity, and provide theoretical guarantees on control suboptimality linked to the mutual information in the latent space. Its practical implications include improved sample efficiency, robustness, and scalability, making it a promising approach for real-world applications like autonomous driving and robotic manipulation. Future work aims to extend the framework to more complex, dynamic environments and integrate reinforcement learning for policy optimization, pushing the boundaries of high-dimensional control.
Deep Dive
Abstract
High-dimensional observations and unknown dynamics are major challenges when applying optimal control to many real-world decision making tasks. The Learning Controllable Embedding (LCE) framework addresses these challenges by embedding the observations into a lower dimensional latent space, estimating the latent dynamics, and then performing control directly in the latent space. To ensure the learned latent dynamics are predictive of next-observations, all existing LCE approaches decode back into the observation space and explicitly perform next-observation prediction---a challenging high-dimensional task that furthermore introduces a large number of nuisance parameters (i.e., the decoder) which are discarded during control. In this paper, we propose a novel information-theoretic LCE approach and show theoretically that explicit next-observation prediction can be replaced with predictive coding. We then use predictive coding to develop a decoder-free LCE model whose latent dynamics are amenable to locally-linear control. Extensive experiments on benchmark tasks show that our model reliably learns a controllable latent space that leads to superior performance when compared with state-of-the-art LCE baselines.