Model-Predictive Control via Cross-Entropy and Gradient-Based Optimization
Proposes a hybrid CEM and gradient descent method to improve high-dimensional model predictive control efficiency.
Key Findings
Methodology
This paper introduces a hybrid optimization framework combining the Cross-Entropy Method (CEM) with gradient descent for action sequence planning in high-dimensional spaces. The approach involves sampling action sequences from a Gaussian distribution, evaluating their rewards using learned dynamics and reward models, then refining the top K sequences via gradient steps. The distribution parameters are updated based on these refined sequences, enabling a balance of global exploration and local exploitation. The process iterates, improving convergence speed and solution quality. Experiments across simulated control tasks demonstrate that this method outperforms pure CEM in convergence speed by approximately 30%, achieves reward improvements of over 15%, and effectively avoids local minima, especially in environments with non-smooth dynamics.
Key Results
- In high-dimensional control environments (e.g., 20D action space), the hybrid method converged 30% faster than pure CEM, with reward gains exceeding 15%. In complex environments with contact discontinuities, it maintained high success rates where pure gradient methods failed. On benchmark tasks like Pendulum and Half-Cheetah, reward improvements averaged 12-18%, with fewer iterations needed. Ablation studies confirmed that combining global sampling with local gradient refinement yields superior results, especially as dimensionality increases.
- In robotic simulation environments, the approach achieved higher task success rates and more stable trajectories. For instance, in the OpenAI Gym Half-Cheetah, the reward increased by 18%, and convergence occurred 40% faster compared to baseline CEM. These results highlight the method’s robustness and efficiency in real-world control scenarios.
- Additional experiments in non-smooth contact environments showed that pure gradient descent often gets stuck in local optima, whereas the hybrid approach effectively navigates complex reward landscapes, demonstrating its practical advantage in challenging settings.
Significance
This work addresses the critical challenge of scalable, efficient planning in high-dimensional control tasks. By integrating the exploration strength of CEM with the fast local convergence of gradient descent, it offers a powerful tool for robotics, autonomous vehicles, and complex simulation environments. The approach significantly reduces computational costs and improves solution quality, paving the way for more reliable and real-time capable control systems. Its ability to handle non-smooth dynamics broadens its applicability to real-world scenarios involving contact, friction, and other discontinuities.
Technical Contribution
The core technical innovation lies in the iterative interleaving of sampling-based global search with gradient-based local refinement. The algorithm maintains a Gaussian distribution over action sequences, which is updated based on the top-performing sequences after gradient refinement. This hybrid process leverages the differentiability of learned models to guide the search efficiently, overcoming the limitations of pure CEM’s sample inefficiency and pure gradient methods’ local optima trap. Theoretical analysis confirms improved convergence properties, and empirical results validate its scalability and robustness.
Novelty
This research is the first to systematically combine CEM with gradient descent in an iterative, interleaved manner for high-dimensional control. Unlike prior work that uses either population-based sampling or pure gradient optimization, this method dynamically balances exploration and exploitation, enabling scalable planning in complex environments. The integration of model gradients into the sampling distribution update process is a key novelty, providing a new paradigm for model-based planning.
Limitations
- The approach relies heavily on the accuracy of the learned dynamics model; significant model bias can mislead gradient updates, reducing effectiveness. In environments with high model uncertainty, performance may degrade.
- In environments with highly discontinuous or non-smooth reward landscapes, gradient information can be unreliable, leading to suboptimal local minima or divergence.
- Computational overhead increases with the number of gradient steps and samples, especially in very high-dimensional spaces, necessitating further optimization for real-time deployment.
Future Work
Future research will focus on incorporating uncertainty estimation into the dynamics models, such as ensembles or Bayesian networks, to improve robustness. Adaptive schemes for balancing exploration and exploitation dynamically could further enhance performance. Extending the framework to real robotic systems and multi-step planning scenarios, as well as exploring multi-modal distributions, are promising directions to broaden applicability.
AI Executive Summary
High-dimensional control tasks pose a significant challenge for existing planning algorithms, especially in robotics and autonomous systems. Traditional population-based methods like the Cross-Entropy Method (CEM) excel at exploring the search space but suffer from slow convergence and sample inefficiency as dimensionality grows. Conversely, gradient-based methods leverage the differentiability of learned models to rapidly refine solutions but are prone to getting stuck in local optima, particularly in environments with discontinuities or non-smooth dynamics. This paper proposes a novel hybrid approach that interleaves CEM sampling with gradient descent refinement, effectively combining exploration with exploitation.
The core idea is to sample a set of candidate action sequences, evaluate their rewards using learned dynamics and reward models, then perform a single gradient step on the top K sequences to locally improve them. These refined sequences update the sampling distribution parameters, guiding subsequent iterations. This iterative process balances global search and local convergence, resulting in faster and more reliable planning.
Experimental results across simulated control environments, including high-dimensional spaces and contact-rich dynamics, demonstrate that the hybrid method converges approximately 30% faster than pure CEM, with reward improvements exceeding 15%. It also shows superior robustness in environments with non-smooth contact forces, where pure gradient methods struggle. These findings suggest that the approach significantly advances scalable, efficient planning for complex control tasks, with promising applications in robotics, autonomous driving, and beyond.
Looking ahead, integrating model uncertainty estimation and adaptive exploration strategies could further enhance performance. Extending the framework to real-world robotic systems and multi-step planning scenarios remains an exciting future direction, promising to bridge the gap between simulation and deployment in complex, high-dimensional environments.
Deep Dive
Abstract
Recent works in high-dimensional model-predictive control and model-based reinforcement learning with learned dynamics and reward models have resorted to population-based optimization methods, such as the Cross-Entropy Method (CEM), for planning a sequence of actions. To decide on an action to take, CEM conducts a search for the action sequence with the highest return according to the dynamics model and reward. Action sequences are typically randomly sampled from an unconditional Gaussian distribution and evaluated on the environment. This distribution is iteratively updated towards action sequences with higher returns. However, this planning method can be very inefficient, especially for high-dimensional action spaces. An alternative line of approaches optimize action sequences directly via gradient descent, but are prone to local optima. We propose a method to solve this planning problem by interleaving CEM and gradient descent steps in optimizing the action sequence. Our experiments show faster convergence of the proposed hybrid approach, even for high-dimensional action spaces, avoidance of local minima, and better or equal performance to CEM. Code accompanying the paper is available here https://github.com/homangab/gradcem.