Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networks (1605.07127v3)

Abstract: We present an algorithm for model-based reinforcement learning that combines Bayesian neural networks (BNNs) with random roll-outs and stochastic optimization for policy learning. The BNNs are trained by minimizing $\alpha$-divergences, allowing us to capture complicated statistical patterns in the transition dynamics, e.g. multi-modality and heteroskedasticity, which are usually missed by other common modeling approaches. We illustrate the performance of our method by solving a challenging benchmark where model-based approaches usually fail and by obtaining promising results in a real-world scenario for controlling a gas turbine.

• The paper presents a framework integrating Bayesian Neural Networks with stochastic inputs, accurately modeling transition dynamics in varied environments.
• The paper employs alpha-divergence minimization (α = 0.5) for training, enhancing policy search compared to traditional variational methods.
• The paper demonstrates effective handling of multi-modal, heteroskedastic systems through rigorous evaluations in benchmark and industrial applications.

Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networks

The paper discusses a novel approach to model-based reinforcement learning (MBRL) that integrates Bayesian Neural Networks (BNNs) in the context of stochastic dynamical systems. The authors propose an innovative framework for learning and policy search where BNNs are employed to model the stochastic transition dynamics of the system under consideration. The goal is to improve the robustness and expressiveness of policy search algorithms by capturing complex statistical structures inherent in these dynamics.

Algorithmic Framework

The paper's core contribution is an algorithm that utilizes BNNs with stochastic input variables for policy learning. This model-based approach leverages the expressive power of BNNs to encapsulate complex patterns such as multi-modality and heteroskedasticity in the transition dynamics of a system. The BNNs model the probabilistic transition function $p(\mathbf{s}_{t+1}|\mathbf{s}_t,\mathbf{a})$, effectively capturing the inherent stochasticity in the environment which is often ignored by deterministic models.

The policy search strategy involves training the BNNs using $\alpha$-divergence minimization with $\alpha = 0.5$, noted to generally perform better than conventional techniques like variational Bayes. The learning process is enhanced with stochastic optimization methods and random roll-outs which facilitate the search for optimal policies based on the transition predictions made by BNNs. This methodology was tested against challenging real-world scenarios, demonstrating its applicability and effectiveness in settings where traditional model-based methods lack precision or fail entirely.

Technical Insights

BNNs function as probabilistic models that maintain a distribution over the neural network weights, thereby modeling uncertainty more accurately than standard neural networks. The inclusion of stochastic input noise $z$ helps delineate the unmodeled stochastic components affecting the system. Training involves approximating the posterior distribution over the weights and noise variables using a novel minimization of the $\alpha$-divergence, which stabilizes the learning over complex stochastic patterns.

Evaluation on benchmark problems such as the Wet-Chicken and industrial applications like gas turbine control validates the model's potential. In these evaluations, the proposed MBRL method solved tasks known for presenting significant stochastic challenges. The results illustrated that BNNs could capture intricate transition distributions through multi-modal and heteroskedastic outputs, surpassing the predictive capabilities of Gaussian Processes and standard MLPs in some scenarios.

Implications and Future Directions

This approach highlights significant potential for addressing challenges in industrial applications where exploration may be limited due to safety constraints. The ability to accurately model and predict stochastic transitions in controlled environments allows for more reliable policy learning, crucial for industrial control systems.

Looking forward, the implications of this research suggest the utility of such models in settings requiring safety guarantees and adaptive exploration strategies. Future research could explore the bounds of BNNs with stochastic inputs in larger scale or more complex dynamical systems, potentially integrating this framework with real-time decision systems.

In conclusion, this paper advances MBRL by integrating BNNs to effectively learn and search policies in stochastic dynamical systems,thus matching the expressive requirements of complex industrial applications. This work forms a basis for further developments in reliable autonomous systems where understanding and predicting uncertainty is paramount.