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Closed-Form Congestion Control Policies Learned via Deep Symbolic Regression for Fronthaul Networks

Core Concepts
This paper proposes a methodology to learn closed-form mathematical expressions (symbolic policies) that approximate the behavior of a baseline reinforcement learning congestion control policy, while maintaining its performance and generalization capabilities. The symbolic policies overcome the challenges of neural network models regarding real-time inference and interpretability.
The paper addresses the challenges of deploying reinforcement learning (RL) models for congestion control in packetized fronthaul networks, which require very high-speed control loops and interpretable decision-making. The key steps are: Train a RL baseline policy specialized for fronthaul-like scenarios using the TD3 algorithm. Collect state-action experiences from the RL baseline policy. Perform deep symbolic regression on the collected dataset to extract closed-form mathematical expressions (symbolic policies) that approximate the RL baseline behavior. The symbolic policies are shown to closely match the overall performance of the RL baseline in terms of link utilization, delay, and fairness, while providing the benefits of real-time inference and interpretability. The paper also analyzes the inner workings of the symbolic policies and their ability to generalize to network scenarios not seen during training.
The network simulations define a multi-agent scenario where senders must cooperate to maximize link utilization and fairness while minimizing round-trip times (RTTs). The observation space consists of four dimensions: intersend time, average RTT, RTT ratio, and packet loss ratio. The action space is unidimensional, with actions used to update the intersend time. The reward function aims to induce policies that increase the transmission rate until the observed RTTs increase or packet losses occur.
"The resulting symbolic policies are interpretable and at the same time, easy to implement in any programming language, which completely overcomes any issues with inference time." "The results show that such policies also closely follow the overall performance of the RL baseline while matching its generalization capabilities."

Key Insights Distilled From

by Jean Martins... at 05-03-2024
Closed-form congestion control via deep symbolic regression

Deeper Inquiries

How could the symbolic regression process be further improved to better capture the nuances of the RL baseline policy's behavior

To enhance the symbolic regression process for capturing the intricacies of the RL baseline policy's behavior more effectively, several improvements can be considered: Token Expansion: Introducing a wider range of mathematical tokens beyond basic arithmetic operations like trigonometric functions, logarithms, or exponential functions can provide the symbolic regression model with more expressive power to capture complex relationships present in the RL policy. Feature Engineering: Incorporating additional features derived from the network environment, such as historical data, network topology information, or traffic patterns, can offer more context for the symbolic regression model to learn from and generate more accurate closed-form expressions. Ensemble Methods: Implementing ensemble methods where multiple symbolic regression models are trained and their outputs are combined can help mitigate overfitting and improve the overall robustness of the learned symbolic policies. Regularization Techniques: Applying regularization techniques like L1 or L2 regularization during the training of the symbolic regression model can prevent overfitting and promote the discovery of more generalizable patterns in the data.

What other applications beyond congestion control could benefit from the proposed methodology of learning interpretable closed-form policies from RL agents

The methodology of learning interpretable closed-form policies from RL agents through symbolic regression can be applied to various other domains beyond congestion control, including: Financial Modeling: Predicting stock prices, portfolio optimization, or risk assessment by learning closed-form policies from RL agents can provide transparent and actionable insights for financial decision-making. Healthcare: Developing personalized treatment plans, predicting patient outcomes, or optimizing hospital resource allocation through interpretable policies derived from RL agents can enhance healthcare delivery and patient care. Autonomous Systems: Enhancing decision-making processes in autonomous vehicles, drones, or robotic systems by learning interpretable policies from RL agents can improve safety, efficiency, and adaptability in dynamic environments. Energy Management: Optimizing energy consumption, grid stability, or renewable energy integration through interpretable policies learned from RL agents can contribute to sustainable energy practices and cost-effective energy management strategies.

How could the symbolic policies be extended to handle more complex network dynamics, such as heterogeneous traffic patterns or dynamic network topologies

To extend the symbolic policies to handle more complex network dynamics such as heterogeneous traffic patterns or dynamic network topologies, the following approaches can be considered: Dynamic Token Selection: Implementing a mechanism where the symbolic regression model dynamically selects relevant tokens based on the observed network dynamics can adapt the symbolic policies to varying traffic patterns and network configurations. Temporal Consideration: Incorporating temporal information into the symbolic regression process, such as recurrent neural networks or attention mechanisms, can enable the model to capture the time-dependent nature of network behaviors and adjust the symbolic policies accordingly. Multi-Agent Reinforcement Learning: Extending the symbolic regression methodology to multi-agent reinforcement learning scenarios can facilitate the development of policies that account for interactions between diverse agents in the network, accommodating heterogeneous traffic patterns and dynamic topologies more effectively. Transfer Learning: Leveraging transfer learning techniques to fine-tune symbolic policies learned from one network scenario to another with different dynamics can expedite the adaptation process and enhance the model's performance in handling diverse network conditions.