This paper proposes a novel deep symbolic regression approach to enhance the
robustness and interpretability of data-driven mathematical expression
discovery. Despite the success of the state-of-the-art method, DSR, it is built
on recurrent neural networks, purely guided by data fitness, and potentially
meet tail barriers, which can zero out the policy gradient and cause
inefficient model updates. To overcome these limitations, we use transformers
in conjunction with breadth-first-search to improve the learning performance.
We use Bayesian information criterion (BIC) as the reward function to
explicitly account for the expression complexity and optimize the trade-off
between interpretability and data fitness. We propose a modified risk-seeking
policy that not only ensures the unbiasness of the gradient, but also removes
the tail barriers, thus ensuring effective updates from top performers. Through
a series of benchmarks and systematic experiments, we demonstrate the
advantages of our approach.

本文提出了一种新颖的深度符号回归方法，以增强数据驱动的数学表达式发现的鲁棒性和解释性。通过使用 transformer 与广度优先搜索相结合来改善学习性能，并使用贝叶斯信息准则（BIC）作为奖励函数来明确考虑表达式复杂性并优化解释性和数据适应性之间的权衡。通过一系列基准测试和系统性实验，我们展示了我们方法的优势。

具备复杂性意识的深度符号回归与稳健风险寻求策略梯度

Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking  Policy Gradients

As mobile networks embrace the 5G era, the interest in adopting Reinforcement
Learning (RL) algorithms to handle challenges in ultra-low-latency and high
throughput scenarios increases. Simultaneously, the advent of packetized
fronthaul networks imposes demanding requirements that traditional congestion
control mechanisms cannot accomplish, highlighting the potential of RL-based
congestion control algorithms. Although learning RL policies optimized for
satisfying the stringent fronthaul requirements is feasible, the adoption of
neural network models in real deployments still poses some challenges regarding
real-time inference and interpretability. This paper proposes a methodology to
deal with such challenges while maintaining the performance and generalization
capabilities provided by a baseline RL policy. The method consists of (1)
training a congestion control policy specialized in fronthaul-like networks via
reinforcement learning, (2) collecting state-action experiences from the
baseline, and (3) performing deep symbolic regression on the collected dataset.
The proposed process overcomes the challenges related to inference-time
limitations through closed-form expressions that approximate the baseline
performance (link utilization, delay, and fairness) and which can be directly
implemented in any programming language. Finally, we analyze the inner workings
of the closed-form expressions.

该论文提出了一种使用强化学习和深度符号回归来处理 5G 时代中超低时延和高吞吐场景下拥塞控制问题的方法。通过训练一个专门针对类似前传网络的拥塞控制策略，并采集基准策略的状态 - 动作经验，使用深度符号回归方法处理实时推理的挑战，从而实现基准策略的性能和泛化能力。该方法能够近似基准性能（链路利用率、延迟和公平性）并可以直接在任何编程语言中实现，并对闭合形式表达式的内部工作进行了分析。

通过深度符号回归实现闭式拥塞控制

Closed-form congestion control via deep symbolic regression

Symbolic regression (SR) is an area of interpretable machine learning that
aims to identify mathematical expressions, often composed of simple functions,
that best fit in a given set of covariates $X$ and response $y$. In recent
years, deep symbolic regression (DSR) has emerged as a popular method in the
field by leveraging deep reinforcement learning to solve the complicated
combinatorial search problem. In this work, we propose an alternative framework
(GFN-SR) to approach SR with deep learning. We model the construction of an
expression tree as traversing through a directed acyclic graph (DAG) so that
GFlowNet can learn a stochastic policy to generate such trees sequentially.
Enhanced with an adaptive reward baseline, our method is capable of generating
a diverse set of best-fitting expressions. Notably, we observe that GFN-SR
outperforms other SR algorithms in noisy data regimes, owing to its ability to
learn a distribution of rewards over a space of candidate solutions.

用深度学习提出的 GFN-SR 框架在符号回归中模拟表达树的构建，通过学习一个随机策略来顺序生成这些树，这种方法能够生成多样的最佳拟合表达式，在噪声数据环境下优于其他符号回归算法。