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Distributional Reinforcement Learning with Information Bottleneck for Uncertainty-Aware DRAM Equalization

Muhammad Usama, Dong Eui Chang

TL;DR

A distributional risk-sensitive reinforcement learning framework integrating Information Bottleneck latent representations with Conditional Value-at-Risk optimization achieves rate-distortion optimal signal compression achieving 51 times speedup over eye diagrams while quantifying epistemic uncertainty through Monte Carlo dropout.

Abstract

Equalizer parameter optimization is critical for signal integrity in high-speed memory systems operating at multi-gigabit data rates. However, existing methods suffer from computationally expensive eye diagram evaluation, optimization of expected rather than worst-case performance, and absence of uncertainty quantification for deployment decisions. In this paper, we propose a distributional risk-sensitive reinforcement learning framework integrating Information Bottleneck latent representations with Conditional Value-at-Risk optimization. We introduce rate-distortion optimal signal compression achieving 51 times speedup over eye diagrams while quantifying epistemic uncertainty through Monte Carlo dropout. Distributional reinforcement learning with quantile regression enables explicit worst-case optimization, while PAC-Bayesian regularization certifies generalization bounds. Experimental validation on 2.4 million waveforms from eight memory units demonstrated mean improvements of 37.1\% and 41.5\% for 4-tap and 8-tap equalizer configurations with worst-case guarantees of 33.8\% and 38.2\%, representing 80.7\% and 89.1\% improvements over Q-learning baselines. The framework achieved 62.5\% high-reliability classification eliminating manual validation for most configurations. These results suggest the proposed framework provides a practical solution for production-scale equalizer optimization with certified worst-case guarantees.

Distributional Reinforcement Learning with Information Bottleneck for Uncertainty-Aware DRAM Equalization

TL;DR

A distributional risk-sensitive reinforcement learning framework integrating Information Bottleneck latent representations with Conditional Value-at-Risk optimization achieves rate-distortion optimal signal compression achieving 51 times speedup over eye diagrams while quantifying epistemic uncertainty through Monte Carlo dropout.

Abstract

Equalizer parameter optimization is critical for signal integrity in high-speed memory systems operating at multi-gigabit data rates. However, existing methods suffer from computationally expensive eye diagram evaluation, optimization of expected rather than worst-case performance, and absence of uncertainty quantification for deployment decisions. In this paper, we propose a distributional risk-sensitive reinforcement learning framework integrating Information Bottleneck latent representations with Conditional Value-at-Risk optimization. We introduce rate-distortion optimal signal compression achieving 51 times speedup over eye diagrams while quantifying epistemic uncertainty through Monte Carlo dropout. Distributional reinforcement learning with quantile regression enables explicit worst-case optimization, while PAC-Bayesian regularization certifies generalization bounds. Experimental validation on 2.4 million waveforms from eight memory units demonstrated mean improvements of 37.1\% and 41.5\% for 4-tap and 8-tap equalizer configurations with worst-case guarantees of 33.8\% and 38.2\%, representing 80.7\% and 89.1\% improvements over Q-learning baselines. The framework achieved 62.5\% high-reliability classification eliminating manual validation for most configurations. These results suggest the proposed framework provides a practical solution for production-scale equalizer optimization with certified worst-case guarantees.
Paper Structure (41 sections, 4 theorems, 32 equations, 15 figures, 9 tables, 1 algorithm)

This paper contains 41 sections, 4 theorems, 32 equations, 15 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Dataset
  3. Proposed Methodology
  4. Problem Formulation
  5. Information Bottleneck Latent Representation
  6. Variational Information Bottleneck Objective
  7. Network Architecture and Training
  8. Monte Carlo Uncertainty Quantification
  9. Latent Space Anchor Point
  10. Distributional Risk-Sensitive Reinforcement Learning
  11. Return Distribution Modeling
  12. CVaR Policy Optimization
  13. Wasserstein-Regularized Reward Function
  14. Actor-Critic Architecture and Training
  15. Generalization and Robustness Guarantees
  16. ...and 26 more sections

Key Result

Theorem 3.1

For encoder $p_{\boldsymbol{\phi}}(\textbf{z}|\textbf{d}_o) = \mathcal{N}(\boldsymbol{\mu}_{\phi}(\textbf{d}_o), \text{diag}(\boldsymbol{\sigma}_{\phi}^2(\textbf{d}_o)))$ and standard Gaussian prior $q_{\boldsymbol{\psi}}(\textbf{z}) = \mathcal{N}(\mathbf{0}, \mathbf{I})$, the Information Bottleneck with equality when $q_{\boldsymbol{\psi}}(\textbf{z}) = p(\textbf{z})$ and $p_{\boldsymbol{\omega}}

Figures (15)

  • Figure 1: The figure shows (a) the server memory system with double-sided DIMMs used to generate our dataset, and (b) a visualization of 1000 sample values for DRAM 1 from the dataset that plots the DRAM output waveform and the corresponding input waveform.
  • Figure 2: Illustration of the signal validity labeling criteria. The rectangular window (80 mV $\times$ 35 ps) is shown in red. (a) An invalid signal where signal transitions intersect the window, and (b) a valid signal where no transitions occur within the window region.
  • Figure 3: Comparison of window area improvement distributions between Deterministic A2C (red) and Risk-Sensitive DR-IB-A2C (blue). The plot highlights the impact of CVaR optimization: while the mean performance is comparable, the risk-sensitive approach significantly shifts the lower tail (worst 10%) to the right, improving the 10th percentile performance from 29.8% to 38.1% (+8.4% absolute gain). This visualizes the trade-off between maximizing expected return and ensuring reliability for worst-case channels.
  • Figure 4: t-SNE visualization comparing latent spaces. (a) Information Bottleneck method exhibits clear cluster separation with anchor positioned near valid cluster centroid. (b) Standard autoencoder shows overlapping clusters with suboptimal anchor placement.
  • Figure 5: Return distribution visualization. (a) Histogram showing full distribution captured by DR-IB-A2C with mean = 24.8 mV$\cdot$UI. (b) Value-based method with mean = 23.2 mV$\cdot$UI demonstrating concentrated distribution that underestimates tail risks (KL divergence = 0.142).
  • ...and 10 more figures

Theorems & Definitions (8)

  • Theorem 3.1: Information Bottleneck Rate-Distortion Bound
  • Theorem 3.2: Distributional Bellman Convergence
  • Theorem 3.3: CVaR Policy Gradient
  • Theorem 3.4: PAC-Bayesian Policy Bound
  • proof
  • proof
  • proof
  • proof