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Escaping Local Optima in the Waddington Landscape: A Multi-Stage TRPO-PPO Approach for Single-Cell Perturbation Analysis

Francis Boabang, Samuel Asante Gyamerah

TL;DR

The paper tackles perturbation modeling in single-cell biology within the rugged, nonconvex Waddington landscape. It introduces a multistage reinforcement learning pipeline that first performs a curvature-aware natural-gradient step under a KL-trust region, followed by PPO clipped fine-tuning, to achieve robust optimization. The method blends exact TRPO-style initialization with efficient PPO refinement and demonstrates improved generalization and predictive accuracy across scRNA-seq, scATAC-seq, and joint datasets, along with reduced reconstruction error and better correlation to ground-truth expression. This approach offers a principled way to navigate nonconvex cellular landscapes, potentially informing perturbation design and multi-omics integration in regenerative medicine and biology.

Abstract

Modeling cellular responses to genetic and chemical perturbations remains a central challenge in single-cell biology. Existing data-driven framework have advanced perturbation prediction through variational autoencoders, chemically conditioned autoencoders, and large-scale transformer pretraining. However, these models are prone to local optima in the nonconvex Waddington landscape of cell fate decisions, where poor initialization can trap trajectories in spurious lineages or implausible differentiation outcomes. While executable gene regulatory networks complement these approaches, automated design frameworks incorporate biological priors through multi-agent optimization. Yet, an approach that is completely data-driven with well-designed initialization to escape local optima and converge to a proper lineage remains elusive. In this work, we introduce a multistage reinforcement learning algorithm tailored for single-cell perturbation modeling. We first compute an explicit natural gradient update using Fisher-vector products and a conjugate gradient solver, scaled by a KL trust-region constraint to provide a safe, curvature-aware the first step for the policy. Starting with these preconditioned parameters, we then apply a second phase of proximal policy optimization (PPO) with clipped surrogates, exploiting minibatch efficiency to refine the policy. We demonstrate that this initialization substantially improves generalization on Single-cell RNA sequencing (scRNA-seq) and Single-cell ATAC sequencing (scATAC-seq) pertubation analysis.

Escaping Local Optima in the Waddington Landscape: A Multi-Stage TRPO-PPO Approach for Single-Cell Perturbation Analysis

TL;DR

The paper tackles perturbation modeling in single-cell biology within the rugged, nonconvex Waddington landscape. It introduces a multistage reinforcement learning pipeline that first performs a curvature-aware natural-gradient step under a KL-trust region, followed by PPO clipped fine-tuning, to achieve robust optimization. The method blends exact TRPO-style initialization with efficient PPO refinement and demonstrates improved generalization and predictive accuracy across scRNA-seq, scATAC-seq, and joint datasets, along with reduced reconstruction error and better correlation to ground-truth expression. This approach offers a principled way to navigate nonconvex cellular landscapes, potentially informing perturbation design and multi-omics integration in regenerative medicine and biology.

Abstract

Modeling cellular responses to genetic and chemical perturbations remains a central challenge in single-cell biology. Existing data-driven framework have advanced perturbation prediction through variational autoencoders, chemically conditioned autoencoders, and large-scale transformer pretraining. However, these models are prone to local optima in the nonconvex Waddington landscape of cell fate decisions, where poor initialization can trap trajectories in spurious lineages or implausible differentiation outcomes. While executable gene regulatory networks complement these approaches, automated design frameworks incorporate biological priors through multi-agent optimization. Yet, an approach that is completely data-driven with well-designed initialization to escape local optima and converge to a proper lineage remains elusive. In this work, we introduce a multistage reinforcement learning algorithm tailored for single-cell perturbation modeling. We first compute an explicit natural gradient update using Fisher-vector products and a conjugate gradient solver, scaled by a KL trust-region constraint to provide a safe, curvature-aware the first step for the policy. Starting with these preconditioned parameters, we then apply a second phase of proximal policy optimization (PPO) with clipped surrogates, exploiting minibatch efficiency to refine the policy. We demonstrate that this initialization substantially improves generalization on Single-cell RNA sequencing (scRNA-seq) and Single-cell ATAC sequencing (scATAC-seq) pertubation analysis.
Paper Structure (12 sections, 8 equations, 2 figures, 3 tables, 1 algorithm)

This paper contains 12 sections, 8 equations, 2 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. TRPO-Preconditioned PPO multistage
  4. Surrogate Objective and Gradient
  5. Fisher-Vector Product and Conjugate Gradient
  6. Natural Gradient Step with KL Scaling
  7. PPO Clipped Fine-Tuning
  8. Evaluation
  9. RNA single cell dataset evaluation results
  10. ATAC single cell dataset evaluation results
  11. Joint RNA and ATAC single cell dataset results
  12. Conclusion

Figures (2)

  • Figure 1: Waddington’s epigenetic landscapes are represented as valleys and hills, and differentiation is depicted as a ball rolling down branching paths. The shape of the landscape encodes both the stability of cell fates and the potential for plastic transitions between states. High plasticity corresponds to shallow valleys or flexible branching points, allowing cells to respond dynamically to perturbations and environmental cues. Understanding how molecular mechanisms reshape this landscape is crucial for interpreting developmental processes, cellular reprogramming, and disease progression gilbert1991epigeneticproteintech2023cell.
  • Figure 2: Single Cell Perturbation Analysis with the Proposed TRPO_PPO Method