Conservative Continuous-Time Treatment Optimization

TL;DR

This paper introduces a conservative continuous-time control framework for treatment optimization that uses a signature-based regularizer to improve robustness and prevent out-of-support control proposals in irregular patient data.

Contribution

It proposes a novel regularization method using signature-based MMD to ensure conservative treatment optimization in continuous-time stochastic models.

Findings

Enhanced robustness over non-conservative methods

Improved treatment outcome optimization

Effective in irregularly sampled patient data

Abstract

We develop a conservative continuous-time stochastic control framework for treatment optimization from irregularly sampled patient trajectories. The unknown patient dynamics are modeled as a controlled stochastic differential equation with treatment as a continuous-time control. Naive model-based optimization can exploit model errors and propose out-of-support controls, so optimizing the estimated dynamics may not optimize the true dynamics. To limit extrapolation, we add a consistent signature-based MMD regularizer on path space that penalizes treatment plans whose induced trajectory distribution deviates from observed trajectories. The resulting objective minimizes a computable upper bound on the true cost. Experiments on benchmark datasets show improved robustness and performance compared to non-conservative baselines.