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Conservative Continuous-Time Treatment Optimization
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Proposes a conservative continuous-time treatment optimization framework that optimizes a neural SDE model's cost plus a signature-kernel conditional MMD penalty keeping treatment plans close to observed trajectory distributions.
Problem
Offline treatment optimization from irregularly sampled patient trajectories is prone to model exploitation: optimizing a learned continuous-time dynamics model can select out-of-support treatment plans whose predicted outcomes are unreliable.
Approach
Model patient dynamics as a controlled SDE with treatment as continuous control, derive an upper bound on the true cost via telescoped one-step discrepancies bounded by conditional IPMs, and instantiate the IPM with a signature-kernel conditional MMD estimator used as a regularizer penalizing out-of-distribution plans.
Key results
- On Cancer (Explicit), the proposed method (lambda=100) reaches average true cost 242.07 vs 467.26 for TE-CDE and 559.74 for INSITE/SINDy.
- On Cancer (Relative), average true cost 73.42 vs 280.97 (TE-CDE) and 333.77 (INSITE/SINDy).
- On Covid-19 target trajectory, true cost 5.61 vs 5.80 (TE-CDE) and 7.59 (INSITE/SINDy); TE-CDE has higher Spearman correlation (0.79 vs 0.51).
Surprising findings
- On Covid-19, TE-CDE achieves the best Spearman rank correlation, above the proposed method.
- On Covid-19, no clear monotonic effect of the regularization strength lambda was observed.
Limitations
- Covid-19 results are mixed: rank correlation is lower than TE-CDE and the lambda trend is non-monotonic.
- Assumptions such as positivity and well-specified neural SDE are hard to satisfy in continuous time; the upper bound relies on IPM scaling constant c and the model class.
- Optimization restricted to parameterized open-loop deterministic controls with single-shooting.
Experimental setup
Datasets: simulated lung cancer PK/PD trajectories simulated Covid-19 dexamethasone trajectories
Benchmarks: Cancer (Explicit) Cancer (Relative) Covid-19 (Target Trajectory)
Metrics: Spearman rank correlation average ground-truth cost of optimized plans
Baselines: TE-CDE INSITE/SINDy
Builds on: neural SDE signature kernel maximum conditional mean discrepancy TE-CDE INSITE
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