Motivation
The project’s cold-start global recovery FAILs from Sobol starts, bottlenecked by local-optimizer depth in 54-D. Gradient-based optimization could help but requires differentiating through the RBPF. Brady et al. (2024, 2026) developed differentiable IMM particle filters for regime learning, but have not applied them to structural macro-finance estimation.
Hypothesis
Making the RBPF differentiable enables gradient-based optimization of the 54-D parameter space, closing the cold-start gap without BOBYQA.
Approach sketch
Adapt the Brady et al. differentiable PF framework to the Leather-Sagi RBPF: replace discrete resampling with a continuous relaxation (Gumbel-Softmax or optimal transport), backpropagate through the Kalman updates and Riccati pricing recursions.
Expected outcome
Gradient-based MLE with convergence from cold starts.
Risks
- AD through the RBPF is 158 s/eval (450x slower than RBPF alone), making gradient-based inner-loop optimization prohibitively slow.
- Continuous relaxation of resampling introduces bias.
- Overlaps with mjls-aware-rbpf-variance-reduction.
Pilot results
(empty)
Lessons learned
Eliminated during /ideate Phase 3 filter. Similar methodology exists, feasibility is marginal given the 158 s/eval AD cost, and the idea overlaps with the existing RBPF improvement idea. The global optimization pipeline idea (global-optimization-pipeline-msre-cre) addresses the same cold-start problem via derivative-free methods (BOBYQA), which are better suited to the noisy MC objective.