Future Directions¶

This page outlines promising, scoped next steps that extend Compitum’s core: constraint‑aware routing, SPD metrics, and Lyapunov‑inspired controllers. These items are not required for launch.

Dual Shadow Pricing (Online Primal–Dual)¶

Goal: Introduce bona fide dual variables (shadow prices) λ for constraints that rise under sustained utilization pressure and fall when slack, enabling interpretable tradeoffs and budget compliance.
Approach: Maintain λ ≥ 0 with a lightweight controller: observe usage u = A @ x_B, track EMA ũ, compute slack s = ũ − ρ·b, update λ ← clip(λ + η·s, 0, λ_max). Optionally price selection via Ũ = U − λ·u.
Certificate: Add constraints.dual_shadow_prices and controller params (eta, alpha, rho).
Scope: Standalone module; default off (observe‑only). Negligible overhead (vector ops in R^m).
Status: Proposed; complements current finite‑difference boundary sensitivity.

Robust Boundary Sensitivity¶

Make epsilon configurable and scaled by constraint norm; optionally probe a small epsilon set and report a stabilized statistic.
Emit the minimal Δb that flips argmax (critical relaxation) to aid audits.

PyLantern Integration (Teaser)¶

PyLantern (a.k.a. Fascia) explores observer‑bounded, curved computation in PyTorch. Integrating selective pieces can provide:
- Observer‑bounded windows for controllers (trust region, duals) with typed, testable surfaces.
- Geometry‑aware utilities where appropriate without sacrificing Torch ergonomics.
This is exploratory and orthogonal; Compitum remains usable without PyLantern.

Expanded Certificates¶

Add optional provenance fields (constraint config hash, epsilon used, metric version) to strengthen audit trails.
Provide compact “active constraints” summary (top‑k by magnitude) for quick dashboards.

Evaluation Tracks¶

Budget‑constrained routing tasks to quantify benefits of dual shadow pricing.
Stress tests on boundary regimes (small utility gap, high entropy) to validate deferral behavior.