The 4-Policy Meta-Class Tournament & Shadow Deployment

In This Component

Elite sequential decision engineering never defaults blindly to a single algorithmic hammer. Project Aegis pits all four of Warren Powell’s canonical policy meta-classes against each other across 100,000 empirical Olist orders under identical stochastic sample paths.

Mathematical Specification of the 4 Policy Classes

1. Policy Function Approximation (PFA)

Myopic geodesic nearest-neighbor routing paired with a static $(s,S)$ replenishment rule:

$X^{\text{PFA}}(S_t)=\arg {\min }_{k\in \mathcal{K}:R_{t,k,i}^{\text{avail}}\ge q_i}{D}_{\text{geo}}(k,\text{cust})$

2. Cost Function Approximation (CFA) Tuned via Knowledge Gradient

Maximizes single-period GAAP contribution plus a parameterized concave inventory preservation buffer, where $\theta \in {\mathbb{R}}^{K\times P}$ is tuned offline via Powell’s Knowledge Gradient (KG) subject to the $\le 3.5\%$ p95 stockout SLA:

$X^{\text{CFA}}(S_t\mid \theta )=\arg {\max }_{x_t\in {\mathcal{X}}_t}\left(C(S_t,x_t)+{\sum }_{k=1}^K{\sum }_i{\theta }_{k,i}\ln \left(R_{t,k,i}^{\text{avail}}-x_{t,k,i}^{\text{route}}{q}_i+1\right)\right)$

3. Value Function Approximation (VFA) via Post-Decision States & CAVE

Decomposes the transition into the deterministic Post-Decision State $S_t^x=S^{M,x}(S_t,x_t)$ and the stochastic shock $S_{t+1}=S^{M,W}(S_t^x,W_{t+1})$, eliminating the outer expectation operator during real-time routing:

$X^{\text{VFA}}(S_t)=\arg {\max }_{x_t\in {\mathcal{X}}_t}\left(C(S_t,x_t)+{\sum }_{k=1}^K{\sum }_i{\bar{V}}_{t,k,i}\left(R_{t,k,i}^x\right)\right)$

Marginal value slopes ${\pi }_{k,i}$ are updated via Powell’s CAVE (Concave Adaptive Value Estimation) algorithm over rolling multi-period lookahead duals.

4. Direct Lookahead Approximation (DLA) with ST-GCN Rollouts

Solves an $H$-step rolling horizon optimization where inter-hub transit delays and regional demand surges are projected forward over the highway/air adjacency graph $A\in {\mathbb{R}}^{K\times K}$ using a Spatio-Temporal Graph Convolutional Network (ST-GCN), committing only the immediate decision $x_t={\tilde{x}}_{t,t}$.