Examples¶

Run any script with python examples/<script>.py.

robust_shortest_path_metrla.py: Conformalized DCRNN_PyTorch forecasts + robust shortest path on METR-LA (requires the examples/DCRNN_PyTorch submodule and its precomputed predictions NPZ).
robust_bike_newsvendor.py: Conformal calibration on UCI Bike Sharing data + robust newsvendor decisions vs nominal.
robust_capacity_planning.py: Synthetic arrival forecasting + robust server capacity sizing with conformal intervals.
robust_fractional_knapsack.py: SBIBM simulator + flow-based posterior samples for robust fractional knapsack.

Bike newsvendor

Region: \(\mathcal{C}(x) = \{c : \|c - \hat{y}(x)\|_2 \le q\}\)
Objective: \(\min_{q \ge 0} \max_{c \in \mathcal{C}(x)} \; c_u (c - q)^+ + c_o (q - c)^+.\)

METR-LA shortest path

Region: \(\mathcal{C}(x) = \bigcup_{k} \{c : \|c - \hat{c}_k\|_2 \le q\}\)
Objective: \(\min_{w} \max_{c \in \mathcal{C}(x)} \langle c, w\rangle \quad \text{s.t. } A w = b,\; 0 \le w \le 1.\)

Fractional knapsack (SBIBM)

Region: \(\mathcal{C}(x) = \bigcup_k \{v : \|v - \hat{v}_k\|_2 \le q\}\) (weights fixed to nominal proxy).
Objective: \(\max_{x} \; \langle v, x\rangle \quad \text{s.t. } \langle w, x\rangle \le B,\; 0 \le x \le 1\), with robust variant using worst-case \(v\).

Capacity planning (synthetic arrivals)

Region: \(\mathcal{C}(x) = \{ \lambda : |\lambda - \hat{\lambda}(x)| \le q\}\) (L2 interval around predicted arrival rate).
Objective: \(\min_{0 \le c \le \bar{c}} \; \max_{\lambda \in \mathcal{C}(x)} \; c_{\text{cap}} \, c + c_{\text{short}} \, (\lambda - \mu c)^+\), where \(c\) is capacity (servers), \(\mu\) is service rate, and \(c_{\text{cap}}, c_{\text{short}}\) are cost coefficients. Inner max is approximated by sampling from \(\mathcal{C}(x)\).

Empirical results (10 trials)¶

method	mean objective	std	paired t-test (robust < nominal)
robust	2560.51	24.30	t = -90.94, p = 5.958e-15
nominal	4370.20	83.10	–

method	mean objective	std	paired t-test (robust < nominal)
robust	109.58	15.56	t = -9.52, p = 2.682e-06
nominal	12112.04	3780.02	–

method	mean objective	std	paired t-test (robust < nominal)
robust	8.0131	1.0061	t = -28.7643, p = 1.807e-10
nominal	45.9437	4.2929	–