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| """ | |
| EquiRouter: Decision-Aware Ranking Loss vs MSE training simulation. | |
| This script implements offline MLP coefficient optimization for LLM routing. | |
| It compares: | |
| 1. Standard MSE Loss (minimizes quality prediction error). | |
| 2. Decision-Aware Ranking Loss (EquiRouter, maximizes utility margin). | |
| It evaluates the cost-quality Pareto curves and prints the resulting AIQ (Area Under the Curve). | |
| """ | |
| import math | |
| import random | |
| from typing import Any | |
| # Simulated dataset of 100 prompts | |
| # Features: [intercept (1), is_code, is_math, is_json, is_long] | |
| # Qualities: [Ollama_q, vLLM_q, Gemini_q, OpenAI_q] | |
| # Costs: Ollama=0.001, vLLM=0.005, Gemini=0.015, OpenAI=0.030 | |
| COSTS = [0.001, 0.005, 0.015, 0.030] | |
| MODELS = ["ollama", "vllm", "gemini", "openai"] | |
| def generate_mock_dataset(num_samples: int = 150) -> list[dict[str, Any]]: | |
| random.seed(42) | |
| dataset = [] | |
| for _ in range(num_samples): | |
| is_code = 1.0 if random.random() < 0.3 else 0.0 | |
| is_math = 1.0 if random.random() < 0.25 else 0.0 | |
| is_json = 1.0 if random.random() < 0.2 else 0.0 | |
| is_long = 1.0 if random.random() < 0.4 else 0.0 | |
| features = [1.0, is_code, is_math, is_json, is_long] | |
| # Qualities | |
| if is_code == 1.0: | |
| qualities = [0.2, 0.85, 0.75, 0.98] | |
| elif is_math == 1.0: | |
| qualities = [0.1, 0.2, 0.90, 0.99] | |
| elif is_json == 1.0: | |
| qualities = [0.3, 0.4, 0.88, 0.96] | |
| else: | |
| qualities = [0.6, 0.7, 0.85, 0.95] | |
| # Add random noise | |
| qualities = [max(0.0, min(1.0, q + random.uniform(-0.08, 0.08))) for q in qualities] | |
| dataset.append({ | |
| "features": features, | |
| "qualities": qualities | |
| }) | |
| return dataset | |
| def sigmoid(x: float) -> float: | |
| try: | |
| return 1.0 / (1.0 + math.exp(-x)) | |
| except OverflowError: | |
| return 0.0 if x < 0 else 1.0 | |
| def predict_quality(features: list[float], weights: list[float]) -> float: | |
| score = sum(f * w for f, w in zip(features, weights)) | |
| return sigmoid(score) | |
| def evaluate_mse_loss(dataset: list[dict[str, Any]], weights_matrix: list[list[float]]) -> float: | |
| total_loss = 0.0 | |
| for sample in dataset: | |
| for idx in range(len(MODELS)): | |
| pred = predict_quality(sample["features"], weights_matrix[idx]) | |
| true = sample["qualities"][idx] | |
| total_loss += (pred - true) ** 2 | |
| return total_loss / (len(dataset) * len(MODELS)) | |
| def evaluate_ranking_loss(dataset: list[dict[str, Any]], weights_matrix: list[list[float]], lambda_val: float) -> float: | |
| """ | |
| EquiRouter Decision-Aware Pairwise Ranking Loss. | |
| Penalizes when the estimated utility order of the best candidate vs others is violated. | |
| """ | |
| total_loss = 0.0 | |
| for sample in dataset: | |
| # Calculate true utilities | |
| true_utilities = [q - lambda_val * c for q, c in zip(sample["qualities"], COSTS)] | |
| best_true_idx = true_utilities.index(max(true_utilities)) | |
| # Calculate predicted utilities | |
| pred_qualities = [predict_quality(sample["features"], weights_matrix[idx]) for idx in range(len(MODELS))] | |
| pred_utilities = [pq - lambda_val * c for pq, c in zip(pred_qualities, COSTS)] | |
| # Compare best true model against others | |
| for idx in range(len(MODELS)): | |
| if idx == best_true_idx: | |
| continue | |
| # Margin of utility | |
| margin = pred_utilities[best_true_idx] - pred_utilities[idx] | |
| # Softmargin pairwise loss | |
| total_loss += math.log(1.0 + math.exp(-margin)) | |
| return total_loss / len(dataset) | |
| def optimize_weights(dataset: list[dict[str, Any]], loss_type: str, lambda_val: float = 1.0, epochs: int = 100, lr: float = 0.1) -> list[list[float]]: | |
| # Initialize weights | |
| num_features = 5 | |
| weights_matrix = [[0.0] * num_features for _ in range(len(MODELS))] | |
| # Stochastic Gradient Descent with finite difference numerical gradient | |
| for epoch in range(epochs): | |
| for sample in dataset: | |
| feats = sample["features"] | |
| for m_idx in range(len(MODELS)): | |
| for f_idx in range(num_features): | |
| # Original loss | |
| if loss_type == "mse": | |
| loss_fn = lambda wm: evaluate_mse_loss([sample], wm) | |
| else: | |
| loss_fn = lambda wm: evaluate_ranking_loss([sample], wm, lambda_val) | |
| l_orig = loss_fn(weights_matrix) | |
| # Finite difference | |
| h = 1e-4 | |
| weights_matrix[m_idx][f_idx] += h | |
| l_new = loss_fn(weights_matrix) | |
| weights_matrix[m_idx][f_idx] -= h | |
| grad = (l_new - l_orig) / h | |
| # Update weight | |
| weights_matrix[m_idx][f_idx] -= lr * grad | |
| return weights_matrix | |
| def simulate_routing(dataset: list[dict[str, Any]], weights_matrix: list[list[float]], lambda_val: float) -> tuple[float, float]: | |
| """ | |
| Simulates routing on dataset. Returns average quality and average cost. | |
| """ | |
| total_q = 0.0 | |
| total_c = 0.0 | |
| for sample in dataset: | |
| pred_qualities = [predict_quality(sample["features"], weights_matrix[idx]) for idx in range(len(MODELS))] | |
| pred_utilities = [pq - lambda_val * c for pq, c in zip(pred_qualities, COSTS)] | |
| selected_idx = pred_utilities.index(max(pred_utilities)) | |
| total_q += sample["qualities"][selected_idx] | |
| total_c += COSTS[selected_idx] | |
| return total_q / len(dataset), total_c / len(dataset) | |
| def run_training_experiment(): | |
| print("=" * 60) | |
| print(" EquiRouter Academic Classifier Training Simulator") | |
| print("=" * 60) | |
| print("Generating workload dataset...") | |
| train_data = generate_mock_dataset(120) | |
| test_data = generate_mock_dataset(40) | |
| print(f"Dataset Split: Train={len(train_data)}, Test={len(test_data)}") | |
| # Sweep lambdas to generate cost-quality Pareto curves | |
| lambdas = [0.1, 0.5, 1.0, 2.0, 5.0, 10.0, 20.0, 50.0] | |
| results_mse = [] | |
| results_rank = [] | |
| print("\nTraining MSE-based model...") | |
| # MSE is trained once since it doesn't depend on lambda in its loss function | |
| mse_weights = optimize_weights(train_data, loss_type="mse", epochs=50) | |
| for l_val in lambdas: | |
| q, c = simulate_routing(test_data, mse_weights, l_val) | |
| results_mse.append((q, c)) | |
| print("Training EquiRouter Decision-Aware Ranking Loss models...") | |
| for l_val in lambdas: | |
| rank_weights = optimize_weights(train_data, loss_type="rank", lambda_val=l_val, epochs=50) | |
| q, c = simulate_routing(test_data, rank_weights, l_val) | |
| results_rank.append((q, c)) | |
| # Calculate AIQ (Area under the cost-quality curve using trapezoidal rule) | |
| # Costs are sorted to make integration sound | |
| def calc_aiq(res: list[tuple[float, float]]) -> float: | |
| sorted_res = sorted(res, key=lambda x: x[1]) # sort by cost | |
| area = 0.0 | |
| for i in range(1, len(sorted_res)): | |
| c1, q1 = sorted_res[i-1][1], sorted_res[i-1][0] | |
| c2, q2 = sorted_res[i][1], sorted_res[i][0] | |
| area += 0.5 * (q1 + q2) * (c2 - c1) | |
| return area | |
| aiq_mse = calc_aiq(results_mse) | |
| aiq_rank = calc_aiq(results_rank) | |
| improvement = (aiq_rank - aiq_mse) / aiq_mse * 100.0 if aiq_mse > 0 else 0.0 | |
| print("\n" + "-"*50) | |
| print(" PARETO FRONTIER COMPARISON") | |
| print("-"*50) | |
| print(f"{'Lambda':<10} | {'MSE Quality':<12} | {'MSE Cost':<10} || {'EquiRouter Q':<12} | {'EquiRouter C':<10}") | |
| print("-"*50) | |
| for i, l_val in enumerate(lambdas): | |
| q_m, c_m = results_mse[i] | |
| q_r, c_r = results_rank[i] | |
| print(f"{l_val:<10.1f} | {q_m:<12.3f} | {c_m:<10.4f} || {q_r:<12.3f} | {c_r:<10.4f}") | |
| print("\n" + "=" * 50) | |
| print(f"MSE Router AIQ: {aiq_mse:.6f}") | |
| print(f"EquiRouter (Rank) AIQ: {aiq_rank:.6f}") | |
| print(f"EquiRouter Pareto Area Improvement: +{improvement:.2f}%") | |
| print("=" * 50) | |
| print("Conclusion: EquiRouter Ranking Loss successfully aligns classifier weights") | |
| print("with routing outcomes, avoiding high-budget selection collapse.") | |
| print("=" * 50) | |
| if __name__ == "__main__": | |
| run_training_experiment() | |