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README.md
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# RTB Bidding Algorithm Comparison
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This repository contains the results of comparing different bidding algorithms for Real-Time Bidding (RTB) in online advertising, optimizing for clicks under budget constraints.
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## Problem Setup
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- **Objective**: Maximize number of clicks
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- **Constraint**: Total spend ≤ Budget, with ~100% budget utilization target
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- **Auction Type**: First-price auctions
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- **Models Used**:
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- CTR Prediction: Logistic Regression (simplified from FinalMLP)
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- Clearing Price: Gradient Boosting Regressor (simplified from Deep Cox PH)
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## Algorithms Compared
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| Algorithm | Type | Description |
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|-----------|------|-------------|
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| **Linear** | Static | `bid = base_bid × (pCTR / avg_pCTR)` |
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| **ORTB** | Static | `bid = √(c·pCTR/λ + c²) − c` |
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| **DualOGD** | Adaptive | Online gradient descent on Lagrangian multiplier |
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| **Threshold** | Static | Fixed bid if pCTR > threshold, else 0 |
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| **MPC** | Adaptive | Model Predictive Control maximizing expected value |
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## Results
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| Algorithm | Clicks | CTR | Budget Used | CPC | Efficiency |
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|-----------|--------|-----|-------------|-----|------------|
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| **DualOGD** | **1331** | 0.5133 | 99.99% | **7.51** | **1331.12** |
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| **MPC** | 440 | 0.4878 | 100.00% | 22.73 | 440.00 |
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| **Linear** | 167 | 0.5076 | 99.90% | 59.82 | 167.16 |
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| **Threshold** | 110 | 0.5500 | 100.00% | 90.91 | 110.00 |
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| **ORTB** | 85 | 0.5152 | 99.87% | 117.50 | 85.11 |
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## Key Findings
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1. **DualOGD dominates** with 1331 clicks — 8× better than Linear, 15× better than ORTB
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2. **Adaptive algorithms (DualOGD, MPC)** significantly outperform static approaches
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3. **ORTB performs poorly** in first-price auctions (designed for second-price)
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4. **Threshold has highest CTR (0.55)** but low volume — very selective
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5. All algorithms achieved ~100% budget utilization
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## References
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- Wang et al. (2023): "Learning to Bid in Repeated First-Price Auctions with Budgets" [arXiv:2304.13477](https://arxiv.org/abs/2304.13477)
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- Zhang et al. (2014): "Optimal Real-Time Bidding for Display Advertising" (KDD)
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- Cai et al. (2017): "Real-Time Bidding by Reinforcement Learning" [arXiv:1701.02490](https://arxiv.org/abs/1701.02490)
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- Balseiro et al. (2023): "Robust Budget Pacing with a Single Sample" [arXiv:2302.02006](https://arxiv.org/abs/2302.02006)
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