**Learning the Empirical
Hardness of Combinatorial Auctions**

**Introduction**

**Why?**

**Related Work**

**Combinatorial Auctions**

**Winner Determination
Problem**

**WDP Case Study**

**Methodology**

**Methodology**

**Methodology**

**WDP Distributions**

**Methodology**

**Problem Size**

**Raw vs. Non-Dominated
Bids**

(64 goods, target of 2000 non-dominated bids)

**Methodology**

**Features**

**Features**

**Methodology**

**Experimental Setup**

**Gross Hardness (256
goods, 1000 bids)**

**Methodology**

**Learning**

**LR: Error**

**LR: Subset Selection**

**LR: Cost of Omission (subset
size 7)**

**Non-Linear Approaches**

**Quadratic vs Linear
Regression**

**Quadratic vs Linear
Regression**

**QR: RMSE vs. Subset Size**

**Cost of Omission (subset
size 6)**

**What’s Next?**

**Summary**