File size: 9,112 Bytes
431ef2b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 | """
TorchSurv-based Clearing Price Distribution Model
Uses deep survival analysis for censored market price prediction.
Right-censored data problem in first-price auctions:
- When you WIN: you observe the exact clearing price (your bid) → uncensored
- When you LOSE: you only know clearing price > your bid → right-censored
This maps exactly to survival analysis:
- "Event" = winning (price observed)
- "Time" = market price
- "Censoring" = losing (only lower bound)
Library: TorchSurv (Novartis, arXiv:2404.10761)
Install: pip install torchsurv
"""
import torch
import torch.nn as nn
import numpy as np
from torch.utils.data import DataLoader, TensorDataset
class MarketPriceModel(nn.Module):
"""
Neural network for predicting market price distribution.
Outputs log-hazard for Cox PH model or distribution parameters.
The survival function S(b|x) = P(market_price > b | features)
Win probability = 1 - S(b|x)
"""
def __init__(self, input_dim, hidden_dims=(256, 128, 64), dropout=0.2):
super().__init__()
layers = []
in_dim = input_dim
for h in hidden_dims:
layers += [
nn.Linear(in_dim, h),
nn.BatchNorm1d(h),
nn.ReLU(),
nn.Dropout(dropout)
]
in_dim = h
layers.append(nn.Linear(in_dim, 1)) # log hazard
self.net = nn.Sequential(*layers)
def forward(self, x):
return self.net(x).squeeze(-1)
class WinProbabilityModel(nn.Module):
"""
Simple binary classifier: P(win | bid_price, features).
Faster alternative to full survival model when only win probability is needed.
"""
def __init__(self, input_dim, hidden_dims=(256, 128, 64), dropout=0.2):
super().__init__()
layers = []
in_dim = input_dim + 1 # +1 for bid_price
for h in hidden_dims:
layers += [
nn.Linear(in_dim, h),
nn.ReLU(),
nn.Dropout(dropout)
]
in_dim = h
layers.append(nn.Linear(in_dim, 1))
layers.append(nn.Sigmoid())
self.net = nn.Sequential(*layers)
def forward(self, features, bid_price):
x = torch.cat([features, bid_price.unsqueeze(-1)], dim=-1)
return self.net(x).squeeze(-1)
class CensoredPriceDataProcessor:
"""
Prepare censored data for market price model training.
In first-price auction simulation:
- won=1: event occurred, time = bid_price (what you paid = your bid)
- won=0: censored, time = bid_price (you only know market_price > your bid)
For the Cox PH model:
- event: 1 if won (uncensored), 0 if lost (censored)
- time: bid_price in both cases (the "time" variable in survival analysis)
"""
def __init__(self):
pass
@staticmethod
def prepare_from_auction_log(features, bids, won, prices=None):
"""
Args:
features: (n, d) impression features
bids: (n,) bid prices submitted
won: (n,) boolean, True if won
prices: (n,) market prices (or None — uses bids as proxy)
Returns:
features_tensor, time_tensor, event_tensor
"""
features = np.asarray(features, dtype=np.float32)
bids = np.asarray(bids, dtype=np.float32)
won = np.asarray(won, dtype=np.float32)
# In first-price: time = bid (the observed value)
time = bids.copy()
# event: 1 if won (we observed the clearing price), 0 if lost
event = won.copy()
return torch.tensor(features), torch.tensor(time), torch.tensor(event)
@staticmethod
def create_dataloader(features, time, event, batch_size=256, shuffle=True):
ds = TensorDataset(features, time, event)
return DataLoader(ds, batch_size=batch_size, shuffle=shuffle)
def train_market_price_model(
model, train_loader, val_loader=None,
epochs=20, lr=1e-3, device='cuda',
save_path='/app/models/market_price_model.pt'
):
"""
Train market price model using Cox PH loss (negative partial log-likelihood).
"""
try:
from torchsurv.loss import cox
except ImportError:
print("torchsurv not installed. Using BCE-based fallback.")
return train_win_prob_fallback(model, train_loader, val_loader, epochs, lr, device, save_path)
model = model.to(device)
optimizer = torch.optim.Adam(model.parameters(), lr=lr, weight_decay=1e-5)
best_loss = float('inf')
for epoch in range(epochs):
model.train()
total_loss = 0.0
for batch_features, batch_time, batch_event in train_loader:
batch_features = batch_features.to(device)
batch_time = batch_time.to(device)
batch_event = batch_event.to(device)
optimizer.zero_grad()
log_hazard = model(batch_features)
# Cox PH negative partial log-likelihood
loss = cox.neg_partial_log_likelihood(
log_hazard,
event=batch_event,
time=batch_time
)
loss.backward()
optimizer.step()
total_loss += loss.item()
avg_loss = total_loss / len(train_loader)
print(f"Epoch {epoch+1}/{epochs} | Loss: {avg_loss:.4f}")
if avg_loss < best_loss:
best_loss = avg_loss
torch.save(model.state_dict(), save_path)
# Load best
model.load_state_dict(torch.load(save_path))
return model
def train_win_prob_fallback(model, train_loader, val_loader, epochs, lr, device, save_path):
"""Fallback: train as binary classifier if TorchSurv not available."""
criterion = nn.BCEWithLogitsLoss()
model_win = nn.Sequential(model.net, nn.Sigmoid()).to(device)
optimizer = torch.optim.Adam(model_win.parameters(), lr=lr)
for epoch in range(epochs):
model_win.train()
total_loss = 0.0
for batch_features, batch_time, batch_event in train_loader:
batch_features = batch_features.to(device)
optimizer.zero_grad()
preds = model_win(batch_features).squeeze(-1)
loss = criterion(preds, batch_event)
loss.backward()
optimizer.step()
total_loss += loss.item()
print(f"Epoch {epoch+1}/{epochs} | BCE Loss: {total_loss/len(train_loader):.4f}")
torch.save(model_win.state_dict(), save_path)
return model_win
class MarketPricePredictor:
"""
Predict win probability and expected cost using trained model.
"""
def __init__(self, model, device='cpu'):
self.model = model.to(device)
self.device = device
self.model.eval()
def predict_win_probability(self, features, bid_prices):
"""
Predict P(win | bid=b, features=x).
Uses survival function: P(win|b,x) = 1 - S(b|x)
Args:
features: (n, d) or (d,) feature tensor/array
bid_prices: (n,) or scalar bid price(s)
Returns:
win_prob: (n,) or scalar
"""
features = torch.as_tensor(features, dtype=torch.float32).to(self.device)
with torch.no_grad():
log_hazard = self.model(features)
# Cox PH: S(t) = exp(-H(t)) where H is cumulative hazard
# Approximate P(win|b) = 1 - exp(-exp(log_hazard))
# This is a rough approximation — full Breslow estimator needed for accuracy
hazard = torch.exp(log_hazard)
survival = torch.exp(-hazard)
win_prob = 1.0 - survival
result = win_prob.cpu().numpy()
return float(result.item()) if result.ndim == 0 else result.squeeze()
def find_optimal_bid(self, features, v, lambd, bid_range=None, n_candidates=50):
"""
Find optimal bid using learned win probability model.
b_t = argmax_b ( (v - b) * P(win|b,x) - λ * b * P(win|b,x) )
Args:
features: (d,) feature vector for this impression
v: value of winning (pCTR × value_per_click)
lambd: dual multiplier
Returns:
optimal_bid
"""
if bid_range is None:
bid_range = (0.1, v * 2.0)
candidates = np.linspace(bid_range[0], bid_range[1], n_candidates)
features_tiled = np.tile(features, (n_candidates, 1))
win_probs = self.predict_win_probability(features_tiled, candidates)
scores = (v - candidates) * win_probs - lambd * candidates * win_probs
best_idx = np.argmax(scores)
return candidates[best_idx]
if __name__ == '__main__':
print("Market Price Model module loaded.")
print("Use train_market_price_model() with censored auction data.")
print("Or use EmpiricalCDF for the simpler non-parametric baseline.")
|