File size: 8,229 Bytes
bff9b48 | 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 | """
Bidding Algorithm Baselines for First-Price Auctions
Includes:
1. LinearBidder — proportional bidding based on pCTR
2. ThresholdBidder — fixed bid if pCTR above threshold
3. ValueShadingBidder — value shading for first-price (bid = v/(1+λ))
4. RLBBidder — simplified MDP-based RL bidding (Cai et al. 2017)
"""
import numpy as np
from collections import deque
class LinearBidder:
"""Simple linear bidding: bid proportional to pCTR."""
def __init__(self, base_bid, avg_pctr, name="Linear"):
self.base_bid = base_bid
self.avg_pctr = avg_pctr
self.name = name
self.total_spent = 0.0
self.remaining_budget = float('inf')
self.total_wins = 0
self.t = 0
def bid(self, pctr, features=None):
self.t += 1
if self.remaining_budget <= 0:
return 0.0
bid = self.base_bid * (pctr / max(self.avg_pctr, 1e-6))
return min(bid, self.remaining_budget)
def update(self, won, cost, pctr, d_t=None):
if won:
self.total_spent += cost
self.remaining_budget -= cost
self.total_wins += 1
def set_budget(self, budget):
self.remaining_budget = budget
def get_stats(self):
return {
'name': self.name,
'spent': float(self.total_spent),
'remaining': float(self.remaining_budget),
'wins': self.total_wins,
't': self.t,
}
class ThresholdBidder:
"""Threshold bidding: fixed bid if pCTR exceeds threshold, else skip."""
def __init__(self, threshold, bid_value, name="Threshold"):
self.threshold = threshold
self.bid_value = bid_value
self.name = name
self.total_spent = 0.0
self.remaining_budget = float('inf')
self.total_wins = 0
self.t = 0
def bid(self, pctr, features=None):
self.t += 1
if self.remaining_budget < self.bid_value:
return 0.0
return self.bid_value if pctr > self.threshold else 0.0
def update(self, won, cost, pctr, d_t=None):
if won:
self.total_spent += cost
self.remaining_budget -= cost
self.total_wins += 1
def set_budget(self, budget):
self.remaining_budget = budget
def get_stats(self):
return {
'name': self.name,
'spent': float(self.total_spent),
'remaining': float(self.remaining_budget),
'wins': self.total_wins,
't': self.t,
}
class ValueShadingBidder:
"""
Value shading for first-price auctions.
bid = v / (1 + λ) where λ is estimated from historical outcomes.
Unlike second-price auctions where you bid your true value,
in first-price auctions you shade your bid below value.
"""
def __init__(self, budget, T, value_per_click, name="ValueShading"):
self.B = budget
self.T = T
self.rho = budget / T
self.vpc = value_per_click
self.name = name
# Shading factor λ
self.lambd = 0.0
self.epsilon = 1.0 / np.sqrt(T)
self.total_spent = 0.0
self.remaining_budget = budget
self.total_wins = 0
self.t = 0
self.competing_bids = []
def bid(self, pctr, features=None):
self.t += 1
v = pctr * self.vpc
if self.remaining_budget <= 0:
return 0.0
# Shade: bid below value based on competition
if len(self.competing_bids) > 0:
avg_competing = np.mean(self.competing_bids)
shade_factor = 1.0 / (1.0 + self.lambd + 0.1)
bid = v * shade_factor
# Clamp to competing bid range
bid = np.clip(bid, avg_competing * 0.5, v * 0.9)
else:
bid = v * 0.5 # Initial exploration
return min(bid, self.remaining_budget)
def update(self, won, cost, pctr, d_t=None):
if won:
self.total_spent += cost
self.remaining_budget -= cost
self.total_wins += 1
if d_t is not None:
self.competing_bids.append(d_t)
cost_feedback = cost if won else 0.0
self.lambd = max(0.0, self.lambd - self.epsilon * (self.rho - cost_feedback))
def get_stats(self):
return {
'name': self.name,
'lambda': float(self.lambd),
'spent': float(self.total_spent),
'remaining': float(self.remaining_budget),
'wins': self.total_wins,
't': self.t,
}
class RLBBidder:
"""
Simplified RLB (Reinforcement Learning for Bidding).
Based on: Cai et al. "Real-Time Bidding by Reinforcement Learning" (WSDM 2017)
arXiv: 1701.02490
Uses a simplified MDP with discretized state space:
State = (budget_bucket, pCTR_bucket)
Action = bid multiplier
Maintains a Q-table updated via temporal difference learning.
"""
def __init__(
self,
budget,
T,
value_per_click,
n_budget_buckets=10,
n_pctr_buckets=5,
n_bid_multipliers=10,
learning_rate=0.1,
discount=0.95,
exploration_rate=0.1,
name="RLB"
):
self.B = budget
self.T = T
self.vpc = value_per_click
self.name = name
self.n_budget = n_budget_buckets
self.n_pctr = n_pctr_buckets
self.n_actions = n_bid_multipliers
# Bid multipliers: 0.1x to 2.0x of value
self.bid_multipliers = np.linspace(0.1, 2.0, n_bid_multipliers)
# Q-table: (budget_bucket, pctr_bucket, action)
self.Q = np.zeros((n_budget_buckets, n_pctr_buckets, n_bid_multipliers))
self.lr = learning_rate
self.gamma = discount
self.epsilon_greedy = exploration_rate
self.total_spent = 0.0
self.remaining_budget = budget
self.total_wins = 0
self.t = 0
# For TD learning
self.last_state = None
self.last_action = None
def _get_state(self, pctr):
"""Discretize state: (budget_ratio_bucket, pctr_bucket)."""
budget_ratio = self.remaining_budget / max(self.B, 1)
budget_bucket = min(int(budget_ratio * self.n_budget), self.n_budget - 1)
pctr_bucket = min(int(pctr * self.n_pctr), self.n_pctr - 1)
return (budget_bucket, pctr_bucket)
def bid(self, pctr, features=None):
self.t += 1
if self.remaining_budget <= 0:
return 0.0
state = self._get_state(pctr)
v = pctr * self.vpc
# ε-greedy action selection
if np.random.random() < self.epsilon_greedy:
action = np.random.randint(self.n_actions)
else:
action = np.argmax(self.Q[state[0], state[1], :])
self.last_state = state
self.last_action = action
bid = min(v * self.bid_multipliers[action], self.remaining_budget)
return bid
def update(self, won, cost, pctr, d_t=None):
if won:
self.total_spent += cost
self.remaining_budget -= cost
self.total_wins += 1
# TD update
if self.last_state is not None:
reward = (pctr * self.vpc) if won else 0.0
new_state = self._get_state(pctr)
# Q-learning update
old_q = self.Q[self.last_state[0], self.last_state[1], self.last_action]
max_future_q = np.max(self.Q[new_state[0], new_state[1], :])
new_q = old_q + self.lr * (reward + self.gamma * max_future_q - old_q)
self.Q[self.last_state[0], self.last_state[1], self.last_action] = new_q
def get_stats(self):
return {
'name': self.name,
'spent': float(self.total_spent),
'remaining': float(self.remaining_budget),
'wins': self.total_wins,
't': self.t,
'q_table_mean': float(np.mean(self.Q)),
}
|