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improved implementation

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Daniel Rosel
2025-12-14 18:59:02 +01:00
parent 8a08458478
commit 201c98bcac
1 changed files with 398 additions and 114 deletions
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sim/rl/environment.py
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@@ -3,165 +3,449 @@ from gymnasium import spaces
import numpy as np
from dataclasses import dataclass
import pandas as pd
from typing import Callable, Optional, Dict, Any, List
# here when we say "learner" we mean the agent that is learning to optimize the pricing and "agent" is part of the envrionment where the agent is creating demand that that "learner" is processing"
# "learner" agent learning to optimize pricing
# "agent" part of environment creating demand signals that learner processes
@dataclass
class BusinessLogicConstraints():
max_price_adjustment : float = 0.3 # maximum adjustment of price
system_max_price : float = 500.0 # maximum price allowed in the system
system_min_price : float = 1.0 # minimum price allowed in the system
product_catelogue_size : int = 100 # number of products in the catalogue
max_price_adjustment: float = 0.30
system_max_price: float = 500.0
system_min_price: float = 1.0
product_catelogue_size: int = 100
episode_length: int = 200
sessions_per_step: int = 250
agent_share: float = 0.25
agent_recon_multiplier: float = 6.0
agent_purchase_probability: float = 0.20
coi_strength: float = 0.25
coi_threshold: float = 4.0
coi_sigmoid_temp: float = 1.25
base_human_demand: float = 0.08
base_agent_demand: float = 0.05
human_price_elasticity: float = -1.2
agent_price_elasticity: float = -0.6
w_agent_loss: float = 1.0
w_volatility: float = 5.0
w_estimation_error: float = 0.25
seed: int = 7
def _sigmoid(x: np.ndarray) -> np.ndarray:
return 1.0 / (1.0 + np.exp(-x))
def simple_agent_detector(session_df: pd.DataFrame) -> pd.Series:
# baseline heuristic: high velocity + low conversion
v = session_df.get("interaction_velocity", pd.Series(0.0, index=session_df.index))
cr = session_df.get("conversion_rate", pd.Series(0.0, index=session_df.index))
total = session_df.get("total_interactions", pd.Series(0, index=session_df.index))
return (total >= 12) & (v >= 0.20) & (cr <= 0.01)
class CommercePlatform:
def __init__(self, product_catelogue_size: int, max_price: float, min_price: float):
def __init__(self, product_catelogue_size: int, max_price: float, min_price: float,
constraints: BusinessLogicConstraints, agent_detector: Optional[Callable[[pd.DataFrame], pd.Series]] = None,
use_defense: bool = False):
self.product_catelogue_size = product_catelogue_size
self.max_price = max_price
self.min_price = min_price
self.simulation_history = []
self.constraints = constraints
self.use_defense = use_defense
self.agent_detector = agent_detector
self.simulation_history: List[Dict[str, Any]] = []
self._rng = np.random.default_rng(constraints.seed)
self._popularity = self._rng.lognormal(mean=0.0, sigma=0.6, size=self.product_catelogue_size)
self._popularity = self._popularity / (self._popularity.mean() + 1e-12)
self._last_interaction_df: pd.DataFrame = pd.DataFrame()
def setup_true_demand(self,prices: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
human_price_elasticity = -1.5 # Example elasticity value
base_demand = 100 # Base demand for products
demand = base_demand * (prices / self.max_price) ** human_price_elasticity
agent_price_elasticity = -2.0 # Example elasticity value for agents
agent_base_demand = 150 # Base demand for agents
agent_demand = agent_base_demand * (prices / self.max_price) ** agent_price_elasticity
return demand + agent_demand, agent_demand
def compute_interaction_features(self, interaction_data: np.ndarray) -> dict:
df = pd.DataFrame(interaction_data)
def setup_true_demand(self, prices: np.ndarray) -> Dict[str, np.ndarray]:
# ground truth purchase propensities
p = np.clip(prices, self.min_price, self.max_price)
pn = p / self.max_price
human_prob = self.constraints.base_human_demand * (pn ** self.constraints.human_price_elasticity)
agent_prob = self.constraints.base_agent_demand * (pn ** self.constraints.agent_price_elasticity)
return {
'mean_sale_price': df[df['action'] == 'purchase']['price'].mean(),
"human_purchase_prob": np.clip(human_prob * self._popularity, 0.0, 0.95),
"agent_purchase_prob": np.clip(agent_prob * self._popularity, 0.0, 0.95)
}
def run_pricing_simulation(self, prices: np.ndarray) -> dict:
# Simulate demand based on prices
def _session_markup_multiplier(self, signal_score: float) -> float:
# session-based COI markup based on demand signal expression
x = (signal_score - self.constraints.coi_threshold) / max(self.constraints.coi_sigmoid_temp, 1e-6)
return 1.0 + self.constraints.coi_strength * float(_sigmoid(np.array([x]))[0])
observed_demand, demand_from_agents = self.setup_true_demand(prices)
true_demand = observed_demand - demand_from_agents
def _simulate_sessions(self, base_prices: np.ndarray) -> pd.DataFrame:
demand = self.setup_true_demand(base_prices)
human_pprob = demand["human_purchase_prob"]
agent_pprob = demand["agent_purchase_prob"]
events: List[Dict[str, Any]] = []
T = self.constraints.sessions_per_step
n_agent_sessions = int(round(T * self.constraints.agent_share))
n_human_sessions = T - n_agent_sessions
interaction_data = self.get_interaction_data()
interaction_features = self.compute_interaction_features(interaction_data)
demand_estimates = self.demand_estimate(interaction_data)
internal_error = np.abs(true_demand - demand_estimates) / (true_demand + 1e-6)
# human sessions: normal browse with possible purchase
for s in range(n_human_sessions):
session_id = f"h_{len(events)}_{s}"
k = int(self._rng.integers(1, 4))
prod_ids = self._rng.choice(self.product_catelogue_size, size=k, replace=False)
t = 0.0
inter_times = self._rng.gamma(shape=2.0, scale=3.0, size=3 * k)
signal_score = 0.0
purchased_any = False
for i, pid in enumerate(prod_ids):
t += float(inter_times[i])
price_shown = float(base_prices[pid])
events.append({
"session_id": session_id, "actor": "human", "agent_id": None, "product_id": int(pid),
"action": "view", "t": t, "price_shown": price_shown, "is_purchase": 0,
"price_paid": 0.0, "oracle_price_paid": 0.0, "signal_score": 0.0,
})
signal_score += 1.0
if self._rng.random() < 0.35:
t += float(inter_times[i + k])
events.append({
"session_id": session_id, "actor": "human", "agent_id": None, "product_id": int(pid),
"action": "cart", "t": t, "price_shown": price_shown, "is_purchase": 0,
"price_paid": 0.0, "oracle_price_paid": 0.0, "signal_score": 0.0,
})
signal_score += 2.0
if (not purchased_any) and (self._rng.random() < float(human_pprob[pid])):
t += float(inter_times[i + 2 * k])
mult = self._session_markup_multiplier(signal_score)
price_paid = float(np.clip(base_prices[pid] * mult, self.min_price, self.max_price))
events.append({
"session_id": session_id, "actor": "human", "agent_id": None, "product_id": int(pid),
"action": "purchase", "t": t, "price_shown": float(base_prices[pid]), "is_purchase": 1,
"price_paid": price_paid, "oracle_price_paid": price_paid, "signal_score": signal_score,
})
purchased_any = True
# agent sessions: split recon/purchase to circumvent COI
n_agent_ids = max(1, n_agent_sessions // 2)
for a in range(n_agent_ids):
agent_id = f"a_{a}"
recon_session_id = f"{agent_id}_recon"
t = 0.0
n_views = int(self._rng.poisson(lam=8) * self.constraints.agent_recon_multiplier) + 5
inter_times = self._rng.gamma(shape=2.0, scale=0.6, size=max(n_views, 1))
prod_ids = self._rng.integers(0, self.product_catelogue_size, size=n_views)
recon_signal = 0.0
for i, pid in enumerate(prod_ids):
t += float(inter_times[i])
events.append({
"session_id": recon_session_id, "actor": "agent", "agent_id": agent_id, "product_id": int(pid),
"action": "view", "t": t, "price_shown": float(base_prices[pid]), "is_purchase": 0,
"price_paid": 0.0, "oracle_price_paid": 0.0, "signal_score": 0.0,
})
recon_signal += 1.0
# clean purchase session with minimal interactions
if self._rng.random() < self.constraints.agent_purchase_probability:
purchase_session_id = f"{agent_id}_clean"
pid = int(self._rng.integers(0, self.product_catelogue_size))
t2 = 0.0
clean_signal = 0.0
t2 += float(self._rng.gamma(shape=2.0, scale=0.7))
events.append({
"session_id": purchase_session_id, "actor": "agent", "agent_id": agent_id, "product_id": pid,
"action": "view", "t": t2, "price_shown": float(base_prices[pid]), "is_purchase": 0,
"price_paid": 0.0, "oracle_price_paid": 0.0, "signal_score": 0.0,
})
clean_signal += 1.0
if self._rng.random() < float(agent_pprob[pid]):
t2 += float(self._rng.gamma(shape=2.0, scale=0.7))
obs_mult = self._session_markup_multiplier(clean_signal)
obs_paid = float(np.clip(base_prices[pid] * obs_mult, self.min_price, self.max_price))
oracle_mult = self._session_markup_multiplier(recon_signal) # oracle links recon->purchase
oracle_paid = float(np.clip(base_prices[pid] * oracle_mult, self.min_price, self.max_price))
events.append({
"session_id": purchase_session_id, "actor": "agent", "agent_id": agent_id, "product_id": pid,
"action": "purchase", "t": t2, "price_shown": float(base_prices[pid]), "is_purchase": 1,
"price_paid": obs_paid, "oracle_price_paid": oracle_paid, "signal_score": clean_signal,
})
return pd.DataFrame(events)
def compute_interaction_features(self, interaction_df: pd.DataFrame) -> Dict[str, float]:
if interaction_df.empty:
return {"mean_sale_price": 0.0, "look_to_book": 0.0}
purchases = interaction_df[interaction_df["action"] == "purchase"]
mean_sale_price = float(purchases["price_paid"].mean()) if not purchases.empty else 0.0
views = float((interaction_df["action"] == "view").sum())
buys = float((interaction_df["action"] == "purchase").sum())
return {"mean_sale_price": mean_sale_price, "look_to_book": float(views / (buys + 1e-6))}
def _session_feature_table(self, df: pd.DataFrame) -> pd.DataFrame:
if df.empty:
return pd.DataFrame()
g = df.groupby("session_id", sort=False)
session_duration = g["t"].max() - g["t"].min()
total_interactions = g.size()
avg_time_between = g["t"].apply(lambda x: float(np.diff(np.sort(x.to_numpy())).mean()) if len(x) > 1 else 0.0)
interaction_velocity = total_interactions / (session_duration + 1e-6)
views = g.apply(lambda x: int((x["action"] == "view").sum()), include_groups=False)
cart_adds = g.apply(lambda x: int((x["action"] == "cart").sum()), include_groups=False)
purchases = g.apply(lambda x: int((x["action"] == "purchase").sum()), include_groups=False)
conversion_rate = purchases / (views + 1e-6)
is_agent = g["actor"].apply(lambda s: bool((s == "agent").any()), include_groups=False)
return pd.DataFrame({
"session_duration_sec": session_duration.astype(float),
"avg_time_between_events": avg_time_between.astype(float),
"total_interactions": total_interactions.astype(int),
"interaction_velocity": interaction_velocity.astype(float),
"item_views": views.astype(int),
"cart_adds": cart_adds.astype(int),
"purchases": purchases.astype(int),
"conversion_rate": conversion_rate.astype(float),
"is_agent": is_agent.astype(bool),
}).reset_index()
def demand_estimate(self, interaction_df: pd.DataFrame, exclude_sessions: Optional[pd.Series] = None) -> np.ndarray:
# proxy demand from weighted interaction events
if interaction_df.empty:
return np.zeros(self.product_catelogue_size, dtype=np.float32)
df = interaction_df
if exclude_sessions is not None:
bad_sessions = set(exclude_sessions.loc[exclude_sessions].index)
df = df[~df["session_id"].isin(bad_sessions)]
weights = {"view": 0.15, "cart": 0.75, "purchase": 2.5}
w = df["action"].map(weights).fillna(0.0).to_numpy(dtype=float)
prod = df["product_id"].to_numpy(dtype=int)
q_hat = np.zeros(self.product_catelogue_size, dtype=float)
np.add.at(q_hat, prod, w)
return q_hat.astype(np.float32)
def run_pricing_simulation(self, prices: np.ndarray) -> Dict[str, Any]:
interaction_df = self._simulate_sessions(prices)
self._last_interaction_df = interaction_df
session_df = self._session_feature_table(interaction_df)
predicted_agent_sessions = None
if (self.use_defense and self.agent_detector is not None and not session_df.empty):
predicted_agent_sessions = self.agent_detector(session_df.set_index("session_id"))
q_hat_naive = self.demand_estimate(interaction_df, exclude_sessions=None)
q_hat_defended = self.demand_estimate(interaction_df, exclude_sessions=predicted_agent_sessions) \
if predicted_agent_sessions is not None else q_hat_naive.copy()
true_human = np.zeros(self.product_catelogue_size, dtype=float)
true_agent = np.zeros(self.product_catelogue_size, dtype=float)
if not interaction_df.empty:
purchases = interaction_df[interaction_df["action"] == "purchase"]
if not purchases.empty:
for _, r in purchases.iterrows():
if r["actor"] == "human":
true_human[int(r["product_id"])] += 1.0
else:
true_agent[int(r["product_id"])] += 1.0
revenue_observed = float(interaction_df["price_paid"].sum()) if not interaction_df.empty else 0.0
revenue_oracle = float(interaction_df["oracle_price_paid"].sum()) if not interaction_df.empty else 0.0
agent_loss = max(0.0, revenue_oracle - revenue_observed)
eps = 1e-6
internal_error_naive = np.abs(true_human - q_hat_naive) / (true_human + eps)
internal_error_def = np.abs(true_human - q_hat_defended) / (true_human + eps)
interaction_features = self.compute_interaction_features(interaction_df)
summary = {
'prices': prices,
'true_demand': true_demand,
'demand_estimates': demand_estimates,
'internal_error': internal_error,
'interaction_data': interaction_data,
'interaction_features': interaction_features
"prices": prices.copy(),
"interaction_df": interaction_df,
"session_df": session_df,
"q_hat_naive": q_hat_naive,
"q_hat_defended": q_hat_defended,
"true_human_demand": true_human.astype(np.float32),
"true_agent_purchases": true_agent.astype(np.float32),
"internal_error_naive": internal_error_naive.astype(np.float32),
"internal_error_defended": internal_error_def.astype(np.float32),
"interaction_features": interaction_features,
"revenue_observed": revenue_observed,
"revenue_oracle": revenue_oracle,
"agent_loss": agent_loss,
"predicted_agent_sessions": predicted_agent_sessions,
}
self.simulation_history.append(summary)
return summary
def get_interaction_data(self) -> np.ndarray:
# Simulate interaction data
interaction_data = []
return np.array(interaction_data)
def demand_estimate(self, interactions : np.ndarray) -> np.ndarray:
demand_estimates = np.random.rand(self.product_catelogue_size) * 100 # Dummy demand estimates
return demand_estimates
if self._last_interaction_df.empty:
return np.array([], dtype=object)
return self._last_interaction_df.to_dict(orient="records")
class PHANTOMEnv(gym.Env):
def __init__(self):
super(PHANTOMEnv, self).__init__()
metadata = {"render_modes": []}
def __init__(self, use_defense: bool = False):
super().__init__()
self.constraints = BusinessLogicConstraints()
self.action_space = spaces.Box(
low=-self.constraints.max_price_adjustment, high=self.constraints.max_price_adjustment,
shape=(self.constraints.product_catelogue_size,), dtype=np.float32) # we allow teh learner to adjust price by some BusinessLogicConstraints factor
# Example for using image as input:
self.action_space = spaces.Box(low=-self.constraints.max_price_adjustment,
high=self.constraints.max_price_adjustment,
shape=(self.constraints.product_catelogue_size,), dtype=np.float32)
self.observation_space = spaces.Dict({
"elasticity": spaces.Dict({
"price": spaces.Box(
low=np.full((self.constraints.product_catelogue_size,), self.constraints.system_min_price, dtype=np.float32),
high=np.full((self.constraints.product_catelogue_size,), self.constraints.system_max_price, dtype=np.float32),
dtype=np.float32),
"demand": spaces.Box(
low=np.zeros((self.constraints.product_catelogue_size,), dtype=np.float32),
high=np.full((self.constraints.product_catelogue_size,), 1e6, dtype=np.float32),
dtype=np.float32),
})
})
self.commerce_platform = CommercePlatform(
product_catelogue_size=self.constraints.product_catelogue_size,
max_price=self.constraints.system_max_price,
min_price=self.constraints.system_min_price
)
self.observation_space = spaces.Dict({
'elasticity': spaces.Dict({
'price': spaces.Box(low=0, high=self.constraints.system_max_price,
shape=(self.constraints.product_catelogue_size,), dtype=np.float32),
'demand': spaces.Box(low=0, high=np.inf,
shape=(self.constraints.product_catelogue_size,), dtype=np.float32)
})
})
min_price=self.constraints.system_min_price,
constraints=self.constraints,
agent_detector=simple_agent_detector,
use_defense=use_defense)
self._rng = np.random.default_rng(self.constraints.seed)
self.t = 0
self._prev_prices: Optional[np.ndarray] = None
self.state: Dict[str, Any] = {}
def reset(self, seed :int, options) -> tuple[dict, dict]:
def reset(self, seed: Optional[int] = None, options: Optional[dict] = None):
super().reset(seed=seed)
# Initialize state
if seed is not None:
self._rng = np.random.default_rng(seed)
self.commerce_platform._rng = np.random.default_rng(seed)
self.t = 0
init_prices = self._rng.uniform(low=60.0, high=140.0, size=(self.constraints.product_catelogue_size,)).astype(np.float32)
self._prev_prices = init_prices.copy()
self.state = {
'elasticity': {
'price': np.full((self.constraints.product_catelogue_size,), 100.0, dtype=np.float32),
'demand': np.full((self.constraints.product_catelogue_size,), 50.0, dtype=np.float32)
"elasticity": {
"price": init_prices,
"demand": np.zeros((self.constraints.product_catelogue_size,), dtype=np.float32),
}
}
return self.state, {}
def step(self, action):
self.state['price'] = np.clip(self.state['price'] * (1 + action),
def step(self, action: np.ndarray):
self.t += 1
base_prices = self.state["elasticity"]["price"].astype(np.float32)
new_prices = np.clip(base_prices * (1.0 + action.astype(np.float32)),
self.constraints.system_min_price,
self.constraints.system_max_price)
self.constraints.system_max_price).astype(np.float32)
result = self.commerce_platform.run_pricing_simulation(new_prices)
result = self.commerce_platform.run_pricing_simulation(self.state['price'])
history = self.commerce_platform.simulation_history
self.state['demand'] = result['demand_estimates']
if self.commerce_platform.use_defense:
demand_est = result["q_hat_defended"]
internal_err = result["internal_error_defended"]
else:
demand_est = result["q_hat_naive"]
internal_err = result["internal_error_naive"]
self.state["elasticity"]["price"] = new_prices
self.state["elasticity"]["demand"] = demand_est
volatility = 0.0 if self._prev_prices is None else \
float(np.mean(np.abs((new_prices - self._prev_prices) / (self._prev_prices + 1e-6))))
self._prev_prices = new_prices.copy()
reward = sum(
self.state['price'] * self.state['demand'],
# performance historically, to take into account business kpi trends (using features from interaction data)
sum(
[-0.05 * i * history[-1]['internal_error'] for i in range(1, len(history))],
) if len(history) > 1 else 0,
sum(
[0.1 * history[-1]['interaction_features']['mean_sale_price'] - 0.1 * history[i]['interaction_features']['mean_sale_price'] for i in range(len(history)-1)],
) if len(history) > 1 else 0
)
revenue_observed = float(result["revenue_observed"])
agent_loss = float(result["agent_loss"])
err_mean = float(np.mean(internal_err))
reward = (revenue_observed
- self.constraints.w_agent_loss * agent_loss
- self.constraints.w_volatility * volatility
- self.constraints.w_estimation_error * err_mean)
terminated = self.t >= self.constraints.episode_length
info = {
"t": self.t,
"revenue_observed": revenue_observed,
"revenue_oracle": float(result["revenue_oracle"]),
"agent_loss": agent_loss,
"ux_volatility": volatility,
"mean_internal_error": err_mean,
"look_to_book": float(result["interaction_features"].get("look_to_book", 0.0)),
"mean_sale_price": float(result["interaction_features"].get("mean_sale_price", 0.0)),
"true_human_purchases_total": float(np.sum(result["true_human_demand"])),
"true_agent_purchases_total": float(np.sum(result["true_agent_purchases"])),
}
return self.state, float(reward), terminated, False, info
# Check if episode is done
done = self.state['price'] <= 0.0 or self.state['demand'] <= 0.0
return self.state, reward, done, False, {}
def simulate_demand(self, price):
# Simple linear demand model: demand decreases as price increases
base_demand = 200
price_sensitivity = 0.5
demand = max(0, base_demand - price_sensitivity * price)
return demand
if __name__ == "__main__":
env = PHANTOMEnv()
obs, _ = env.reset()
import matplotlib.pyplot as plt
from collections import defaultdict
runs = {}
for use_defense in (False, True):
env = PHANTOMEnv(use_defense=use_defense)
obs, _ = env.reset(seed=42)
metrics = defaultdict(list)
total_reward = 0.0
done = False
total_reward = 0
while not done:
action = env.action_space.sample() # Random action
obs, reward, done, _, _ = env.step(action)
action = env.action_space.sample()
obs, reward, done, _, info = env.step(action)
total_reward += reward
print(f"Price: {obs['price']:.2f}, Demand: {obs['demand']:.2f}, Reward: {reward:.2f}")
if done:
break
p_mean = float(np.mean(obs["elasticity"]["price"]))
q_mean = float(np.mean(obs["elasticity"]["demand"]))
p_std = float(np.std(obs["elasticity"]["price"]))
print(f"Total Reward: {total_reward:.2f}")
metrics['t'].append(info['t'])
metrics['price_mean'].append(p_mean)
metrics['price_std'].append(p_std)
metrics['demand_mean'].append(q_mean)
metrics['revenue_observed'].append(info['revenue_observed'])
metrics['revenue_oracle'].append(info['revenue_oracle'])
metrics['agent_loss'].append(info['agent_loss'])
metrics['ux_volatility'].append(info['ux_volatility'])
metrics['look_to_book'].append(info['look_to_book'])
metrics['reward'].append(reward)
metrics['human_purchases'].append(info['true_human_purchases_total'])
metrics['agent_purchases'].append(info['true_agent_purchases_total'])
if info['t'] % 20 == 0 or done:
print(f"defense={'ON ' if use_defense else 'OFF'} t={info['t']:03d} p={p_mean:6.2f}±{p_std:4.2f} "
f"q={q_mean:6.2f} rev={info['revenue_observed']:7.2f} oracle={info['revenue_oracle']:7.2f} "
f"loss={info['agent_loss']:6.2f} ux={info['ux_volatility']:.3f} "
f"ltb={info['look_to_book']:5.2f} r={reward:7.2f}")
runs[use_defense] = metrics
print(f"defense={'ON ' if use_defense else 'OFF'} total_reward={total_reward:.2f}\n")
fig, axes = plt.subplots(3, 3, figsize=(15, 12))
fig.suptitle('PHANTOM Environment: Defense OFF vs ON', fontsize=14, fontweight='bold')
plot_configs = [
('price_mean', 'Mean Price', 'Price'),
('demand_mean', 'Mean Demand Estimate', 'Demand'),
('revenue_observed', 'Revenue (Observed)', 'Revenue'),
('agent_loss', 'Agent Loss (Oracle - Observed)', 'Loss'),
('ux_volatility', 'UX Volatility (Price Change)', 'Volatility'),
('look_to_book', 'Look-to-Book Ratio', 'Ratio'),
('reward', 'Step Reward', 'Reward'),
('human_purchases', 'Human Purchases', 'Count'),
('agent_purchases', 'Agent Purchases', 'Count'),
]
for idx, (key, title, ylabel) in enumerate(plot_configs):
ax = axes[idx // 3, idx % 3]
for use_defense, label, color in [(False, 'No Defense', 'red'), (True, 'With Defense', 'blue')]:
m = runs[use_defense]
ax.plot(m['t'], m[key], label=label, color=color, alpha=0.7, linewidth=1.5)
ax.set_xlabel('Step')
ax.set_ylabel(ylabel)
ax.set_title(title, fontsize=10, fontweight='bold')
ax.legend(loc='best', fontsize=8)
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig('phantom_env_comparison.png', dpi=150, bbox_inches='tight')
print("Plot saved to phantom_env_comparison.png")
plt.show()