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10_Wiki/Topics/Topic_Programming/From_Other/Feedback-Loops.md

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+---
+id: wiki-2026-0508-feedback-loops
+title: Feedback Loops
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [Feedback Control, Closed Loop, Cybernetic Feedback]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.9
+verification_status: applied
+tags: [systems, control-theory, cybernetics, dynamics]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: python
+  framework: control-systems
+---
+
+# Feedback Loops
+
+## 매 한 줄
+> **"매 system output 의 input 의 re-entry — 매 stability 또는 amplification 의 결정"**. 매 1948 Wiener 의 Cybernetics 가 unifying frame. 매 2026 의 RLHF, autoscaling, climate tipping points, social media engagement loop 의 modern instances.
+
+## 매 핵심
+
+### 매 2 polarities
+- **Negative (balancing)**: 매 deviation 의 dampen — 매 thermostat, homeostasis, PID controller.
+- **Positive (reinforcing)**: 매 deviation 의 amplify — 매 viral growth, asset bubble, ice-albedo feedback, runaway selection.
+
+### 매 5 archetypes (Senge)
+- **Limits to growth**: 매 reinforcing + balancing — 매 S-curve.
+- **Shifting the burden**: 매 quick fix 의 underlying issue 의 weaken.
+- **Tragedy of the commons**: 매 individual reinforcing → collective collapse.
+- **Fixes that fail**: 매 short-term fix 의 long-term backfire.
+- **Success to the successful**: 매 winner-take-all reinforcing.
+
+### 매 stability concepts
+- **Gain**: 매 output/input ratio.
+- **Phase margin**: 매 stability buffer (>45° robust).
+- **Time delay**: 매 instability driver (Bode-Nyquist).
+- **Setpoint vs. error**: 매 target — actual.
+
+### 매 응용
+1. PID controller (industrial process).
+2. RLHF (LLM 의 preference loop).
+3. Autoscaling (Kubernetes HPA, target CPU).
+4. Insulin-glucose homeostasis.
+5. Market price discovery.
+
+## 💻 패턴
+
+### PID controller
+```python
+class PID:
+    def __init__(self, kp: float, ki: float, kd: float, setpoint: float):
+        self.kp, self.ki, self.kd = kp, ki, kd
+        self.setpoint = setpoint
+        self.integral = 0.0
+        self.prev_error = 0.0
+
+    def step(self, measurement: float, dt: float) -> float:
+        error = self.setpoint - measurement
+        self.integral += error * dt
+        derivative = (error - self.prev_error) / dt if dt > 0 else 0
+        self.prev_error = error
+        return self.kp * error + self.ki * self.integral + self.kd * derivative
+```
+
+### Logistic growth (limits-to-growth archetype)
+```python
+import numpy as np
+from scipy.integrate import odeint
+
+def logistic(N, t, r, K):
+    return r * N * (1 - N / K)
+
+t = np.linspace(0, 50, 500)
+N = odeint(logistic, y0=1, t=t, args=(0.3, 1000))
+# Reinforcing (rN) + balancing ((1 - N/K))
+```
+
+### Autoscaling reactive loop
+```python
+def autoscale_step(current_replicas: int, cpu_utilization: float,
+                   target: float = 0.7, max_replicas: int = 100) -> int:
+    desired = int(current_replicas * cpu_utilization / target)
+    return max(1, min(desired, max_replicas))
+```
+
+### Reinforcement learning (RLHF reward model loop)
+```python
+def rlhf_iteration(policy, reward_model, prompts, ppo_optimizer):
+    rollouts = [policy.generate(p) for p in prompts]
+    rewards = [reward_model.score(p, r) for p, r in zip(prompts, rollouts)]
+    advantages = compute_advantages(rewards)
+    ppo_optimizer.step(policy, rollouts, advantages)
+    # Loop closes: policy → output → reward → policy update
+```
+
+### Stability check (root locus)
+```python
+import numpy as np
+from scipy.signal import TransferFunction, bode
+
+# Open-loop transfer function
+sys = TransferFunction([1], [1, 2, 3, 1])  # 3rd order
+w, mag, phase = bode(sys)
+# Phase margin: phase at gain crossover + 180°
+```
+
+### Detect runaway positive feedback
+```python
+def detect_runaway(time_series: list[float], window: int = 10, threshold: float = 1.5) -> bool:
+    """Exponential growth detector — log-linear fit slope."""
+    import numpy as np
+    if len(time_series) < window:
+        return False
+    y = np.log(np.maximum(time_series[-window:], 1e-9))
+    slope = np.polyfit(range(window), y, 1)[0]
+    return slope > np.log(threshold) / window
+```
+
+## 매 결정 기준
+| 상황 | Approach |
+|---|---|
+| Process regulation, setpoint tracking | PID (negative feedback) |
+| Growth modeling | logistic / Gompertz (mixed) |
+| Cascading failure prevention | rate limiters + circuit breakers |
+| Slow process w/ delay | feed-forward + smith predictor |
+| ML training | RLHF / GRPO with KL regularization |
+
+**기본값**: 매 negative feedback 의 default for stability. 매 positive feedback 의 explicit guard (rate limit, kill switch).
+
+## 🔗 Graph
+- 부모: [[Cybernetics Foundations|Cybernetics]] · [[Control Theory]] · [[Systems_Thinking|Systems Thinking]]
+- 응용: [[RLHF]] · [[Homeostasis (항상성)|Homeostasis]]
+
+## 🤖 LLM 활용
+**언제**: 매 archetype identification, 매 PID gain initial estimation, 매 system dynamics diagram 의 stock-flow conversion.
+**언제 X**: 매 safety-critical control gain tuning — 매 hardware-in-the-loop testing, 매 actual phase margin verification 필수.
+
+## ❌ 안티패턴
+- **Ignoring delay**: 매 time-delay 의 PID 의 instability — 매 dead-time compensation 필요.
+- **High gain assumption = better tracking**: 매 oscillation, 매 noise amplification.
+- **Open-loop control for safety-critical**: 매 disturbance rejection X — 매 closed-loop 필수.
+- **Reinforcing loop 의 무방어 deploy**: 매 viral metric 의 optimization — 매 social harm runaway (engagement maximization → polarization).
+
+## 🧪 검증 / 중복
+- Verified (Wiener "Cybernetics" 1948, Åström & Murray "Feedback Systems" 2nd ed, Sterman "Business Dynamics" 2000, Senge "Fifth Discipline" rev. ed).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — PID, Senge archetypes, RLHF/autoscaling 추가 |