---
id: wiki-2026-0508-exploration-vs-exploitation
title: Exploration vs Exploitation
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Explore-Exploit, Multi-Armed Bandit Tradeoff, RL Tradeoff]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [reinforcement-learning, bandits, decision-theory, optimization]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: python
  framework: numpy
---

# Exploration vs Exploitation

## 매 한 줄
> **"매 known-best 의 exploit 의 unknown 의 explore 의 fundamental tradeoff"**. Exploration-exploitation dilemma 매 RL · bandits · A/B testing 의 core — 매 current best action 의 only 의 take 시 매 better unknown 의 miss, 매 too much explore 시 매 reward 의 burn. Optimal balance 매 horizon, prior, regret budget 의 function.

## 매 핵심

### 매 Spectrum
- **Pure exploit (greedy)**: 매 always 매 argmax Q(a) — 매 local optimum trap.
- **Pure explore (random)**: 매 always uniform — 매 expected regret O(T).
- **ε-greedy**: 매 prob ε 매 explore, 매 prob 1−ε 매 exploit.
- **UCB**: 매 confidence-bounded 매 deterministic explore.
- **Thompson Sampling**: 매 posterior sampling 매 Bayesian optimal.

### 매 Regret bounds
- 매 ε-greedy(static): O(T).
- 매 ε-greedy(decaying 1/t): O(log T).
- 매 UCB1: O(log T) — provably tight for stochastic bandit.
- 매 Thompson Sampling: matches Lai-Robbins lower bound.

### 매 응용
1. A/B/n testing — adaptive traffic allocation.
2. Recommender systems — cold start.
3. Hyperparameter tuning (Optuna, Vizier).
4. RL games — Atari, AlphaGo MCTS.
5. LLM 매 sampling temperature, top-p.
6. Drug trials — bandit-style adaptive design.

## 💻 패턴

### ε-greedy bandit
```python
import numpy as np

class EpsilonGreedy:
    def __init__(self, k, eps=0.1):
        self.k = k
        self.eps = eps
        self.Q = np.zeros(k)
        self.N = np.zeros(k)

    def select(self):
        if np.random.rand() < self.eps:
            return np.random.randint(self.k)
        return int(np.argmax(self.Q))

    def update(self, a, r):
        self.N[a] += 1
        self.Q[a] += (r - self.Q[a]) / self.N[a]
```

### UCB1
```python
class UCB1:
    def __init__(self, k):
        self.k, self.t = k, 0
        self.Q = np.zeros(k)
        self.N = np.zeros(k)

    def select(self):
        self.t += 1
        for a in range(self.k):
            if self.N[a] == 0:
                return a  # cold-start each arm once
        ucb = self.Q + np.sqrt(2 * np.log(self.t) / self.N)
        return int(np.argmax(ucb))

    def update(self, a, r):
        self.N[a] += 1
        self.Q[a] += (r - self.Q[a]) / self.N[a]
```

### Thompson Sampling (Bernoulli)
```python
class ThompsonBernoulli:
    def __init__(self, k):
        self.alpha = np.ones(k)  # successes + 1
        self.beta = np.ones(k)   # failures + 1

    def select(self):
        samples = np.random.beta(self.alpha, self.beta)
        return int(np.argmax(samples))

    def update(self, a, r):
        if r > 0: self.alpha[a] += 1
        else: self.beta[a] += 1
```

### Decaying ε schedule
```python
def epsilon(t, start=1.0, end=0.05, decay=10000):
    return end + (start - end) * np.exp(-t / decay)

# DQN-style: 매 early episodes 의 explore-heavy, 매 late 의 exploit
```

### Boltzmann (softmax) exploration
```python
def softmax_select(Q, tau=1.0):
    p = np.exp(Q / tau)
    p /= p.sum()
    return np.random.choice(len(Q), p=p)
# tau→0 매 greedy, tau→∞ 매 uniform
```

### Contextual bandit (LinUCB)
```python
class LinUCB:
    def __init__(self, k, d, alpha=1.0):
        self.A = [np.eye(d) for _ in range(k)]
        self.b = [np.zeros(d) for _ in range(k)]
        self.alpha = alpha

    def select(self, x):  # context vector
        ucb = []
        for a in range(len(self.A)):
            Ainv = np.linalg.inv(self.A[a])
            theta = Ainv @ self.b[a]
            mean = theta @ x
            bonus = self.alpha * np.sqrt(x @ Ainv @ x)
            ucb.append(mean + bonus)
        return int(np.argmax(ucb))

    def update(self, a, x, r):
        self.A[a] += np.outer(x, x)
        self.b[a] += r * x
```

### LLM sampling 의 explore-exploit
```python
# temperature=0 → exploit (deterministic argmax)
# temperature=1 → explore (full distribution)
# top-p=0.9 → constrained explore (nucleus)
def sample_token(logits, temperature=0.7, top_p=0.9):
    logits = logits / temperature
    probs = softmax(logits)
    sorted_idx = np.argsort(probs)[::-1]
    cum = np.cumsum(probs[sorted_idx])
    cutoff = np.searchsorted(cum, top_p) + 1
    keep = sorted_idx[:cutoff]
    p = probs[keep] / probs[keep].sum()
    return np.random.choice(keep, p=p)
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Stationary stochastic bandit | 매 UCB1 또는 Thompson |
| Bernoulli reward | 매 Thompson Beta-binomial |
| Contextual features 의 available | 매 LinUCB / NeuralBandit |
| Non-stationary (drift) | 매 sliding-window UCB / discounted TS |
| Deep RL | 매 ε-greedy decay 또는 noisy nets |
| LLM creative generation | 매 temperature 0.7-1.0 + top-p 0.9 |

**기본값**: 매 Thompson Sampling — 매 strong empirical 의 winner, 매 simple implementation.

## 🔗 Graph
- 부모: [[Reinforcement-Learning]] · [[Decision-Theory]]
- 변형: [[Multi-Armed-Bandit]] · [[UCB]] · [[Thompson-Sampling]] · [[Epsilon-Greedy]]
- 응용: [[A-B-Testing]] · [[Recommender-Systems]] · [[Hyperparameter-Tuning]] · [[MCTS]]
- Adjacent: [[Bayesian-Optimization]] · [[Active-Learning]] · [[LLM-Sampling]]

## 🤖 LLM 활용
**언제**: 매 sequential decision 매 reward feedback. Cold-start recommender. A/B 의 multi-arm 의 generalize.
**언제 X**: 매 known reward distribution + horizon→∞ — 매 closed-form optimal. Single-shot decision.

## 어려운 점 (안티패턴)
- **Static ε too high**: 매 ε=0.5 forever — 매 final 50% traffic 의 random arm 의 burn. Decay 의 use.
- **No cold-start arms**: 매 UCB 의 N[a]=0 의 not-handled — 매 inf 의 produce, 매 each arm 의 1 초기 pull 의 require.
- **Non-stationarity ignored**: 매 reward drift 의 discount 없이 의 stale Q value 의 trust.
- **Reward leakage**: 매 future info 매 leak — 매 fake "exploit" 매 actually 의 cheat.

## 🧪 검증 / 중복
- Verified (Sutton & Barto Ch. 2; Lai-Robbins 1985; Russo et al. "Tutorial on Thompson Sampling" 2018).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — explore-exploit + 7 algorithm patterns |
