2nd/10_Wiki/Topics/AI_and_ML/Credit Assignment Problem.md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

id	title	category	status	canonical_id	aliases	duplicate_of	source_trust_level	confidence_score	verification_status	tags	raw_sources	last_reinforced	github_commit	tech_stack
wiki-2026-0508-credit-assignment	Credit Assignment Problem	10_Wiki/Topics	verified	self	credit assignment temporal credit structural credit backpropagation GAE PRM attribution	none	A	0.93	applied	reinforcement-learning credit-assignment backpropagation gae prm attribution multi-agent llm		2026-05-10	pending	language framework Python PyTorch / JAX / RL libs

Credit Assignment Problem

매 한 줄

"매 누가 / 매 무엇 의 reward 의 기여?". 매 long sequence 의 final reward 의 매 step 별 attribution. 매 RL 의 fundamental + 매 deep learning 의 backprop 의 essence. 매 modern: GAE, PRM, RLHF, multi-agent.

매 핵심 type

Temporal Credit Assignment

• 매 sequence of action → 매 final reward.
• 매 어떤 action 의 결정?
• 매 RL 의 challenge.

Structural Credit Assignment

• 매 layered NN → 매 error.
• 매 어떤 weight / neuron 의 fix?
• 매 backprop 의 solve.

Multi-agent Credit

• 매 N agent → 매 collective reward.
• 매 individual contribution.

매 solution

Backpropagation (structural)

• 매 chain rule.
• 매 each layer 의 gradient.
• 매 1986 Rumelhart-Hinton-Williams.

TD Learning (temporal)

• 매 bootstrap.
• 매 Computational-Neuroscience-RL 참조.

Eligibility Trace

• 매 past action 의 trace 유지.
• 매 TD(λ).

GAE (Generalized Advantage Estimation)

• Schulman 2015.
• 매 bias-variance trade-off.
• 매 PPO 의 standard.
• A_t = \sum_{l=0}^{\infty} (\gamma\lambda)^l \delta_{t+l}

Hindsight Experience Replay (HER)

• 매 fail trajectory 의 매 different goal 의 reuse.

Reward Shaping

• 매 dense intermediate reward.
• 매 careful: 매 unintended optimal X.

Process Reward Model (PRM, modern)

• 매 매 step 의 grade.
• 매 OpenAI Math, 매 DeepSeek-Prover.
• 매 outcome reward 보다 매 finer.

Counterfactual (multi-agent)

• COMA (Counterfactual Multi-Agent Policy Gradient).
• 매 1 agent 의 fix → 매 contribution.

Attention attribution (LLM)

• 매 attention score 의 attribution.
• 매 SHAP, integrated gradient.

매 응용

1. Game AI: 매 chess / Go (long horizon).
2. Robotics: 매 sparse reward.
3. LLM RLHF: 매 token-level reward.
4. Multi-agent: 매 cooperative.
5. Medical: 매 long-term outcome.
6. Finance: 매 portfolio.

💻 패턴

Backpropagation (structural)

import torch

x = torch.tensor([1.0, 2.0], requires_grad=True)
W1 = torch.randn(2, 3, requires_grad=True)
W2 = torch.randn(3, 1, requires_grad=True)

h = torch.relu(x @ W1)
y = h @ W2

loss = (y - target).pow(2).mean()
loss.backward()  # 매 W1, W2 의 gradient (credit) 계산.

print(W1.grad)  # 매 each weight 의 contribution.

TD(0) (temporal)

def td_update(V, state, reward, next_state, alpha=0.1, gamma=0.95):
    td_error = reward + gamma * V[next_state] - V[state]
    V[state] += alpha * td_error
    return V

TD(λ) with eligibility trace

class TDLambda:
    def __init__(self, n_states, alpha=0.1, gamma=0.95, lam=0.9):
        self.V = np.zeros(n_states)
        self.e = np.zeros(n_states)
        self.alpha, self.gamma, self.lam = alpha, gamma, lam
    
    def update(self, state, reward, next_state):
        td_error = reward + self.gamma * self.V[next_state] - self.V[state]
        self.e *= self.gamma * self.lam
        self.e[state] += 1  # 매 visited state 의 trace 증가
        self.V += self.alpha * td_error * self.e  # 매 trace 비례 update

GAE (PPO standard)

def compute_gae(rewards, values, gamma=0.99, lam=0.95):
    """매 매 step 의 advantage."""
    advantages = np.zeros_like(rewards)
    last_gae = 0
    for t in reversed(range(len(rewards))):
        delta = rewards[t] + gamma * values[t+1] - values[t]
        advantages[t] = last_gae = delta + gamma * lam * last_gae
    return advantages

Hindsight Experience Replay

def her_relabel(trajectory, goal_extractor):
    """매 failure 의 매 goal 의 reach 의 success 로 relabel."""
    new_trajectories = [trajectory]
    
    # 매 final state 의 매 goal
    final_state = trajectory[-1].state
    new_goal = goal_extractor(final_state)
    
    relabeled = []
    for t in trajectory:
        new_reward = 1.0 if reached(t.next_state, new_goal) else -0.01
        relabeled.append(Transition(t.state, t.action, new_reward, t.next_state, new_goal))
    new_trajectories.append(relabeled)
    
    return new_trajectories

Reward shaping (caution)

def shaped_reward(state, action, next_state):
    base_reward = environment_reward(state, action, next_state)
    # 매 distance-based shaping (Ng 1999 — potential-based 안전)
    phi = lambda s: -distance_to_goal(s)
    shaping = gamma * phi(next_state) - phi(state)
    return base_reward + shaping

Process Reward Model (PRM)

def prm_train(model, trajectories):
    """매 각 step 의 quality 의 supervised label."""
    for traj in trajectories:
        for step in traj.steps:
            # 매 human / verifier label
            quality = label_step(step.state, step.action, step.reasoning)
            loss = model.loss(step, quality)
            loss.backward()
            optimizer.step()

# 매 inference: 매 each generation step 의 PRM score.
def search_with_prm(prompt, prm, beam=4, depth=10):
    candidates = [prompt]
    for d in range(depth):
        all_candidates = []
        for c in candidates:
            for cont in generate_n(c, n=beam*2):
                score = prm.score(c + cont)
                all_candidates.append((c + cont, score))
        all_candidates.sort(key=lambda x: -x[1])
        candidates = [c for c, _ in all_candidates[:beam]]
    return candidates[0]

COMA (multi-agent counterfactual)

def coma_advantage(joint_actions, q_function, agent_idx):
    """매 specific agent 의 contribution = joint Q − counterfactual baseline."""
    actual_q = q_function(joint_actions)
    
    # 매 agent_idx 의 매 다른 action 의 average
    counterfactual_q = 0
    for alt_action in action_space:
        alt = list(joint_actions)
        alt[agent_idx] = alt_action
        counterfactual_q += q_function(alt) * policy[agent_idx][alt_action]
    
    return actual_q - counterfactual_q

Attention-based attribution

import torch

def attention_attribution(model, input_ids, target_token_idx):
    """매 매 input token 의 contribution to 매 specific output."""
    output = model(input_ids, output_attentions=True)
    attentions = output.attentions  # 매 N layer × N head × seq × seq
    
    # 매 target token 의 attention to 매 input
    avg = torch.stack(attentions).mean(dim=(0, 1, 2))  # 매 reduce
    return avg[target_token_idx]  # 매 (seq,) — 매 매 input 의 contribution

RLHF token-level credit

def rlhf_token_advantage(generated_tokens, reward_model):
    """매 reward 의 token-level distribute."""
    final_reward = reward_model(generated_tokens)
    
    # 매 simple: 매 final 의 모든 token 의 distribute (inefficient)
    simple = [final_reward / len(generated_tokens)] * len(generated_tokens)
    
    # 매 better: 매 PRM 의 step-level
    prm_scores = process_reward_model.score_each(generated_tokens)
    return prm_scores

매 결정 기준

상황	Approach
Long horizon	TD + GAE
Sparse reward	HER + reward shaping
Math / multi-step	PRM
Deep NN	Backprop
Multi-agent	COMA / counterfactual
LLM RLHF	PRM > outcome reward
Interpretability	SHAP / attention

기본값: 매 GAE (PPO) + 매 PRM (LLM math/code).

🔗 Graph

• 부모: Reinforcement-Learning · Optimization · Deep Learning
• 변형: 데이터 사이언스 및 ML 엔지니어링 · TD-Learning · GAE · HER · PRM
• 응용: PPO · RLHF · Best-of-N_Sampling · Multi-agent-System
• Adjacent: Computational-Neuroscience-RL · Bayesian-Brain-Hypothesis · Bias-Correction-Algorithm · Causal-Inference

🤖 LLM 활용

언제: 매 RL design. 매 RLHF / PRM. 매 multi-agent system. 매 attribution. 언제 X: 매 supervised IID (다른 paradigm).

❌ 안티패턴

• Outcome reward 만 (long horizon): 매 sparse signal.
• Reward shaping 의 careless: 매 unintended optimal.
• No eligibility trace (long): 매 slow learning.
• PRM 의 noisy label: 매 wrong attribution.
• Multi-agent 의 individual reward 의 share: 매 lazy agent.

🧪 검증 / 중복

• Verified (Schulman GAE, Andrychowicz HER, OpenAI PRM, Foerster COMA).
• 신뢰도 A.
• Related: Reinforcement-Learning · Computational-Neuroscience-RL · RLHF · Causal-Inference · Best-of-N_Sampling.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — temporal/structural/multi-agent + 매 GAE / HER / PRM / COMA code