|
| 1 | +""" |
| 2 | +Implementation of MCTS + Self-refine algorithm. |
| 3 | +
|
| 4 | +Reference: |
| 5 | +1. "Accessing GPT-4 level Mathematical Olympiad Solutions via Monte |
| 6 | +Carlo Tree Self-refine with LLaMa-3 8B: A Technical Report" |
| 7 | +2. https://github.com/BrendanGraham14/mcts-llm/ |
| 8 | +3. https://github.com/trotsky1997/MathBlackBox/ |
| 9 | +4. https://github.com/openreasoner/openr/blob/main/reason/guided_search/tree.py |
| 10 | +""" |
| 11 | + |
| 12 | +from __future__ import annotations |
| 13 | + |
| 14 | +import math |
| 15 | +from collections import deque |
| 16 | + |
| 17 | +import numpy as np |
| 18 | +import tqdm |
| 19 | +from coati.reasoner.guided_search.llm import chat_completion |
| 20 | +from coati.reasoner.guided_search.prompt_store.base import PromptCFG |
| 21 | +from pydantic import BaseModel |
| 22 | + |
| 23 | + |
| 24 | +class MCTSNode(BaseModel): |
| 25 | + """ |
| 26 | + Node for MCTS. |
| 27 | + """ |
| 28 | + |
| 29 | + answer: str |
| 30 | + parent: MCTSNode = None |
| 31 | + children: list[MCTSNode] = [] |
| 32 | + num_visits: int = 0 |
| 33 | + Q: int = 0 |
| 34 | + rewards: list[int] = [] |
| 35 | + |
| 36 | + def expand_node(self, node) -> None: |
| 37 | + self.children.append(node) |
| 38 | + |
| 39 | + def add_reward(self, reward: int) -> None: |
| 40 | + self.rewards.append(reward) |
| 41 | + self.Q = (np.min(self.rewards) + np.mean(self.rewards)) / 2 |
| 42 | + |
| 43 | + |
| 44 | +class MCTS(BaseModel): |
| 45 | + """ |
| 46 | + Simulation of MCTS process. |
| 47 | + """ |
| 48 | + |
| 49 | + problem: str |
| 50 | + max_simulations: int |
| 51 | + cfg: PromptCFG |
| 52 | + C: float = 1.4 |
| 53 | + max_children: int = 2 |
| 54 | + epsilon: float = 1e-5 |
| 55 | + root: MCTSNode = None |
| 56 | + |
| 57 | + def initialization(self): |
| 58 | + """ |
| 59 | + Root Initiation. |
| 60 | + """ |
| 61 | + # Dummy answer as root. |
| 62 | + base_answer = self.sample_base_answer() |
| 63 | + self.root = MCTSNode(answer=base_answer) |
| 64 | + self.self_evaluate(self.root) |
| 65 | + |
| 66 | + def is_fully_expanded(self, node: MCTSNode): |
| 67 | + return len(node.children) >= self.max_children or any(child.Q > node.Q for child in node.children) |
| 68 | + |
| 69 | + def select_node(self) -> MCTSNode: |
| 70 | + """ |
| 71 | + Select next node to explore. |
| 72 | + """ |
| 73 | + candidates: list[MCTSNode] = [] |
| 74 | + to_explore = deque([self.root]) |
| 75 | + |
| 76 | + while to_explore: |
| 77 | + current_node = to_explore.popleft() |
| 78 | + if not self.is_fully_expanded(current_node): |
| 79 | + candidates.append(current_node) |
| 80 | + to_explore.extend(current_node.children) |
| 81 | + |
| 82 | + if not candidates: |
| 83 | + return self.root |
| 84 | + |
| 85 | + return max(candidates, key=self.compute_uct) |
| 86 | + |
| 87 | + def self_evaluate(self, node: MCTSNode): |
| 88 | + """ |
| 89 | + Sample reward of the answer. |
| 90 | + """ |
| 91 | + reward = self.sample_reward(node) |
| 92 | + node.add_reward(reward) |
| 93 | + |
| 94 | + def back_propagation(self, node: MCTSNode): |
| 95 | + """ |
| 96 | + Back propagate the value of the refined answer. |
| 97 | + """ |
| 98 | + parent = node.parent |
| 99 | + while parent: |
| 100 | + best_child_Q = max(child.Q for child in parent.children) |
| 101 | + parent.Q = (parent.Q + best_child_Q) / 2 |
| 102 | + parent.num_visits += 1 |
| 103 | + parent = parent.parent |
| 104 | + |
| 105 | + def compute_uct(self, node: MCTSNode): |
| 106 | + """ |
| 107 | + Compute UCT. |
| 108 | + """ |
| 109 | + if node.parent is None: |
| 110 | + return -100 |
| 111 | + return node.Q + self.C * math.sqrt(math.log(node.parent.num_visits + 1) / (node.num_visits + self.epsilon)) |
| 112 | + |
| 113 | + def simulate(self): |
| 114 | + self.initialization() |
| 115 | + for _ in tqdm.tqdm(range(self.max_simulations)): |
| 116 | + node = self.select_node() |
| 117 | + child = self.self_refine(node) |
| 118 | + node.expand_node(child) |
| 119 | + self.self_evaluate(child) |
| 120 | + self.back_propagation(child) |
| 121 | + |
| 122 | + return self.get_best_answer() |
| 123 | + |
| 124 | + def get_best_answer(self): |
| 125 | + to_visit = deque([self.root]) |
| 126 | + best_node = self.root |
| 127 | + |
| 128 | + while to_visit: |
| 129 | + current_node = to_visit.popleft() |
| 130 | + if current_node.Q > best_node.Q: |
| 131 | + best_node = current_node |
| 132 | + to_visit.extend(current_node.children) |
| 133 | + |
| 134 | + return best_node.answer |
| 135 | + |
| 136 | + def self_refine(self, node: MCTSNode): |
| 137 | + """ |
| 138 | + Refine node. |
| 139 | + """ |
| 140 | + critique_response = chat_completion( |
| 141 | + messages=[ |
| 142 | + { |
| 143 | + "role": "system", |
| 144 | + "content": self.cfg.critic_system_prompt, |
| 145 | + }, |
| 146 | + { |
| 147 | + "role": "user", |
| 148 | + "content": "\n\n".join( |
| 149 | + [ |
| 150 | + f"<problem>\n{self.problem}\n</problem>", |
| 151 | + f"<current_answer>\n{node.answer}\n</current_answer>", |
| 152 | + ] |
| 153 | + ), |
| 154 | + }, |
| 155 | + ], |
| 156 | + model=self.cfg.model, |
| 157 | + base_url=self.cfg.base_url, |
| 158 | + max_tokens=self.cfg.max_tokens, |
| 159 | + ) |
| 160 | + critique = critique_response.choices[0].message.content |
| 161 | + assert critique is not None |
| 162 | + refined_answer_response = chat_completion( |
| 163 | + messages=[ |
| 164 | + { |
| 165 | + "role": "system", |
| 166 | + "content": self.cfg.refine_system_prompt, |
| 167 | + }, |
| 168 | + { |
| 169 | + "role": "user", |
| 170 | + "content": "\n\n".join( |
| 171 | + [ |
| 172 | + f"<problem>\n{self.problem}\n</problem>", |
| 173 | + f"<current_answer>\n{node.answer}\n</current_answer>", |
| 174 | + f"<critique>\n{critique}\n</critique>", |
| 175 | + ] |
| 176 | + ), |
| 177 | + }, |
| 178 | + ], |
| 179 | + model=self.cfg.model, |
| 180 | + base_url=self.cfg.base_url, |
| 181 | + max_tokens=self.cfg.max_tokens, |
| 182 | + ) |
| 183 | + refined_answer = refined_answer_response.choices[0].message.content |
| 184 | + assert refined_answer is not None |
| 185 | + |
| 186 | + return MCTSNode(answer=refined_answer, parent=node) |
| 187 | + |
| 188 | + def sample_base_answer(self): |
| 189 | + response = chat_completion( |
| 190 | + messages=[ |
| 191 | + { |
| 192 | + "role": "system", |
| 193 | + "content": "The user will provide a problem. Solve the problem. The response should begin with [reasoning process]...[Verification]... and end with [Final Answer]. \nThe answer is [answer] \n#### [answer].", |
| 194 | + }, |
| 195 | + { |
| 196 | + "role": "user", |
| 197 | + "content": f"<problem>\n {self.problem} \n</problem> \nLet's think step by step", |
| 198 | + }, |
| 199 | + ], |
| 200 | + model=self.cfg.model, |
| 201 | + base_url=self.cfg.base_url, |
| 202 | + max_tokens=self.cfg.max_tokens, |
| 203 | + ) |
| 204 | + assert response.choices[0].message.content is not None |
| 205 | + return response.choices[0].message.content |
| 206 | + |
| 207 | + def sample_reward(self, node: MCTSNode): |
| 208 | + """ |
| 209 | + Calculate reward. |
| 210 | + """ |
| 211 | + messages = [ |
| 212 | + { |
| 213 | + "role": "system", |
| 214 | + "content": self.cfg.evaluate_system_prompt, |
| 215 | + }, |
| 216 | + { |
| 217 | + "role": "user", |
| 218 | + "content": "\n\n".join( |
| 219 | + [ |
| 220 | + f"<problem>\n{self.problem}\n</problem>", |
| 221 | + f"<answer>\n{node.answer}\n</answer>", |
| 222 | + ] |
| 223 | + ), |
| 224 | + }, |
| 225 | + ] |
| 226 | + for attempt in range(3): |
| 227 | + try: |
| 228 | + response = chat_completion( |
| 229 | + messages=messages, |
| 230 | + model=self.cfg.model, |
| 231 | + base_url=self.cfg.base_url, |
| 232 | + max_tokens=self.cfg.max_tokens, |
| 233 | + ) |
| 234 | + assert response.choices[0].message.content is not None |
| 235 | + return int(response.choices[0].message.content) |
| 236 | + except ValueError: |
| 237 | + messages.extend( |
| 238 | + [ |
| 239 | + { |
| 240 | + "role": "assistant", |
| 241 | + "content": response.choices[0].message.content, |
| 242 | + }, |
| 243 | + { |
| 244 | + "role": "user", |
| 245 | + "content": "Failed to parse reward as an integer.", |
| 246 | + }, |
| 247 | + ] |
| 248 | + ) |
| 249 | + if attempt == 2: |
| 250 | + raise |
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