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arise-skill-evolution-hierarchical-rl Build reusable skill libraries for mathematical reasoning through hierarchical RL. Maintain a high-level skills manager that summarizes successful solution traces and selects relevant strategies to condition future rollouts.
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name arise-skill-evolution-hierarchical-rl title ARISE: Agent Reasoning with Intrinsic Skill Evolution in Hierarchical RL version 0.0.2 engine skillxiv-v0.0.2-claude-opus-4.6 license MIT url https://arxiv.org/abs/2603.16060 keywords ["Skill Learning","Hierarchical Reinforcement Learning","Strategy Reuse","Mathematical Reasoning","Emergent Abilities"] description Build reusable skill libraries for mathematical reasoning through hierarchical RL. Maintain a high-level skills manager that summarizes successful solution traces and selects relevant strategies to condition future rollouts.
ARISE: Hierarchical RL with Intrinsic Skill Evolution
Current language model reasoning treats each problem independently, recomputing similar strategies repeatedly. ARISE enables agents to accumulate and reuse successful reasoning strategies through hierarchical reinforcement learning. A high-level Skills Manager maintains a library of reusable strategies by summarizing successful solution traces and selecting relevant skills to condition future reasoning. The worker (reasoning model) generates solutions informed by retrieved skills, creating a feedback loop where reasoning and skill library quality co-evolve. This approach shows consistent improvements over baselines on mathematical and competition benchmarks, with particularly strong gains on out-of-distribution problems.
The key insight: emergent reusable patterns from problem-solving can be preserved and leveraged to bootstrap future reasoning more efficiently.
Core Concept
ARISE operates through a hierarchical loop:
Problem Solving — Worker generates solution trajectoryTrace Summarization — Skills Manager extracts generalizable patterns from successful tracesSkill Library Update — Add summarized skills to reusable librarySkill Retrieval — For new problems, retrieve relevant skillsConditioned Reasoning — Worker uses retrieved skills to guide future rolloutsCo-Evolution — Both worker and skill quality improve iteratively
This creates a virtuous cycle where accumulated problem-solving experience directly improves future reasoning.
Architecture Overview
Problem Solver (Worker) — Generates step-by-step solutions using chain-of-thoughtSolution Trace Logger — Records all intermediate steps and decisionsSkill Summarizer — Extracts generalizable solution patterns from tracesSkill Library — Stores skill descriptions and embeddings for retrievalSkill Retriever — Semantic search to find relevant skills for new problemsHierarchical Reward Structure — Separate rewards for trace quality and skill utilityCo-Evolution Optimizer — Joint training of worker and skills manager
Implementation Steps
Start by defining the skill representation and summarization mechanism.
from dataclasses import dataclass
from
import
List
Dict
Optional
import
as
from
import
@dataclass
class
SolutionTrace
"""Record of solution steps for a single problem."""
str
List
str
str
bool
int
@dataclass
class
Skill
"""Reusable reasoning strategy."""
str
List
str
float
int
class
SkillManager
"""Maintain library of reusable solution strategies."""
def
__init__
self, max_skills=1000 , embedding_dim=768
self
self
self
self
100
def
summarize_trace
self, trace: SolutionTrace
Optional
str
"""Extract generalizable skill from successful solution trace."""
if
not
return
None
self
f"""Skill for {trace.problem_types} :
Problem pattern: {trace.problem[:100 ]}
Key approach: {' -> ' .join(key_steps[:3 ])}
Reasoning: {self._generate_explanation(trace.steps)} """
return
def
_identify_key_steps
self, steps: List [str ], num_key=3
List
str
"""Identify most important steps using heuristics."""
for
in
if
any
in
for
in
'define'
'assume'
'derive'
'compute'
'observe'
'conclude'
80
return
if
else
def
_generate_explanation
self, steps: List [str ]
str
"""Create concise explanation of reasoning strategy."""
if
len
1
return
f"Start: {steps[0 ][:50 ]} ... Then: {steps[-1 ][:50 ]} ..."
return
0
100
if
else
""
def
add_skill
self, skill_text: str , problem_types: List [str ] = None
"""Add new skill to library."""
if
len
self
self
for
in
self
self
try
self
0
if
0
self
0
self
0
except
self
or
0.5
0
self
def
retrieve_relevant_skills
self, problem: str , query_embedding=None ,
k=3
List
"""Find most relevant skills for a problem."""
if
not
self
return
if
is
None
self
if
1
self
0
0
0
self
1
for
in
self
0
lambda
0
True
return
for
in
def
update_skill_stats
self, skill: Skill, helped: bool
"""Update statistics on skill effectiveness."""
1
0.1
1
Now implement the hierarchical training loop with the worker and skills manager.
import torch
from torch.optim import AdamW
class HierarchicalReasoningTrainer :
"""Train worker and skill manager jointly."""
def __init__ (self, reasoning_model, skill_manager ):
self .worker = reasoning_model
self .skill_manager = skill_manager
self .optimizer = AdamW(reasoning_model.parameters(), lr=1e-5 )
def generate_with_skills (self, problem: str , num_samples=4 ) -> List [str ]:
"""Generate solutions conditioned on retrieved skills."""
skills = self .skill_manager.retrieve_relevant_skills(problem, k=3 )
skill_context = "Relevant strategies:\n"
for i, skill in enumerate (skills, 1 ):
skill_context += f"{i} . {skill.description[:200 ]} \n"
prompt = f"{skill_context} \nProblem: {problem} \nSolution:"
solutions = []
for _ in range (num_samples):
solution = self .worker.generate(prompt, max_length=500 ,
temperature=0.7 )
solutions.append(solution)
return solutions
def step (self, problem: str , reference_answer: str = None ,
num_samples=4 ):
"""One training step: solve, evaluate, extract skills, update."""
solutions = self .generate_with_skills(problem, num_samples)
traces = []
best_solution = None
best_correctness = False
for solution in solutions:
correct = self ._check_correctness(solution, reference_answer)
trace = SolutionTrace(
problem=problem,
steps=solution.split('\n' ),
final_answer=solution.split('\n' )[-1 ],
correctness=correct,
num_steps=len (solution.split('\n' ))
)
traces.append(trace)
if correct and not best_correctness:
best_solution = solution
best_correctness = True
if best_solution:
best_trace = next (t for t in traces
if t.final_answer in best_solution)
skill_text = self .skill_manager.summarize_trace(best_trace)
if skill_text:
self .skill_manager.add_skill(skill_text, problem_types=[])
skills = self .skill_manager.retrieve_relevant_skills(problem)
for skill in skills:
self .skill_manager.update_skill_stats(skill, True )
trace_rewards = []
for trace in traces:
trace_quality = 1.0 if trace.correctness else 0.0
efficiency = 1.0 if 3 <= trace.num_steps <= 10 else 0.5
trace_rewards.append(0.7 * trace_quality + 0.3 * efficiency)
trace_rewards = torch.tensor(trace_rewards, dtype=torch.float32)
logprobs = self .worker.compute_logprobs(solutions)
loss = -(trace_rewards * logprobs).mean()
self .optimizer.zero_grad()
loss.backward()
torch.nn.utils.clip_grad_norm_(self .worker.parameters(), 1.0 )
self .optimizer.step()
return loss.item(), float (trace_rewards.mean())
def _check_correctness (self, solution: str ,
reference_answer: str = None ) -> bool :
"""Verify solution correctness."""
lines = solution.strip().split('\n' )
predicted_answer = lines[-1 ] if lines else ""
if reference_answer:
return self ._answers_match(predicted_answer, reference_answer)
return len (predicted_answer) > 0
def _answers_match (self, predicted: str , reference: str ) -> bool :
"""Check if answers match (handles multiple formats)."""
pred_num = self ._extract_number(predicted)
ref_num = self ._extract_number(reference)
if pred_num is not None and ref_num is not None :
return abs (pred_num - ref_num) < 1e-6
return predicted.lower() == reference.lower()
def _extract_number (self, text: str ) -> Optional [float ]:
"""Extract numerical answer from text."""
import re
match = re.search(r'-?\d+\.?\d*' , text)
return float (match .group()) if match else None
def train (self, problems: List [str ],
reference_answers: List [str ] = None ,
num_steps: int = 100 ):
"""Full training loop."""
losses = []
rewards = []
for step in range (num_steps):
idx = np.random.randint(len (problems))
problem = problems[idx]
reference = reference_answers[idx] if reference_answers else None
loss, reward = self .step(problem, reference)
losses.append(loss)
rewards.append(reward)
if (step + 1 ) % 10 == 0 :
avg_loss = np.mean(losses[-10 :])
avg_reward = np.mean(rewards[-10 :])
num_skills = len (self .skill_manager.skills)
print (f"Step {step+1 } : Loss={avg_loss:.4 f} , "
f"Reward={avg_reward:.3 f} , Skills={num_skills} " )
Practical Guidance Hyperparameters and When to Use:
Skill library size 500-2000; larger libraries are more comprehensive but slower to search
Retrieve top-3 to top-5 skills; more skills provide diversity, fewer are faster
Use when solving problems from a coherent domain (math, code, logic puzzles)
Particularly effective for problems with recurring patterns or sub-problems
For one-off problems requiring unique reasoning (no reusable patterns)
When problem domains are highly diverse (skill retrieval becomes unreliable)
For latency-critical applications (skill retrieval and selection add overhead)
Skill library becoming stale; periodically refresh by removing unused skills
Skill summarization capturing noise rather than generalizable patterns; use multiple successful traces
Retrieved skills being irrelevant to the current problem; improve embedding/similarity metric
Worker overfitting to particular skill combinations; add randomization in skill selection
Reference 