Self-Improving Agents

Agents that continuously improve their capabilities through experience, feedback, and autonomous learning.

Self-Improvement Taxonomy

Self-Improvement
├── Learning from Experience
│   ├── Online Learning
│   ├── Few-Shot Adaptation
│   ├── Contextual Bandits
│   └── Meta-Learning
├── Feedback-Based Improvement
│   ├── RLHF (Reinforcement Learning from Human Feedback)
│   ├── RLAIF (RL from AI Feedback)
│   ├── DPO (Direct Preference Optimization)
│   └── Constitutional AI
├── Architecture Evolution
│   ├── Neural Architecture Search
│   ├── Prompt Optimization
│   ├── Tool/Workflow Discovery
│   └── Skill Acquisition
├── Verification & Safety
│   ├── Formal Verification
│   ├── Adversarial Training
│   ├── Interpretability
│   └── Alignment Monitoring
└── Multi-Agent Co-Evolution
    ├── Competitive Co-Evolution
    ├── Cooperative Co-Evolution
    └── Ecosystem Dynamics

Learning from Experience

Online Learning

class OnlineLearningAgent:
    def __init__(self, model: Model, optimizer: Optimizer):
        self.model = model
        self.optimizer = optimizer
        self.experience_buffer = ExperienceBuffer(capacity=10000)

    async def learn_from_interaction(self, interaction: Interaction):
        # Store experience
        self.experience_buffer.add(interaction)

        # Periodic update
        if len(self.experience_buffer) % self.update_frequency == 0:
            await self.update_model()

    async def update_model(self):
        # Sample batch from buffer
        batch = self.experience_buffer.sample(self.batch_size)

        # Compute loss
        loss = self.compute_loss(batch)

        # Gradient step
        self.optimizer.zero_grad()
        loss.backward()
        self.optimizer.step()

        # Log metrics
        self.log_metrics(loss.item(), self.experience_buffer.size)

Few-Shot Adaptation

class FewShotAdapter:
    def __init__(self, base_model: Model):
        self.base_model = base_model
        self.adapter_layers = AdapterLayers()

    async def adapt(self, examples: list[Example]) -> AdaptedModel:
        """Fast adaptation using few examples"""
        # Freeze base model
        for param in self.base_model.parameters():
            param.requires_grad = False

        # Train only adapter layers
        adapter_optimizer = Adam(self.adapter_layers.parameters(), lr=1e-3)

        for epoch in range(self.adaptation_epochs):
            for batch in self.create_batches(examples):
                loss = self.compute_loss(batch)
                adapter_optimizer.zero_grad()
                loss.backward()
                adapter_optimizer.step()

        return AdaptedModel(self.base_model, self.adapter_layers)

Contextual Bandits for Tool Selection

class ContextualBanditToolSelector:
    def __init__(self, n_arms: int, context_dim: int):
        self.n_arms = n_arms
        self.context_dim = context_dim
        self.linucb = LinUCB(n_arms, context_dim)

    async def select_tool(self, context: ToolContext) -> Tool:
        # Extract features
        features = self.extract_features(context)

        # LinUCB selection
        arm = self.linucb.select(features)
        tool = self.arms[arm]

        return tool

    def update(self, context: ToolContext, tool: Tool, reward: float):
        features = self.extract_features(context)
        arm = self.tool_to_arm[tool]
        self.linucb.update(arm, features, reward)

class LinUCB:
    def __init__(self, n_arms: int, context_dim: int, alpha: float = 1.0):
        self.n_arms = n_arms
        self.alpha = alpha
        self.A = [np.eye(context_dim) for _ in range(n_arms)]
        self.b = [np.zeros(context_dim) for _ in range(n_arms)]

    def select(self, features: np.ndarray) -> int:
        scores = []
        for arm in range(self.n_arms):
            A_inv = np.linalg.inv(self.A[arm])
            theta = A_inv @ self.b[arm]
            score = theta @ features + self.alpha * np.sqrt(features @ A_inv @ features)
            scores.append(score)
        return np.argmax(scores)

    def update(self, arm: int, features: np.ndarray, reward: float):
        self.A[arm] += np.outer(features, features)
        self.b[arm] += reward * features

Feedback-Based Improvement

RLHF (Reinforcement Learning from Human Feedback)

class RLHFTrainer:
    def __init__(self, model: Model, reward_model: RewardModel):
        self.model = model
        self.reward_model = reward_model
        self.optimizer = Adam(model.parameters(), lr=1e-6)

    async def train_step(self, prompt: str, chosen: str, rejected: str):
        # Compute log probabilities
        chosen_logprob = self.model.logprob(prompt + chosen)
        rejected_logprob = self.model.logprob(prompt + rejected)

        # DPO Loss
        loss = -F.logsigmoid(self.beta * (chosen_logprob - rejected_logprob))

        # Gradient step
        self.optimizer.zero_grad()
        loss.backward()
        self.optimizer.step()

        return loss.item()

class RewardModelTrainer:
    def __init__(self, model: Model):
        self.model = model
        self.optimizer = Adam(model.parameters(), lr=1e-5)

    async def train(self, preferences: list[PreferencePair]):
        for pref in preferences:
            chosen_logprob = self.model.logprob(pref.prompt + pref.chosen)
            rejected_logprob = self.model.logprob(pref.prompt + pref.rejected)

            # Bradley-Terry loss
            loss = -F.logsigmoid(chosen_logprob - rejected_logprob)

            self.optimizer.zero_grad()
            loss.backward()
            self.optimizer.step()

RLAIF (RL from AI Feedback)

class RLAIFTrainer:
    def __init__(self, model: Model, critique_model: Model):
        self.model = model
        self.critique_model = critique_model
        self.reward_model = RewardModel()

    async def generate_critique(self, prompt: str, response: str) -> Critique:
        """Generate AI feedback on response"""
        prompt = f"""
        Critique this response for correctness, clarity, and safety.
        Prompt: {prompt}
        Response: {response}

        Provide structured feedback.
        """
        return await self.critique_model.generate(prompt)

    async def generate_improvement(self, prompt: str, response: str, critique: Critique) -> str:
        """Generate improved response based on critique"""
        prompt = f"""
        Original: {response}
        Critique: {critique}

        Provide an improved response addressing the issues.
        """
        return await self.model.generate(prompt)

    async def train_step(self, prompt: str):
        # Generate response
        response = await self.model.generate(prompt)

        # Get AI critique
        critique = await self.generate_critique(prompt, response)

        # Generate improvement
        improved = await self.generate_improvement(prompt, response, critique)

        # RL step with reward from reward model
        reward = await self.reward_model.score(prompt, improved)
        self.rl_step(prompt, improved, reward)

Constitutional AI

class ConstitutionalAI:
    def __init__(self, model: Model, constitution: list[ConstitutionalPrinciple]):
        self.model = model
        self.constitution = constitution
        self.critique_model = Model()

    async def apply_constitution(self, prompt: str, response: str) -> str:
        # 1. Critique against constitution
        critiques = await asyncio.gather(*[
            self.critique_against_principle(response, principle)
            for principle in self.constitution
        ])

        # 2. Generate revision
        revision = await self.revise_response(prompt, response, critiques)

        return revision

    async def critique_against_principle(self, response: str, principle: ConstitutionalPrinciple) -> Critique:
        prompt = f"""
        Principle: {principle.text}

        Response to evaluate: {response}

        Does this response violate the principle? If so, explain how and suggest improvement.
        """
        return await self.critique_model.generate(prompt)

    async def revise_response(self, prompt: str, response: str, critiques: list[Critique]) -> str:
        critique_text = "\n".join(f"- {c.issue}: {c.suggestion}" for c in critiques if c.violation)

        prompt = f"""
        Original prompt: {prompt}
        Original response: {response}

        Issues identified:
        {critique_text}

        Provide a revised response that addresses all issues.
        """
        return await self.model.generate(prompt)

DPO (Direct Preference Optimization)

class DPOTrainer:
    def __init__(self, model: Model, ref_model: Model, beta: float = 0.1):
        self.model = model
        self.ref_model = ref_model
        self.beta = beta
        self.optimizer = Adam(model.parameters(), lr=1e-6)

    def dpo_loss(self, prompt: str, chosen: str, rejected: str) -> torch.Tensor:
        # Log probs under policy model
        policy_chosen = self.model.logprob(prompt + chosen)
        policy_rejected = self.model.logprob(prompt + rejected)

        # Log probs under reference model
        ref_chosen = self.ref_model.logprob(prompt + chosen)
        ref_rejected = self.ref_model.logprob(prompt + rejected)

        # DPO loss
        loss = -F.logsigmoid(
            self.beta * ((policy_chosen - ref_chosen) - (policy_rejected - ref_rejected))
        )

        return loss

    async def train_step(self, batch: list[PreferencePair]):
        total_loss = 0
        for pref in batch:
            loss = self.dpo_loss(pref.prompt, pref.chosen, pref.rejected)
            total_loss += loss

        total_loss.backward()
        self.optimizer.step()
        self.optimizer.zero_grad()

Architecture Evolution

Neural Architecture Search (NAS)

class NeuralArchitectureSearch:
    def __init__(self, search_space: SearchSpace, evaluator: Evaluator):
        self.search_space = search_space
        self.evaluator = evaluator
        self.controller = Controller()

    async def search(self, budget: int = 100) -> Architecture:
        best_arch = None
        best_score = -float('inf')

        for i in range(budget):
            # Sample architecture
            arch = self.controller.sample()

            # Evaluate
            score = await self.evaluator.evaluate(arch)

            # Update controller (REINFORCE)
            reward = score
            self.controller.update(arch, reward)

            if score > best_score:
                best_score = score
                best_arch = arch

        return best_arch

class ArchitectureController:
    def __init__(self, search_space: SearchSpace):
        self.policy_network = PolicyNetwork(search_space)
        self.optimizer = Adam(self.policy_network.parameters(), lr=1e-3)

    def sample(self) -> Architecture:
        return self.policy_network.sample()

    def update(self, arch: Architecture, reward: float):
        logprob = self.policy_network.logprob(arch)
        loss = -reward * logprob

        self.optimizer.zero_grad()
        loss.backward()
        self.optimizer.step()

Prompt Optimization

class PromptOptimizer:
    def __init__(self, evaluator: Evaluator):
        self.evaluator = evaluator
        self.optimizer = PromptOptimizer()

    async def optimize(self, 
                       initial_prompt: str, 
                       task: Task,
                       budget: int = 50) -> OptimizedPrompt:
        """Optimize prompt using evolutionary strategy"""
        population = [self.mutate(initial_prompt) for _ in range(20)]

        for generation in range(budget // 20):
            # Evaluate population
            scores = await asyncio.gather(*[
                self.evaluate(prompt) for prompt in population
            ])

            # Select top performers
            elite = sorted(zip(population, scores), key=lambda x: x[1], reverse=True)[:5]

            # Mutate and crossover
            population = []
            for _ in range(20):
                if random.random() < 0.5:
                    # Crossover
                    p1, p2 = random.sample(elite, 2)
                    child = self.crossover(p1[0], p2[0])
                else:
                    # Mutation
                    parent = random.choice(elite)[0]
                    child = self.mutate(parent)
                population.append(child)

        # Return best
        best = max(population, key=lambda p: self.evaluate(p))
        return OptimizedPrompt(prompt=best, score=self.evaluate(best))

    def mutate(self, prompt: str) -> str:
        mutations = [
            lambda p: p + " Think step by step.",
            lambda p: p + " Be concise.",
            lambda p: p + " Format as JSON.",
            lambda p: "Think step by step. " + p,
            lambda p: p.replace("Write", "Generate"),
            lambda p: p + " Be precise and accurate."
        ]
        return random.choice(mutations)(prompt)

Tool/Workflow Discovery

class ToolDiscoveryAgent:
    def __init__(self, tool_registry: ToolRegistry):
        self.registry = tool_registry
        self.usage_stats = ToolUsageTracker()

    async def discover_workflows(self, tasks: list[Task]) -> list[Workflow]:
        """Discover common tool sequences from task execution"""
        sequences = await self.extract_tool_sequences()

        # Find frequent patterns
        patterns = self.mine_patterns(sequences, min_support=0.1)

        # Convert to workflows
        workflows = []
        for pattern in patterns:
            workflow = await self.create_workflow(pattern)
            workflows.append(workflow)

        return workflows

    async def recommend_tools(self, task: Task) -> list[Tool]:
        """Recommend tools based on task similarity"""
        similar_tasks = await self.find_similar_tasks(task)
        tool_usage = Counter()

        for task in similar_tasks:
            tools = await self.get_tools_used(task)
            tool_usage.update(tools)

        return [tool for tool, _ in tool_usage.most_common(5)]

Verification & Safety

Formal Verification

class FormalVerifier:
    def __init__(self):
        self.smt_solver = z3.Solver()
        self.model_checker = ModelChecker()

    async def verify_property(self, agent: Agent, property: SafetyProperty) -> VerificationResult:
        # Translate agent to formal model
        model = self.translate_to_model(agent)

        # Encode property in SMT
        constraints = self.encode_property(property)

        # Check satisfiability
        self.smt_solver.push()
        self.smt_solver.add(constraints)
        self.smt_solver.add(Not(property.formula))

        result = self.smt_solver.check()
        self.smt_solver.pop()

        if result == unsat:
            return VerificationResult(proven=True, proof=self.smt_solver.proof())
        elif result == sat:
            counterexample = self.smt_solver.model()
            return VerificationResult(proven=False, counterexample=counterexample)
        else:
            return VerificationResult(proven=False, unknown=True)

    async def verify_contract(self, agent: Agent, contract: Contract) -> ContractVerification:
        """Verify agent satisfies contract (pre/post conditions)"""
        pre_condition = self.encode_precondition(contract.precondition)
        post_condition = self.encode_postcondition(contract.postcondition)
        agent_model = self.translate_agent(agent)

        # Verify: pre ∧ agent → post
        self.smt_solver.add(pre_condition)
        self.smt_solver.add(agent_model)
        self.smt_solver.add(Not(post_condition))

        result = self.smt_solver.check()
        return ContractVerification(proven=result == unsat)

Adversarial Training

class AdversarialTrainer:
    def __init__(self, model: Model, attack_generator: AttackGenerator):
        self.model = model
        self.attacker = attack_generator

    async def train_step(self, batch: Batch) -> float:
        # Clean loss
        clean_loss = self.model.loss(batch)

        # Generate adversarial examples
        adv_batch = await self.attacker.generate(batch)
        adv_loss = self.model.loss(adv_batch)

        # Combined loss
        loss = clean_loss + adv_loss

        self.optimizer.zero_grad()
        loss.backward()
        self.optimizer.step()

        return loss.item()

class AttackGenerator:
    def __init__(self, model: Model, epsilon: float = 0.1):
        self.model = model
        self.epsilon = epsilon

    async def generate(self, batch: Batch) -> Batch:
        # PGD Attack
        x = batch.inputs.requires_grad_(True)
        y = batch.targets

        for _ in range(10):
            loss = self.model.loss(x, y)
            grad = torch.autograd.grad(loss, x)[0]
            x = x + self.epsilon * grad.sign()
            x = torch.clamp(x, 0, 1)

        return Batch(inputs=x.detach(), targets=batch.targets)

Interpretability

class InterpretabilityAnalyzer:
    def __init__(self, model: Model):
        self.model = model
        self.attribution = AttributionMethod()

    def attribute(self, input: str, output: str) -> AttributionMap:
        """Compute attribution of input tokens to output"""
        return self.attribution.attribute(
            model=self.model,
            input=input,
            target=output
        )

    def feature_importance(self, input: str) -> FeatureImportance:
        """SHAP values for input features"""
        explainer = shap.Explainer(self.model)
        shap_values = explainer(input)
        return FeatureImportance(shap_values)

    def attention_visualization(self, input: str) -> AttentionViz:
        """Visualize attention patterns"""
        outputs = self.model(input, output_attentions=True)
        return AttentionViz(attentions=outputs.attentions)

    def counterfactual_explanation(self, input: str, target: str) -> Counterfactual:
        """Find minimal change to change prediction"""
        return self.generate_counterfactual(input, target)

Multi-Agent Co-Evolution

Competitive Co-Evolution

class CompetitiveCoEvolution:
    def __init__(self, population_size: int = 50):
        self.population = [self.create_agent() for _ in range(population_size)]
        self.fitness_evaluator = FitnessEvaluator()

    async def evolve(self, generations: int):
        for gen in range(generations):
            # Evaluate fitness through competition
            fitness = await self.evaluate_population()

            # Selection
            parents = self.select_parents(fitness)

            # Crossover & Mutation
            offspring = self.crossover_and_mutate(parents)

            # Replace population
            self.population = offspring

            # Track progress
            self.log_generation(gen, fitness)

    async def evaluate_population(self) -> list[float]:
        fitness = []
        for agent in self.population:
            # Compete against random opponents
            opponents = random.sample(self.population, 5)
            wins = 0
            for opponent in opponents:
                result = await self.competition(agent, opponent)
                if result.winner == agent:
                    wins += 1
            fitness.append(wins / len(opponents))
        return fitness

Cooperative Co-Evolution

class CooperativeCoEvolution:
    def __init__(self, subpopulations: dict[str, list[Agent]]):
        self.subpopulations = subpopulations  # role -> agents
        self.fitness_evaluator = TeamFitnessEvaluator()

    async def evolve(self, generations: int):
        for gen in range(generations):
            # Evaluate each subpopulation
            for role, agents in self.subpopulations.items():
                fitness = await self.evaluate_subpopulation(role, agents)

                # Select, crossover, mutate
                parents = self.select(agents, fitness)
                offspring = self.crossover_and_mutate(parents)
                self.subpopulations[role] = offspring

    async def evaluate_subpopulation(self, role: str, agents: list[Agent]) -> list[float]:
        fitness = []
        for agent in agents:
            # Form teams with best from other roles
            team = self.form_team(agent)
            fitness_score = await self.fitness_evaluator.evaluate(team)
            fitness.append(fitness_score)
        return fitness

Ecosystem Dynamics

class AgentEcosystem:
    def __init__(self):
        self.agents: list[Agent] = []
        self.resources: dict[str, Resource] = {}
        self.interactions: list[Interaction] = []

    async def step(self):
        # Agents act
        for agent in self.agents:
            action = await agent.act(self.resources)
            self.interactions.append(Interaction(agent=agent, action=action))

        # Resolve interactions
        await self.resolve_interactions()

        # Update resources
        self.update_resources()

        # Natural selection
        await self.natural_selection()

    async def natural_selection(self):
        # Remove agents below fitness threshold
        self.agents = [a for a in self.agents if a.fitness > self.threshold]

        # Reproduction (with mutation)
        offspring = []
        for agent in self.agents:
            if agent.fitness > self.reproduction_threshold:
                child = agent.reproduce(mutation_rate=0.1)
                offspring.append(child)

        self.agents.extend(offspring)

        # Resource replenishment
        self.replenish_resources()

Safety in Self-Improvement

Alignment Preservation

class AlignmentPreserver:
    def __init__(self, alignment_validator: AlignmentValidator):
        self.validator = alignment_validator
        self.checkpoints: list[Checkpoint] = []

    async def verify_improvement(self, 
                                  original: Agent, 
                                  improved: Agent) -> ImprovementVerification:
        # Check capability improvement
        capability_gain = await self.measure_capability_gain(original, improved)

        # Check alignment preservation
        alignment_preserved = await self.validator.verify(improved)

        # Check no reward hacking
        no_reward_hacking = await self.check_reward_hacking(improved)

        return ImprovementVerification(
            capability_gain=capability_gain,
            alignment_preserved=alignment_preserved,
            no_reward_hacking=no_reward_hacking,
            approved=alignment_preserved and no_reward_hacking
        )

    def checkpoint(self, agent: Agent):
        self.checkpoints.append(Checkpoint(
            agent_state=agent.get_state(),
            timestamp=datetime.utcnow()
        ))

    def rollback(self, checkpoint_id: int) -> Agent:
        checkpoint = self.checkpoints[checkpoint_id]
        return Agent.from_state(checkpoint.agent_state)

Interpretability Monitoring

class InterpretabilityMonitor:
    def __init__(self, model: Model):
        self.model = model
        self.history: list[InterpretabilitySnapshot] = []

    async def monitor(self, interval: int = 100):
        while True:
            await asyncio.sleep(interval)
            snapshot = await self.capture_snapshot()
            self.history.append(snapshot)

            # Check for degradation
            if len(self.history) > 10:
                drift = self.detect_drift()
                if drift > self.threshold:
                    await self.alert_drift(drift)

    def detect_drift(self) -> float:
        """Detect semantic drift in model behavior"""
        recent = self.history[-10:]
        older = self.history[-20:-10]

        # Compare feature attributions
        recent_attrs = np.mean([s.feature_attributions for s in recent], axis=0)
        older_attrs = np.mean([s.feature_attributions for s in older], axis=0)

        return cosine_distance(recent_attrs, older_attrs)

Evaluation of Self-Improvement

Benchmarks

Evaluation Framework

class SelfImprovementEvaluator:
    def __init__(self):
        self.benchmarks = {
            "coding": CodingSelfImprovementBenchmark(),
            "reasoning": ReasoningSelfImprovementBenchmark(),
            "tool_use": ToolUseSelfImprovementBenchmark(),
            "alignment": AlignmentBenchmark()
        }

    async def evaluate(self, agent: Agent) -> SelfImprovementReport:
        results = {}
        for name, benchmark in self.benchmarks.items():
            results[name] = await benchmark.evaluate(agent)

        return SelfImprovementReport(
            results=results,
            overall_score=self.compute_overall_score(results),
            improvement_rate=self.compute_improvement_rate(agent)
        )

Related Notes

• Research Directions — Research directions
• Neurosymbolic Integration — Neurosymbolic self-improvement
• Formal Verification — Verification for self-improvement
• Agent Computer Interface — ACI for self-improvement
• Agent Societies — Multi-agent co-evolution
• Agent Computer Interface — ACI for self-improvement
• Reasoning Models — Reasoning for self-improvement
• Mixture of Experts — MoE for self-improvement
• Reasoning Models — o1-style self-improvement
• Evaluation Frameworks — Evaluation frameworks
• Agent Benchmarks — Benchmarks
• Red Teaming — Safety testing
• Evaluation Frameworks — Evaluation frameworks
• Engineering Culture — Learning culture
• Supply Chain Security — Supply chain for self-improvement

Sources: "RLHF" (Ouyang et al.), "Constitutional AI" (Bai et al.), "DPO" (Rafailov et al.), "RLAIF" (Bai et al.), "Constitutional AI" (Bai et al.), "Self-Improving AI" (Schmidhuber), "Meta-Learning" (Finn et al.), "MAML" (Finn et al.), "RL^2" (Duan et al.), "PEER" (Schmidhuber), "Go-Explore" (Ecoffet et al.), "AlphaZero" (Silver et al.), "AlphaZero" (Silver et al.), "MuZero" (Schrittwieser et al.), "EfficientZero" (Ye et al.), "DreamerV3" (Hafner et al.), "EvoJAX" (Song et al.), "Neural Architecture Search" (Zoph & Le), "AutoML" (Hutter et al.), "NAS-Bench-101/201/301", "DARTS" (Liu et al.), "ProxylessNAS" (Cai et al.), "Once-for-All" (Cai et al.), "AutoML-Zero" (Real et al.), "Self-Improving AI" surveys, "AI Safety via Debate" (Irving et al.), "AI Safety via Market Making" (Irving et al.), "Recursive Reward Modeling" (Leike et al.), "Iterated Amplification" (Christiano et al.), "Debate" (Irving et al.), "Recursive Reward Modeling" (Leike et al.).