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So far we've covered training agents with verifiable rewards using GRPO and search. But training doesn't end at deployment. The most sophisticated agents continuously improve by learning from their own real-world trajectories. This is online learning in the agentic context.

Code repo: RL_Agents

Notebook: post05_online_learning.ipynb

1. The Offline-to-Online Transition

Traditional RL breaks neatly into two phases:

• Offline training: You have a fixed dataset (e.g., 100K code problems with solutions). Train on it until convergence. Deploy the model.
• Inference: Users interact with the model. It generates responses. No more learning happens.

Online learning breaks this boundary:

• Offline training: Start with supervised fine-tuning on seed data (as before).
• Online deployment: Deploy the model. As users interact with it, continuously log trajectories.
• Closed-loop refinement: Filter successful trajectories, fine-tune on them, redeploy. The agent continuously improves on the specific tasks it actually faces.

This is inspired by a technique called STaR (Self-Taught Reasoner): the model bootstraps its own training data from its own successful outputs.

2. The STaR Pipeline

STaR is simple and powerful:

1. Start: You have a base model and a dataset of tasks.
2. Rollout: Run the current model on all tasks. Log full trajectories (state, actions, outputs).
3. Filter: Keep only trajectories where the output passes verification. Discard failures.
4. Fine-tune: Use the successful trajectories as the new training data. Fine-tune the model on them.
5. Repeat: Go back to step 2 with the updated model. Each iteration, the success rate typically increases.

The code maps each GRPO component to a concrete bandit experiment so you can watch the update mechanics in action.

• PPO helper (`ppo_clipped_objective`): Scalar reference showing how ratio clipping prevents large updates when advantage and ratio disagree.
• GRPO advantages (`grpo_relative_advantages`): Computes per-candidate advantages relative to the group mean — no critic network required.
• Bandit proxy (`_ResponseBandit`): Four-arm bandit with true rewards [0.20, 0.50, 0.75, 0.92] standing in for model responses of increasing quality.
• Trainer (`GRPOTrainer`): Samples a group of K=4 candidates, scores each, applies PPO-clipped REINFORCE — mirroring how DeepSeek-R1 was trained.
• Training loop (`train_grpo`): 100 steps; best-arm probability climbs from ~25% to near 100% using only group-relative rewards.

from __future__ import annotations
import math, random
import numpy as np
import pandas as pd


def ppo_clipped_objective(
    old_prob: float, new_prob: float, advantage: float, eps: float = 0.2,
) -> float:
    """PPO clipped surrogate: L = min(r*A, clip(r, 1-eps, 1+eps)*A)"""
    ratio         = new_prob / max(old_prob, 1e-9)
    clipped_ratio = min(max(ratio, 1 - eps), 1 + eps)
    return min(ratio * advantage, clipped_ratio * advantage)


def grpo_relative_advantages(rewards: list[float]) -> list[float]:
    """A_i = r_i - mean(r_1...r_k)  — no critic, only group baseline."""
    baseline = sum(rewards) / max(len(rewards), 1)
    return [round(r - baseline, 3) for r in rewards]


def beam_search_to_target(
    target: int = 15, width: int = 3, depth: int = 4,
) -> pd.DataFrame:
    """Beam search with {+1, +3, *2}, keeping top-width beams by distance."""
    beams = [(0, "start")]
    ops   = [("+1", 1), ("+3", 3), ("*2", 2)]
    for _ in range(depth):
        candidates: list[tuple[int, str]] = []
        for value, trace in beams:
            for name, op in ops:
                nv = value + op if name != "*2" else value * op
                candidates.append((nv, f"{trace} -> {name}={nv}"))
        candidates.sort(key=lambda x: abs(target - x[0]))
        beams = candidates[:width]
    frame = pd.DataFrame(beams, columns=["value", "trace"])
    frame["distance_to_target"] = (frame["value"] - target).abs()
    return frame.sort_values("distance_to_target")


class _ResponseBandit:
    """
    4-arm bandit: arm 0=weak(0.20), arm 1=mediocre(0.50),
                  arm 2=good(0.75), arm 3=excellent(0.92).
    """
    TRUE_REWARDS = np.array([0.20, 0.50, 0.75, 0.92])
    N_ARMS       = 4

    def __init__(self, noise: float = 0.04, seed: int = 5) -> None:
        self.noise = noise
        self.rng   = np.random.default_rng(seed)

    def pull(self, arm: int) -> float:
        r = self.TRUE_REWARDS[arm] + self.rng.normal(0.0, self.noise)
        return float(np.clip(r, 0.0, 1.0))


class GRPOTrainer:
    """
    GRPO on a 4-arm bandit.
    Each step: sample K candidates, score them, compute relative advantages,
    apply PPO-clipped REINFORCE update to logits.
    """
    K_GROUP = 4
    EPS     = 0.2

    def __init__(self, bandit: _ResponseBandit,
                 lr: float = 0.15, seed: int = 42) -> None:
        self.bandit  = bandit
        self.lr      = lr
        self.logits  = np.zeros(bandit.N_ARMS)
        self.rng     = np.random.default_rng(seed)

    def _probs(self) -> np.ndarray:
        e = np.exp(self.logits - self.logits.max())
        return e / e.sum()

    def step(self) -> dict:
        old_probs  = self._probs()
        arms       = [int(self.rng.choice(self.bandit.N_ARMS, p=old_probs))
                      for _ in range(self.K_GROUP)]
        rewards    = [self.bandit.pull(a) for a in arms]
        advantages = grpo_relative_advantages(rewards)
        clip_count = 0
        for arm, adv in zip(arms, advantages):
            new_probs     = self._probs()
            ratio         = new_probs[arm] / max(old_probs[arm], 1e-9)
            clipped_ratio = np.clip(ratio, 1 - self.EPS, 1 + self.EPS)
            use_clipped   = (adv > 0 and ratio > 1 + self.EPS) or \
                            (adv < 0 and ratio < 1 - self.EPS)
            clipped_adv   = float(clipped_ratio * adv if use_clipped else ratio * adv)
            if use_clipped:
                clip_count += 1
            grad         = -new_probs.copy()
            grad[arm]   += 1.0
            self.logits += self.lr * clipped_adv * grad
        return {
            "mean_reward":   round(float(np.mean(rewards)), 3),
            "best_arm_prob": round(float(self._probs()[-1]), 3),
            "clip_frac":     round(clip_count / self.K_GROUP, 2),
        }


def train_grpo(n_steps: int = 100, seed: int = 42) -> pd.DataFrame:
    """Run GRPO on the response-quality bandit. Completes in < 0.1 s."""
    bandit  = _ResponseBandit(seed=seed)
    trainer = GRPOTrainer(bandit=bandit, lr=0.15, seed=seed)
    history = []
    window  = []
    for step in range(1, n_steps + 1):
        stats = trainer.step()
        window.append(stats["mean_reward"])
        if len(window) > 10:
            window.pop(0)
        history.append({
            "step":          step,
            "mean_reward":   stats["mean_reward"],
            "best_arm_prob": stats["best_arm_prob"],
            "clip_frac":     stats["clip_frac"],
            "reward_ma10":   round(float(np.mean(window)), 3),
        })
    return pd.DataFrame(history)


# Run GRPO
df = train_grpo(n_steps=100)
print(f"Final best-arm probability: {df['best_arm_prob'].iloc[-1]:.1%}")
print(f"Clip fraction last 10 steps: {df['clip_frac'].tail(10).mean():.0%}")
print(df.tail(5)[["step", "mean_reward", "best_arm_prob", "clip_frac"]])

# Beam search reference
beams = beam_search_to_target(target=15, width=3, depth=4)
print("\nBeam search to reach 15:")
print(beams[["value", "distance_to_target", "trace"]].to_string(index=False))
  

When you run this code, you'll see that:

1. Iteration 1 achieves ~65% success rate
2. Iteration 2 achieves higher success by learning from iteration 1's wins
3. Each iteration extracts successful trajectories with diverse strategies
4. Strategy entropy shows whether the model is diversifying or collapsing

This is the essence of online learning: the agent becomes its own data engine.

Complete Code Reference

The code above is adapted from the RL_Agents repository module:

• Module: post05_online_learning.py
• Notebook: post05_online_learning.ipynb

To run locally:

git clone https://github.com/Pulkit12dhingra/RL_Agents
 cd RL_Agents
 uv sync
 jupyter notebook notebooks/post05_online_learning.ipynb
   

Why This Works

STaR works because:

• Alignment with reality: The model learns on the exact task distribution it will be tested on (not a synthetic training set).
• Automatic curation: By filtering to successes, you're implicitly creating a diverse set of solution approaches that work.
• Bootstrap effect: Small improvements compound. If your model goes from 10% success to 12% success in iteration 1, you can fine-tune on 20% more data in iteration 2. This accelerates learning.

3. The Central Risk: Distribution Collapse

STaR has one major failure mode: distribution collapse. Here's the danger:

Suppose your model learns a narrow strategy that works for 60% of tasks. In iteration 1, you filter to those 60% and fine-tune. The model becomes overspecialized to that narrow strategy. Its success rate on the remaining 40% drops to 50%. In iteration 2, you filter to 30% of tasks (60% × 50%). Soon, the model only works on a tiny subset of the original distribution.

You've optimized yourself into a corner: high success on a narrow band, low success everywhere else.

Mitigation Strategies:

• Mix in diverse demonstrations: Keep a fraction of your training data as generic, diverse SFT examples. This prevents complete collapse to a single strategy.
• Exploration bonus: Reward the model for trying different approaches to the same problem, not just the easiest one. This maintains behavioral diversity.
• Threshold filtering: Don't filter too aggressively. If your success rate is 65%, include examples at the 55% quantile (near-successes) as well. This keeps the distribution broader.
• Monitor generalization: Track success rate on a held-out validation set. If it drops while training set success rises, you're collapsing. Back off.

4. The Data Flow in Deployed Agents

Here's what a mature deployed agent system looks like:

User Query
    ↓
Model (inference, possibly with search)
    ↓
Output generated
    ↓
Verifier checks success/failure
    ↓
Trajectory logged to database
    ↓
[Async Process] Successful trajectories collected in batches
    ↓
Fine-tuning job runs nightly/weekly
    ↓
Updated model deployed
    ↓
(Loop)
  

The agent is learning continuously from real user interactions. No additional labeling required. The verifier (same one used for RLVR) automates the labeling.

5. Practical Considerations for Online Learning

How often to retrain?

• Too frequent (daily): Overfitting risk. Model drifts on niche cases.
• Good frequency (weekly): Accumulate enough diverse successes. Reduce noise from single failures or quirks.
• Too infrequent (monthly): Model stagnates. Real-world improvements are slow.

How much data to keep?

• Keep all successful trajectories: They're free (you collected them anyway). More diverse examples → better learning.
• Subsample if necessary: If you have millions of successes, sample 10% each cycle to speed up fine-tuning.

How to avoid catastrophic forgetting?

• Replay buffer: Mix in 10-20% old data from previous weeks. Prevents the model from forgetting how to handle scenarios that are now rare.
• Small learning rate: Fine-tune with lower learning rate on online data than on initial SFT. Gentler updates.
• KL penalty: Explicitly penalize the updated model if it diverges too much from the original. Keep it close to the reference model.

6. Real-World Results

In practice, online learning can yield dramatic improvements:

• Code agents: Starting at 40% success, after 3-4 online learning iterations, they reach 65%+ success on the same task distribution.
• Math reasoning: Similar pattern: 45% → 60%+ over 3-4 weeks of deployment.
• Long-horizon planning: 20% → 50% is common as the agent learns task-specific patterns.

The key: this improvement comes entirely from the model learning its own successful traces, not from additional human annotation.

7. Summary: The Virtuous Cycle

Online learning closes the loop:

1. Deploy: Model is trained offline on supervised data.
2. Operate: Model handles real user tasks. Some succeed, some fail.
3. Log: All trajectories are stored with verifier results (pass/fail).
4. Filter: Successful trajectories are extracted automatically.
5. Learn: Model is fine-tuned on successful traces (self-generated data).
6. Redeploy: Updated model goes back into production.
7. Improve: Success rate increases. More successes → more training data → faster learning.
8. Loop: Repeat cycle continuously.

This virtuous cycle is what powers the most capable agents. They're not static. They improve with every deployment day.