Critic-Free Single-Rollout Asynchronous RL
for Agentic Language Models
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Can we train an agent reliably with
one rollout per prompt,
even when trajectories arrive asynchronously?
A prompt-local baseline requires sibling rewards.
Workers can submit each completed trajectory independently.
Repeated samples support within-prompt comparison.
The same 128 trajectories cover four times as many prompts.
One trajectory per prompt
Store sampled-token log μᵢ
Mixed behavior snapshots
No sibling-group wait
Center, screen, average
Discard the used batch
“Fresh” means not previously used for an update. A fresh trajectory can still be stale.
Histories follow dᵗμ.
Continuation values come from μ.
The inner expectation uses π.
At π = μ, the local gradient matches policy gradient.
J(π) = Eτ∼π[R(τ)] denotes expected return.
The ratio corrects the action distribution at each stored history.
Stored histories still follow μ.
The target return depends on histories from πθ.
Assumptions: bounded behavior advantages, common environment and prompt distribution, fixed horizon with absorbing padding.
Center rewards across the next batch of completed trajectories.
Retain token IS and screen each complete trajectory for drift.
Average within each trajectory before averaging across the batch.
| Binary reward example | Rᵢ | Aᵢ when R̄ = 0.8 |
|---|---|---|
| Success | 1 | +0.2 |
| Failure | 0 | −0.8 |
For general scalar rewards, a negative Aᵢ means below-batch-mean return.
p = μᵢ(aᵢ,ₜ ∣ hᵢ,ₜ), q = πθ(aᵢ,ₜ ∣ hᵢ,ₜ)
| Reduction | Weight on mean trajectory loss Lᵢ | Effect |
|---|---|---|
| Sample mean | 1 / B | Equal explicit trajectory weight |
| Token mean | Tᵢ / ∑ⱼ Tⱼ | More weight on longer trajectories |
Long failures contain useful steps as well as errors. Coarse negative feedback can grow with length.
Averaging changes length weighting. It does not identify which tokens caused success or failure.
Aᵢ, mᵢ and behavior probabilities are held fixed during the update.
Numerical guard: float32 log-ratio, clamped to [−30, 30] before exponentiation.
| Setting | Model | Evaluation |
|---|---|---|
| Long CoT | R1-Distill-Qwen-1.5B | AIME24/25, avg@32 |
| Math reasoning | Qwen2.5-Math-1.5B | Five benchmarks, avg@16 |
| Python tools | Qwen2.5-7B / Qwen3-30B-A3B | AMC23, Minerva, AIME25 |
| Interactive tasks | Qwen2.5-7B-Instruct | ALFWorld seen / unseen |
Benchmark means weight tasks equally. avg@k is mean per-sample accuracy, not pass@k.
| Qwen2.5-Math-1.5B | Group size | Rollouts | Five-task mean (%) |
|---|---|---|---|
| Base model | — | 0 | 19.5 |
| C-RF + NTF (published) | 1 | 512k | 35.3 |
| GRPO (published) | 16 | 512k | 36.3 |
| FlashREINFORCE | 1 | 256k | 38.0 |
FlashREINFORCE: peak-mean checkpoint at step 2,000.
Published baselines use synchronous training and 1,000 updates.
R1-Distill-Qwen-1.5B, policy lag ≈ 4. Raw avg@32 evaluations; line segments connect checkpoints.
With sequence trust. Each point averages a consecutive 200-update window.
| Qwen2.5-7B, step 600 | AMC23 | Minerva | AIME25 | Mean | Calls |
|---|---|---|---|---|---|
| GRPO | 51.2 | 32.3 | 7.5 | 30.3 | 0.00 |
| FlashREINFORCE | 60.6 | 28.8 | 21.7 | 37.0 | 3.25 |
GRPO stops calling the tool within roughly 200 steps.
FlashREINFORCE retains multi-turn tool use.
Matched steps and rollout budgets. Calls are averaged over the 100 updates ending at the checkpoint.
| Step 800, 102.4k rollouts | Lag | AMC23 | Minerva | AIME25 | Mean |
|---|---|---|---|---|---|
| GRPO | ≈1 | 93.8 | 40.4 | 46.7 | 60.3 |
| FlashREINFORCE | ≈8 | 95.6 | 44.9 | 60.8 | 67.1 |
Three-task mean accuracy
at the same rollout budget
Flash: δ = 10⁻², no routing replay. Evaluation: avg@4; thinking disabled.
R3 uses routing replay and δ = 10⁻³. Raw avg@4 evaluations, joined without smoothing.
| Method | Group size | Seen (%) | Unseen (%) |
|---|---|---|---|
| GRPO (published) | 8 | 78.6 | 76.8 |
| C-RF + NTF (published) | 1 | 90.5 | 86.3 |
| FlashREINFORCE | 1 | 98.3 | 96.5 |
FlashREINFORCE uses 12.8k training trajectories
and evaluates at step 200.
C-RF also uses one rollout per prompt, so prompt coverage alone does not explain the difference.
| Schedule | Mean (%) |
|---|---|
| Fresh batch each step | 28.45 |
| 4 sequential minibatches | 26.80 |
Math: 800 steps, 102.4k trajectories.
| Learning signal | Mean (%) |
|---|---|
| Batch-centered | 36.2 |
| Positive-only | 9.8 |
7B tools, step 700. Calls: 3.30 vs 0.00.
| Continuation from step 900 | Reward | Length | Calls | Truncation |
|---|---|---|---|---|
| Starting checkpoint | 0.430 | 2,573 | 3.87 | 18.8% |
| Sample mean, ≈150 steps | 0.477 | 2,518 | 4.01 | 17.2% |
| Token mean, ≈150 steps | 0.403 | 3,947 | 2.18 | 45.3% |
Token-level penalties do not directly reward shorter responses.
Possible mechanism: coarse negative feedback weakens useful behavior. The specific causal chain remains unverified.
| Math, same δ = 10⁻³ | Last step | AMC23: peak / last | Outcome |
|---|---|---|---|
| Sequence-level | 2,160 | 55.6 / 53.1 | Stable |
| Token-local | 1,237 | 51.9 / 26.3 | Collapsed |
Deleting a token loss leaves later stored histories unchanged.
Rejecting a trajectory removes all of its stored-history contributions.
The comparison changes admission granularity. It is not a gate-on versus gate-off experiment.
Batch-mean baseline
Flash loss, token IS and gate
Within-prompt mean baseline
No standard-deviation normalization
Late mean advantage for group centering
across seven paired evaluations after step 3,000
R1, policy lag 4, 128 trajectories per update. Curves remain broadly similar through approximately 4,000 updates.
Evidence spans long CoT, 30B MoE tool use, mathematical reasoning and ALFWorld.
Related directions: REINFORCE / RLOO, GRPO, C-RF + NTF, DPPO and Trust Region Masking.
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| R1 mean accuracy (%) | With gate | Without gate | Difference |
|---|---|---|---|
| Step 4,992 | 32.2 | 30.6 | +1.6 pp |
| Around step 5,900 | 33.7 | 30.6 | +3.1 pp |
Final evaluation steps differ slightly: 5,896 versus 5,888.
Trajectory rejection in the reported
Math run with δ = 3×10⁻³
Aᵢ = Rᵢ − R̄ remains defined.
Cross-prompt score calibration becomes important.
Return-to-go can use intermediate feedback.
Total-reward centering alone does not assign step credit.
Easy and hard successes receive the same scalar advantage within a batch.
More data does not automatically remove bias from a chosen surrogate.
The batch has zero reward-driven policy gradient.
Difficulty curricula, mixed tasks, exploration or resampling.
For independent equal-success-probability samples: P(uniform batch) = pᴮ + (1 − p)ᴮ.
Monitor ratios and drift.
Control update size and queue delay.
Calibrate scores and inspect outliers.
Consider repeated scoring or conditional baselines.
Dedicated noisy-reward experiments are still needed.
| Reduction | Explicit trajectory weight |
|---|---|
| Sample mean | 1 / B |
| Token mean | Tᵢ / ∑ⱼ Tⱼ |
| Optional failure-token filter | Peak mean (%) | Peak step |
|---|---|---|
| No filtering, q = 1.0 | 37.0 | 600 |
| Light filtering, q = 0.9 | 39.4 | 700 |
| Aggressive filtering, q = 0.2 | 32.2 | 200 |
7B Python tools. Each row reports its own peak, not a matched checkpoint.
Observed token-mean continuation: length 2,573 to 3,947; truncation 18.8% to 45.3%.
The reported 0.13% Math trajectory rejection rate does not generalize to all agent workloads.
| Design choice | What changes |
|---|---|
| No critic | Baseline estimation |
| Token-only IS | History mismatch remains |
| Sampled-action KL | Admission statistic and behavior storage |
| Sample mean | Trajectory-length weighting |
No systematic memory–gradient-error–convergence frontier is reported.
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