Jiajun Fan
Research Notes

One Subtraction Ends the Exploration–Exploitation Trade‑off


RL fine-tuning of a generative model runs on one dial. Turn it up and the model keeps its diversity but stops improving; turn it down and it chases reward until it collapses into template output. The dial is a single coefficient applied identically to every sample. This note is about what happens when you stop treating it as a constant.

Drag the advantage. That is the whole method.

βtot  =  β0  −  A+0.00 = 1.00

Average sample. The advantage is near zero, so the coefficient stays at its baseline 1.00 and the sample barely moves the policy.

One subtraction, and the dilemma dissolves. Every RL fine-tuning method before this one picks a single β and applies it to every sample: raise it and the model is protected but cannot improve, lower it and it improves until it collapses. ADRPO — Adaptive Divergence Regularized Policy Optimization — makes β a function of the sample — Equation 4 in the paper is literally βtot = β0 − A. Good samples get freedom, bad samples get held down, and nobody has to tune the trade-off. β0 = 1 with A clipped to [−1, 1] is the paper’s text-to-image setting.

Fixed regularisation PPO · GRPO · DPO · ORW-CFM-W2 low advantage high advantage regularisation β one β for every sample Good samples are held back. Bad samples are not held back enough. ADRPO regularisation follows the sample low advantage high advantage hold back let it run Every sample gets the constraint its own quality earns. β = β0 − A one term, no new networks
The whole method is one subtraction. Conventional RL fine-tuning applies a fixed divergence coefficient β to every sample. ADRPO subtracts that sample’s own advantage estimate, so a generation the reward model likes is allowed to move further from the reference policy, and a poor one is held closer to it. The advantage is already computed for the policy gradient — the adaptation is free.

The short version

Six things one subtraction bought

Each is stated with the number that carries it, and shown in full further down.

1
One fixed knob cannot serve both jobs

Strong regularisation protects the pre-trained model but caps the reward. Weak regularisation chases reward and invites collapse or hacking. Every sample gets the same β, whether it deserves it or not.

§01 · the dilemma
2
Let the sample choose its own constraint

ADRPO sets β = β0 − A. High-advantage samples are regularised less and exploited harder; low-advantage samples are pulled back toward the reference model. One term, no extra networks, no architecture change.

§02 · the fix
3
Negative advantage does more than down-weight

Reward-weighting can only give a bad sample a small positive push. An advantage-weighted objective flips the gradient sign and pushes the policy away from that sample — actively suppressing poor generations instead of politely ignoring them.

§02 · the fix
4
A 2B model beat a 12B one

Fine-tuned SD3 at 2B parameters outscores FLUX.1-Dev (12B) and SANA-1.5 (4.8B) on ClipScore, aesthetics and human preference. Adaptive regularisation bought more than a 6× parameter increase would have.

§03 · text-to-image
5
The only method that raised reward without spending diversity

Every competing method trades one for the other. ADRPO finishes at 5.13 diversity against the base model’s 5.08 — level to within seed noise, while posting the highest alignment score in the table.

§04 · the Pareto front
6
It transfers to LLMs and to audio

On Qwen3, ADRPO escapes a local optimum by deliberately raising entropy and converges at GRPO’s reward. On MMAU a 7B model reaches 76.0, past Gemini 2.5 Pro and GPT-4o Audio.

§05 · §06

01 — The dilemma

The coefficient that has to be two things at once

Every mainstream RL fine-tuning objective — PPO, GRPO, DPO, and W2-regularised flow matching — carries a divergence penalty scaled by a fixed β. That single number is asked to do two opposing jobs simultaneously: keep the policy near the pre-trained model so it does not forget or collapse, and get out of the way so the policy can actually improve.

The bind is that the right answer differs per sample. A generation the reward model scores highly is a direction worth committing to; holding it back is pure loss. A poor generation is exactly where you want the reference model’s pull to be strongest. A constant cannot express that, so practitioners tune β to a compromise that is wrong for both cases.

β too high
Capabilities preserved, nothing learned
The penalty dominates. The policy stays close to the reference model, diversity survives, and reward barely moves. Safe and useless.
β too low
Reward climbs, the model narrows
Constraint effectively removed. Reward optimisation runs unchecked into catastrophic forgetting, mode collapse, or reward hacking — template-like generations that score well and look identical.

02 — The fix

Subtract the advantage

ADRPO replaces the constant with β = β0 − A, where A is the advantage estimate already being computed for the policy gradient. Nothing is added to the model, no second network is trained, and the objective stays a drop-in for existing methods. What changes is that the constraint now varies inversely with sample quality.

mechanism
Exploitation where the signal is good
High advantage means low β: the divergence penalty shrinks and the policy is free to commit to a direction the reward model already endorses.
mechanism
Exploration where it is not
Low or negative advantage means high β: the penalty grows, pulling the update back toward the reference policy and preserving what the pre-trained model knew.
for flow matching
Advantage-weighted, not reward-weighted
Reward weights are non-negative, so a bad sample can only be down-weighted. Weighting by advantage lets the sign invert, so negative-advantage samples are actively pushed away from rather than quietly ignored — and average samples, where A ≈ 0, cost almost no gradient at all.
stability
Clipped, and cheap
Advantages are clipped to [Amin, Amax] so the coefficient cannot run away. The advantage is already computed for the policy gradient, so the overhead over the base method is negligible.
The exploration–exploitation trade-off stops being a hyperparameter you guess before training, and becomes something the run resolves per sample, continuously.

03 — Text-to-image

A 2B model past a 12B one

ADRPO was applied to SD3 (2B parameters) on DrawBench prompts with CLIP score as the reward, against offline DPO, reward-ranked RAFT, fixed-β ORW-CFM-W2, and two much larger models that were never RL-tuned at all. It leads on task metrics, image quality and human preference at the same time.

Text-to-image — alignment, quality, preferenceSD3 backbone · DrawBench · mean of 3 seeds · each metric on its own axis — ClipScore 28.5–33.5, Aesthetic 4.30–6.50, PicScore 18.80–23.20
SD3 + ADRPOours · 2B
32.97 ClipScore
6.27 Aesthetic
22.78 PicScore
SANA-1.54.8B, no RL
32.18 ClipScore
5.89 Aesthetic
21.85 PicScore
FLUX.1-Dev12B, no RL
31.72 ClipScore
5.95 Aesthetic
21.83 PicScore
SD3 + ORW-CFM-W2fixed W2 regularisation
31.42 ClipScore
5.29 Aesthetic
20.97 PicScore
SD3 + DPOoffline preference
31.30 ClipScore
5.82 Aesthetic
21.31 PicScore
SD3 + RAFTreward-ranked FT
29.35 ClipScore
4.54 Aesthetic
19.21 PicScore
SD32B base model
29.27 ClipScore
5.53 Aesthetic
20.81 PicScore
SD3 + ADRPO (2B, ours)baselines and larger modelsthree bars per model: ClipScore · Aesthetic · PicScore
Every metric in Table 1 — switch and watch who moves

Six metrics, one table, nothing cherry-picked. The red line is the un-tuned SD3 the fine-tuned rows all start from. Click through the metrics and the shape of the problem shows: RAFT falls behind the base model on four of the six, ORW-CFM-W2 buys alignment and pays in diversity, and ADRPO is the only row that is at or above the base model on every one — and it leads all six outright. Two of the rows are larger models — 6× and 2.4× its parameter count.

04 — The Pareto front

Reward went up. Diversity did not go down.

This is the result that is hard to get by tuning a constant. Reward-ranked fine-tuning buys almost no alignment at all (29.35 against the base model’s 29.27) and still flattens the output distribution to pay for it — diversity falls from 5.08 to 1.85, a textbook collapse. Fixed-β W2 regularisation is gentler but still pays 3.86. ADRPO finishes at 5.13 against the base model’s 5.08 — unchanged to within the reported seed noise (±0.47 and ±0.52) — while posting the highest alignment score in the table. It is the only row that buys alignment without paying for it.

29 30 31 32 33 2 3 4 5 ClipScore — prompt alignment → ClipDiversity → SD3 + ADRPO ours · 2B · 32.97 / 5.13 SANA-1.5 FLUX.1-Dev SD3 + ORW-CFM-W2 SD3 + DPO SD3 + RAFT reward-ranked FT · 29.35 / 1.85 SD3 2B base model · 29.27 / 5.08
Every point is a row of Table 1. Horizontal: prompt alignment. Vertical: generation diversity. The dashed lines mark the un-tuned SD3 base model, so the tinted quadrant is the region where a method improved alignment without paying for it in diversity. Only one point is in it. RAFT shows the failure mode most clearly — it buys a little alignment by collapsing diversity from 5.08 to 1.85. The middle cluster, in full: DPO 31.30 / 4.78, ORW-CFM-W2 31.42 / 3.86, FLUX.1-Dev 31.72 / 4.29, SANA-1.5 32.18 / 4.31.

05 — Language models

An emergent willingness to explore

The same objective drops into GRPO for LLM fine-tuning by making the KL coefficient advantage-dependent. Tracked in reward–entropy space on Qwen2 (0.5B) and Qwen3 (0.6B), with RM-Gemma-2B supplying the reward, ADRPO and GRPO take visibly different paths. GRPO holds high entropy throughout and moves sideways — lots of exploration, little reward found. ADRPO first tightens into a low-entropy region, then deliberately raises entropy again to break out of the local optimum it landed in, and converges at 5× GRPO’s final reward.

Nobody designed that behaviour. It falls out of the coefficient: once a region stops producing advantage, regularisation rises, the policy loosens, and exploration resumes on its own. The absence of that mechanism is why GRPO’s later checkpoints often score worse than earlier ones while ADRPO improves monotonically — no early stopping required.

06 — Audio reasoning

And it holds in a third modality

Continuous flow matching and discrete token generation are different enough that a shared mechanism is worth testing on a third case. Qwen2.5-Omni-7B was fine-tuned on AVQA with verifiable rewards and evaluated on MMAU.

MMAU — multi-modal audio reasoningaccuracy % · sound / music / speech / total · bars span 55–85%
ADRPOours · Qwen2.5-Omni-7B
81.98 sound
70.06 music
75.98 speech
76.0 total
GRPOfixed β = 0.04
77.18 sound
70.66 music
74.77 speech
74.2 total
Gemini 2.5 Proproprietary
75.08 sound
68.26 music
71.47 speech
71.6 total
Qwen2.5-Omni-7Bbase model
72.37 sound
64.37 music
69.07 speech
68.6 total
GPT-4o Audioproprietary
64.56 sound
56.29 music
66.67 speech
62.5 total
ADRPO (7B)GRPO, base model, proprietary systems
2B > 12B
SD3 + ADRPO outscores FLUX.1-Dev on alignment, aesthetics and human preference
5.13
final diversity, level with the base model’s 5.08 — the only method that did not pay for alignment
GRPO’s final reward on Qwen3 LLM fine-tuning
76.0%
MMAU total, above Gemini 2.5 Pro (71.6) and GPT-4o Audio (62.5)

07 — Robustness

The one hyperparameter it adds barely matters

Adaptive regularisation introduces a clipping range for the advantage. If performance were delicately balanced on it, the method would have traded one tuning problem for another. Sweeping it over a 4× span moves the total by less than half a point, and every setting still beats fixed-β GRPO.

Advantage-clipping ablationMMAU total accuracy % · bars span 73.5–76.6% — the three ADRPO settings vary by 0.4 points
0.5 × β0±0.02
76.1
1 × β0±0.04 · recommended
76.0
2 × β0±0.08
75.7
GRPOfixed β, no adaptation
74.2
ADRPO, any clipping rangefixed-β GRPO baseline

08 — What it means

The trade-off was never the problem. Treating it as constant was.

Exploration versus exploitation is usually framed as something you resolve before training by picking a coefficient, and live with afterwards. The result here is that the information needed to resolve it properly is already sitting in the training loop: the advantage estimate says, for this particular sample, whether the policy has found something worth committing to. Subtracting it turns a global compromise into a local decision.

What makes the result more than a tuning trick is the range it survives. The same one-term change holds across continuous flow matching with a Wasserstein penalty, discrete LLM generation with a KL penalty, and multi-modal audio reasoning — three architectures, two divergence measures, one subtraction, and a 2B model that outperforms a 12B one.

NeurIPS 2025 — read the paper →SD3 · Qwen2 · Qwen3 · Qwen2.5-Omniflow matching & LLMsW2 & KL divergenceUIUC