Implicit Expert Forcing (IEF) in RL

• Implicit Expert Forcing is a reinforcement learning method that uses in-context expert demonstrations to steer policy exploration without explicit gradient updates.
• It integrates on-policy and expert-conditioned rollouts within the ICPO framework to enhance diversity, scalability, and performance, particularly in mathematical reasoning tasks.
• By leveraging existing demonstration datasets, IEF reduces computational costs while promoting stable, efficient adaptation and broader solution coverage.

Implicit Expert Forcing (IEF) is a reinforcement learning strategy introduced within the In-Context Steered Policy Optimization (ICPO) paradigm to expand policy exploration and enable LLMs to benefit from expert guidance without explicit imitation losses or reliance on external model rollouts. IEF leverages the in-context learning capabilities of contemporary LLMs by conditioning rollouts on expert demonstrations that are included as part of the prompt, thereby steering the generative process without parameter updates toward an external expert. This mechanism yields stable, scalable, and efficient reinforcement learning adaptation, particularly in mathematical reasoning tasks.

1. Motivation and Problem Setting

IEF arises from the need to overcome the inherent limitations of on-policy reinforcement learning for LRMs. On-policy algorithms such as Group Relative Policy Optimization (GRPO) restrict exploration to the support of the current policy, resulting in narrow trajectory diversity and an increased risk of premature convergence to suboptimal solutions. While previous approaches utilize expert trajectories from stronger or external models to drive exploration, they are constrained by the significant computational cost and limited accessibility of such models.

IEF is motivated by the following objectives:

• Expand exploration scope beyond the current policy distribution.
• Provide expert guidance without requiring advanced or external LLM outputs.
• Harness the in-context learning capability of the target LRM by steering its reasoning process using existing datasets of demonstrations.
• Enhance reinforcement learning post-training efficiency and generalization for reasoning-intensive domains.

2. Formalization and Theoretical Foundations

Traditional expert forcing aligns a student model’s policy $\pi_\theta$ with a reference expert policy $\pi_\phi$ using explicit objectives, typically through behavioral cloning or Kullback-Leibler regularization. This process demands external expert rollouts and direct gradient alignment, which is both resource-intensive and prone to over-imitation at the expense of exploration.

IEF diverges fundamentally by employing in-context learning: expert behavior is imparted to $\pi_\theta$ via conditioning on sampled expert demonstrations $\mathcal{D}$ in the input prompt, requiring no gradients or updates from the expert model. This "implicit" mechanism adjusts trajectory distributions using context alone.

Formally:

• Given expert demonstrations $\mathcal{D}$ and a task query $q$, the input $x_{\rm exp} = [\mathcal{D}; q]$ induces expert-steered rollouts:

$$\tau_{\rm exp} \sim \pi_\theta(\tau \mid x_{\rm exp})$$

• According to the hypothesis-class perspective on ICL [Hendel et al., 2023], transformer decoding is expressed as:

$$T([\mathcal{D}, q]) = \mathcal{F}(q; A(\mathcal{D}))$$

where $A(\mathcal{D})$ computes a latent "task vector" $\vartheta$ which modulates $\mathcal{F}$ to generate expert-like responses for $q$.

Thus, the IEF rollout distribution is:

$$\pi_\theta^{\mathrm{IEF}}(\tau \mid q) = \pi_\theta(\tau \mid [\mathcal{D}; q]) = \pi_{\mathcal{F}}(\tau \mid q; \vartheta)$$

This suggests that expert region coverage is implicitly expanded by in-context conditioning, not direct parameter optimization.

3. Algorithmic Integration: Mixed-Policy GRPO with IEF

ICPO integrates IEF by generating mixed groups of trajectories for each prompt:

• For each prompt $q$:
  • Sample $N_{\mathrm{on}}$ on-policy rollouts: $\tau_i \sim \pi_{\theta_{\mathrm{old}}}(q)$.
  • Sample $N_{\mathrm{off}}$ expert-conditioned rollouts: construct $x_{\mathrm{exp}} = [\text{sampled demos};\, q]$, then $$\tau_j \sim \pi_{\theta_{\mathrm{old}}}(x_{\mathrm{exp}})$$.

Aggregate all rollouts as $$\{\tau_i^{\mathrm{on}}\}\cup\{\tau_j^{\mathrm{off}}\}$$, and perform group-normalized advantage calculation:

$$\hat{A}_i = \frac{R(\tau_i) - \text{mean}(G_{\mathrm{on}} \cup G_{\mathrm{off}})}{\text{std}(G_{\mathrm{on}} \cup G_{\mathrm{off}})}$$

where $G$ denotes reward sets.

The mixed-policy GRPO objective incorporates both on-policy and IEF rollouts:

$$\begin{aligned} \mathcal{J}_{\mathrm{Mixed}}(\theta) =& \mathbb{E}_{\tau \sim \pi_{\theta_{\mathrm{old}}}^{\mathrm{on-policy}}}\left[ \frac{1}{|\tau|} \sum_{t=1}^{|\tau|} \operatorname{CLIP}(r_{t}(\theta),\, \hat{A}(\tau),\, \epsilon) \right] \ &+ \mathbb{E}_{\tau \sim \pi_{\theta_{\mathrm{old}}}^{\mathrm{IEF}}}\left[ \frac{1}{|\tau|} \sum_{t=1}^{|\tau|} \operatorname{CLIP}(\hat{r}_{t}(\theta),\, \hat{A}(\tau),\, \epsilon) \right] \end{aligned}$$

with

$$\hat{r}_{j,t}(\theta) = \frac{\pi_\theta(\tau_{j,t}\mid \tau_{j,<t})}{\pi^{\mathrm{IEF}}_\theta(\tau_{j,t}\mid \tau_{j,<t})}$$

Key practical components include:

• Generation of expert-conditioned rollouts by prefixing prompts with randomly sampled demonstrations.
• Grouping (usually one IEF and seven on-policy samples per prompt).
• Filtering high-reward IEF rollouts via Expert Region Reject Sampling (ERRS).
• Applying an annealed expert bonus to early successful IEF rollouts to accelerate learning.

4. Comparison to Traditional Expert Forcing and Related Paradigms

IEF presents several operational contrasts with explicit expert forcing and other off-policy methods:

Aspect	Traditional Expert Forcing	Implicit Expert Forcing (IEF)
Expert	Requires external model ($\pi_\phi$)	Leverages in-context demos from data
Mechanism	Explicit gradient alignment/cloning	Context-driven steering; no external gradient
Computation	Expensive—needs expert model inference	Efficient—requires only prompt construction
Update	Direct imitation loss	Indirect via RL on IEF rollouts
Exploration	Often limited to expert region	Expands support, maintains adaptation
Generalization	Prone to over-imitation	Promotes diverse, novel trajectory coverage

IEF capitalizes on the transformer’s native in-context adaptation, making it resource-efficient and robust for practical RL fine-tuning.

5. Impact on Policy Exploration and Learning Dynamics

By introducing expert-conditioned rollouts, IEF:

• Enables the policy to encounter and learn from solution regions typically unreachable by strict on-policy exploration.
• Drives coverage and diversity, correcting previously unsolved prompts and encouraging new reasoning paths.
• Balances imitation with innovation; IEF rollouts are filtered and rewarded within RL post-processing, so exploration persists.
• Empirically achieves higher accuracy, inter-trajectory semantic diversity, and "flipped-correct" rates (transitioning incorrect to correct answers).

Training dynamics demonstrate increased entropy, KL divergence, and longer, more varied trajectories, while transition rates for "newly solved" prompt groups increase.

6. Empirical Results and Ablation Studies

IEF's contribution to RL performance is quantifiable and dominant:

• On mathematical reasoning benchmarks, IEF-enhanced ICPO achieves improvements of up to +4.17 absolute accuracy points over GRPO (Qwen3-1.7B) and +2.15 over GRPO (Qwen3-8B).
• Ablation analyses show removal of IEF most significantly reduces performance (ICPO: 65.78, –IEF: 63.76), underscoring its centrality.
• IEF supports data efficiency, requiring only existing demonstration datasets and no external LLM inference.

Variant	Qwen3-8B Accuracy
ICPO	65.78
– RS	65.04
– ERRS	64.99
– IEF	63.76

Compared to LUFFY (Yan et al., 21 Apr 2025) (which needs an external advanced LLM and explicit gradient alignment), ICPO using IEF achieves best-in-class exploration coverage and data efficiency.

7. Practical Considerations, Limitations, and Future Directions

IEF’s reliance on in-context conditioning minimizes computational cost and facilitates deployment in settings where external expert models are unavailable. Filtering and reward shaping further stabilize training, but selection of context demonstrations and tuning of bonus parameters impact efficacy and may require empirical calibration.

Open research directions include:

• Optimization of demonstration sampling strategies for maximal expert region coverage.
• Extending IEF-based exploration to other RL architectures and non-reasoning domains.
• Rigorous theoretical characterization of IEF’s generalization properties across model families.

A plausible implication is that IEF can serve as a general paradigm for gradient-free, expert-guided RL fine-tuning wherever demonstration datasets exist and in-context learning is effective.

---

Implicit Expert Forcing (IEF), as formalized within ICPO (Huang et al., 30 Oct 2025), introduces a robust, context-driven mechanism for policy exploration in RL for LLMs, enabling efficient incorporation of expert knowledge strictly via prompt construction. The result is enhanced generalization, stability, and solution diversity in post-training for complex reasoning tasks.