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AdviSD: Learning to Advise Frontier LLMs via Targeted Multi-Turn Self-Distillation

Rishabh Agrawal, Hejie Cui, Shasha Li, Shanchan Wu, Sercan Ö. Arık

arXiv:2609.38142v1cs.AIcs.CLcs.LG

TL;DR

Episode rewards do not specify which advice decisions should change, and plausible corrections need not alter a frozen executor’s behavior. AdviSD combines outcome-based learning with selective self-distillation using score contrasts on recorded responses. It outperforms advisor-GRPO on the reported in-domain benchmarks and also shows out-of-domain and cross-model transfer.

  • Problem

    Episode rewards summarize task performance but do not specify which advisor decisions should have been different.

    Source: §1 · p. 1

  • Method

    AdviSD combines outcome-based GRPO with selective self-distillation, using a feedback-conditioned teacher and score contrasts on the same recorded executor response to select advice decisions.

    Source: §5.2 · p. 6, §8 · p. 12

  • Results

    AdviSD exceeds advisor-GRPO by 4.2–6.4 percentage points on BFCL-v3 and 3.9–5.1 score points on EnvScaler, and improves out-of-domain macro-averages by 2.7–3.6 points over standalone execution.

    Source: §1 · p. 2, §7 · p. 11

  • Takeaways & Limitations

    In the shared-parameter model, retaining corrections that favor useful advice less strongly less often raises the advisor’s eventual performance.

    Source: §1 · p. 2, §4.2 · p. 5

    In the shared-parameter model, a higher learning limit need not mean faster learning from the start because the effect of reducing distillation depends on the parameter’s position relative to a0.

    Source: §6 · p. 8

Abstract

from arXiv · show

A small trainable advisor can steer a frozen language-model executor using natural-language advice. In addition to learning from task rewards, the advisor can use feedback from completed interactions to improve its advice. However, a plausible correction need not change execution, yet learning from such corrections can still affect the advisor's future decisions in other contexts. In a shared-parameter model, we prove that such corrections can limit learning if their targets favor useful advice less strongly than those of other corrections. Keeping them less often than the rest improves the model's eventual performance compared to learning from every correction. Motivated by this, our method, Advisor Self-Distillation (AdviSD), pairs outcome-based reinforcement learning with self-distillation from a feedback-conditioned copy of the advisor selectively. Reflection proposes corrections, and the advisor scores the same recorded executor response with and without its issued advice, using the magnitude of the difference to select decisions for supervision. This approach does not require executor likelihoods or additional executor rollouts. Experiments with Qwen3-8B advisors for Gemini and Claude show that AdviSD outperforms advisor-GRPO by 4.2-6.4 percentage points on BFCL-v3 and by 3.9-5.1 score points on EnvScaler. The trained advisors generalize to out-of-domain tasks and transfer across different executor versions and model families. AdviSD also beats matched-count random selection, supporting the value of its selection rule.

1. Introduction

The paper studies how a trainable advisor can improve guidance to a frozen executor when episode rewards do not identify which advice decisions should change. AdviSD selects feedback-based supervision using the advisor’s score contrast on a recorded executor response, and the paper analyzes why correction selection can affect learning.

1. Introduction

  • Completed interactions provide responses, tool results, task checks, and episode rewards for reflection, but plausible revisions can be redundant for a given executor.For example, elaborating flight-search advice may add little when the executor already searches unaided, unlike advice correcting a booking failure.Source: §1 · p. 1

A theoretical account of correction selection

  • The shared-parameter analysis shows that corrections from persistent failures can limit learning when their targets favor useful advice less strongly than other corrections.Retaining those corrections less often raises eventual performance, whereas matched-rate random thinning leaves the limit unchanged without reward learning.Source: §1 · p. 2

AdviSD: multi-turn advising with targeted feedback

  • AdviSD separates proposing revisions from choosing where to learn, using score differences on the same recorded response with and without issued advice to select supervision.A feedback-conditioned copy of the pre-update advisor teaches the trainable advisor; selection needs neither executor likelihoods nor additional executor rollouts.Source: §1 · p. 2

Empirical results

  • AdviSD exceeds advisor-GRPO by 4.2–6.4 percentage points on BFCL-v3 and 3.9–5.1 score points on EnvScaler with Qwen3-8B advisors for Gemini and Claude.It also improves out-of-domain macro-averages by 2.7–3.6 points over standalone execution and transfers across executor versions and model families.Source: §1 · pp. 2–3
  • AdviSD’s 2.5–4.9-point advantage over matched-count random selection supports selecting which decisions to supervise beyond merely reducing supervision.The analysis links lower retention of corrections from persistent failures to higher eventual performance when those corrections favor useful advice less strongly.Source: §1 · p. 2

2. Related Work

Related work covers adapting frozen models through prompts or smaller guiding models, feedback-conditioned distillation, and predictive contrasts for selection. AdviSD applies targeted feedback-conditioned distillation to an advisor whose guidance acts through a separate executor.

Advising and prompt optimization

  • Advisor-GRPO follows outcome-based training through a response-level tool-use interface, while AdviSD adds targeted feedback-conditioned self-distillation.GEPA optimizes reusable instructions; Directional Stimulus Prompting, Matryoshka Pilot, and Advisor Models train smaller models to guide frozen ones (Agrawal et al., 2026a; Asawa et al., 2026; Li et al., 2025, 2023).Source: §2 · p. 3

Feedback-conditioned distillation

Predictive contrasts and selection

  • AdviSD contrasts paired predictions on a separate executor’s recorded response, using the contrast magnitude to select auxiliary advisor supervision while leaving GRPO advantages unchanged.This differs from predictive-contrast approaches that refine a policy directly performing the task.Source: §2 · p. 3

3. Background and Problem Formulation

The problem formulation models an advisor making repeated decisions before a frozen executor responds, with task reward assigned at episode end. Training combines episode-level GRPO with feedback-conditioned self-distillation on selected advice decisions.

Advising a frozen executor

  • Before each executor response, the advisor samples advice or abstains; the frozen executor responds using its native history and any issued advice.The advisor decides again before each response, including after tool results and for text-only responses; parallel tool calls within a response share one decision.Source: §3 · p. 3

Two learning signals

  • GRPO uses each episode’s normalized reward advantage for every advisor token generated in that episode, including abstentions.The formulation denotes the clipped GRPO loss with reference-policy regularization as Lbase (Shao et al., 2024).Source: §3 · p. 3
  • Feedback-conditioned self-distillation trains the student, which sees only the original context, to match a fixed teacher copy that also sees completed-interaction feedback.AdviSD selects decisions for this auxiliary supervision, including originally abstaining decisions flagged by reflection, while leaving GRPO advantages unchanged.Source: §3 · p. 4

4. Why the Choice of Corrections Matters

The analysis distinguishes matching a feedback-conditioned teacher from improving execution, then studies how retained corrections determine a shared-parameter advisor’s learning limit. Its conclusions depend on correction types having different execution sensitivity and teacher preferences.

4.1. A single update through the executor

  • Teacher agreement alone does not establish execution improvement: at an insensitive prefix, changing token probabilities cannot improve the local execution objective, though shared parameters can affect advice elsewhere.The actual teacher’s descent direction includes a residual that can reinforce or oppose value ascent.Source: §4.1 · p. 4

4.2. Repeated updates and the learning limit

  • In the repeated-update model, advice 1 is more successful than advice 2 in sensitive situations, while both induce the same execution law in insensitive situations.The model assumes fixed execution laws and a shared log-odds parameter across both situation types.Source: §4.2 · pp. 4–5
  • The analysis assumes insensitive-failure teachers favor advice 1 less than sensitive-failure teachers, so persistent insensitive failures can increasingly shape retained supervision as sensitive failures recede.The retained mixture’s mean target log-odds decreases as the advisor improves and sensitive failures become less frequent.Source: §4.2 · p. 5
  • With distillation alone, the shared-parameter model converges to a unique equilibrium, and retaining insensitive corrections less often than sensitive ones raises both the equilibrium and expected success.Scaling both retention probabilities equally or changing episode size or proposal cap leaves the limit unchanged.Source: §4.2 · p. 5
  • The model’s situation-type retention rule motivates AdviSD’s observable predictive contrast and a matched-count random control when reward learning is added.With reward learning, exposure can also affect eventual performance, so the control separates targeted selection from reduced supervision.Source: §4.2 · p. 5

5. AdviSD: Advisor Self-Distillation

AdviSD separates proposing advice corrections from selecting decisions for learning, then uses targeted self-distillation to train the advisor alongside reward learning.

5.1. Reflection proposes corrections

  • Reflection uses executor responses, tool outcomes, and checks to flag up to b_refl advice decisions for correction in each eligible imperfect episode.Proposed advice is based on information available at the original decision, even when later events explain a failure.Source: §5.1 · p. 6

5.2. A paired score selects where to learn

  • The pre-update advisor scores the same recorded executor response with and without issued advice, using the contrast magnitude to select decisions without executor likelihoods or extra rollouts.Both contexts share the pre-response history and tool schemas; they differ only in the issued advice.Source: §5.2 · p. 6
  • A donor-advice pilot sets the fixed selection threshold, while flagged original abstentions bypass the numeric gate because their paired contexts are identical.A proposal to abstain after advice was issued must still pass the numeric gate.Source: §5.2 · p. 6

5.3. Self-distillation from targeted feedback

  • At retained decisions, a feedback-conditioned teacher sees reflection feedback prepended to the original context, while the student sees only that original context.Both predict along the originally sampled advice, including <NO_ADVICE>; the teacher distributions are computed from the pre-update advisor and held fixed during optimization.Source: §5.3 · pp. 6–7

6. Targeted Supervision: Reward Learning and Calibration

The analysis combines reward learning with distillation in a shared-parameter model, examining how correction selection and supervision frequency affect learning limits.

Reward learning and selection

  • Selection changes both the mean retained teacher target and episode-level supervision exposure; under the model, it gives more weight to the sensitive teacher.Reward learning favors higher expected success, while distillation pulls toward retained teachers’ mean target.Source: §6 · p. 7

Learning dynamics

  • Selection can raise the learning limit without speeding early progress: below a0, reducing distillation can slow progress, while above a0 it reduces a downward pull.The sign of the effect depends on the parameter value.Source: §6 · p. 8

Reward learning and selection

  • With positive reward learning, reward-only ascent approaches best achievable success, while fixed-weight distillation yields a finite balance where selection gives higher success than no gating.The theorem compares the two combined rules with each other; finite-budget gains over outcome-only GRPO are tested separately.Source: §6 · p. 8

Calibration and controls

  • A matched-count random control tests whether selecting particular corrections helps beyond reducing supervision, while donor calibration sets the gate threshold from advice on other tasks.The control matches per-episode retention counts on its own rollouts; donor-advice quantiles bound pilot-sample gate passage.Source: §6 · p. 8

7. Experiments

Experiments compare trained advisors and controls on in-domain benchmarks, then test correction selection, out-of-domain generalization, executor transfer, and training progress.

Setup and evaluation

  • Evaluation uses three independent runs and fixed test sets of 320 BFCL-v3 tasks and 200 EnvScaler tasks, reporting mean and sample standard deviation across run averages.The trained-method checkpoint is validation-selected and evaluated four times on the test set for each run.Source: §7 · p. 8

In-domain performance

  • 4.2–6.4 percentage points on BFCL-v3 and 3.9–5.1 score points on EnvScaler separate AdviSD from advisor-GRPO, with AdviSD highest on both aggregates for both executors.Gains over GRPO are larger in BFCL’s augmented categories than in Base for both executors.Source: Table 1 · p. 9, §7 · p. 9

Correction selection and abstention supervision

  • 2.5–4.9 points over matched-count random selection and 3.2–5.1 over no gating favor AdviSD’s selection rule; removing the abstention bypass lowers performance by 0.6–1.7 points.The inverted gate trails GRPO on both benchmarks with both executors.Source: §7 · pp. 10–11, Table 2 · p. 10

Transfer without retraining

  • AdviSD leads all four cross-version and cross-family BFCL-v3 transfer comparisons and exceeds transferred GRPO by 3.1 percentage points in both cross-family directions.Cross-family scores remain below those of AdviSD advisors trained for the evaluation executor.Source: Figure 2 · p. 10, §7 · pp. 11–12
  • Without retraining, AdviSD leads the four-benchmark out-of-domain macro-average for both executors, exceeding standalone execution by 2.7 points with Gemini and 3.6 with Claude.AdviSD has the highest mean, outright or tied, in 17 of 18 comparisons, while performance varies by task.Source: Table 3 · p. 11, §7 · p. 11

Training progress

  • On BFCL-v3 validation with Claude Sonnet 4.6, AdviSD leads the compared methods from update 20 onward, with a late-training margin over GRPO of roughly four percentage points.The curve reports mean and sample standard deviation over three independent training runs.Source: Figure 3 · p. 12, §7 · p. 12

8. Conclusion

AdviSD combines task rewards with targeted self-distillation to train small advisors for frozen frontier executors.

Conclusion

  • AdviSD separates proposing corrections from selecting which advice decisions to supervise, using paired scores of the same recorded executor response with and without issued advice.A feedback-conditioned teacher supervises retained decisions, and the shared-parameter analysis motivates the matched-count random control.Source: §8 · p. 12
  • AdviSD has the highest in-domain aggregates on BFCL-v3 and EnvScaler among compared methods and leads out-of-domain macro-averages and transfer comparisons without retraining.Its gains over ungated and matched-count random supervision support choosing where to learn beyond merely reducing supervision.Source: §8 · p. 12

Appendices

The appendix defines notation for the local execution-value analysis, the repeated-learning model, and AdviSD’s paired contexts and selection contrasts.

A. Notation and scope

  • The local analysis treats θ as the advisor’s parameter vector, while the learning model uses one scalar logit shared across situations.Its scope assumes independent opportunities, uniform proposals, and stationary conditional statistics; it does not model the full reflector, evolving language model, or optimizer.Source: A. Notation and scope · p. 18
  • The local notation distinguishes the student’s next-token distribution, the teacher distribution, execution law, expected task score, local execution value, and teacher-dependent gradient residual.The execution law excludes the advice text and describes executor responses and outcomes after a token choice and completion by the pre-update advisor.Source: A. Notation and scope · p. 18
  • The repeated-learning model tracks the opportunity count, failure-proposal cap, execution-insensitivity probability, retention probability, exposure, and composition of retained teacher log-odds.The method notation separately names the reflection flag cap, paired contexts with and without issued advice, feedback block, signed score contrast, and pilot-donor threshold.Source: A. Notation and scope · p. 18

B. A single update through the executor

The single-update analysis separates matching a feedback-conditioned teacher from improving execution: the gradient contains an execution-value component and a teacher-dependent residual. The appendix then considers how retained corrections affect learning over repeated interactions.

B. A single update through the executor

  • Lemma 1 separates matching a feedback-conditioned teacher from improving execution because advice-token distributions and executor responses determine different quantities.The analysis compares them at one recorded prefix while holding the completion and execution laws fixed; the local execution value averages expected token scores under the student’s next-token probabilities.Source: B. A single update through the executor · pp. 19–20
  • Fitting the reference teacher yields an execution-value gradient component, while fitting another teacher adds a residual that can reinforce or oppose value ascent.When execution is insensitive to the next token, the local value component is zero, yet teacher fitting can still move the advisor; near-insensitivity makes the value component small under controlled reward range and gradient scale.Source: B. A single update through the executor · pp. 20–21
  • The comparison is local to pre-update parameters and does not establish the result of a finite optimization step or a full-policy execution gradient.The fixed-prefix derivative does not differentiate the continuation policy or the probability of visiting the recorded prefix.Source: B. A single update through the executor · p. 21

C. Retained corrections and the learning limit

  • The repeated-learning analysis makes explicit that updates alter later advice, failures, and the corrections available for training.It first studies a two-teacher model, then adds reward learning, and finally allows stationary random teachers and action-dependent selection.Source: C. Retained corrections and the… · pp. 21–22

C.1. Proof of Theorem 1 in the two-teacher model

The proofs characterize when selectively retaining corrections can improve limiting learning by changing the retained-target composition, while uniform thinning changes exposure rather than composition. They qualify the result by noting that it depends on retained targets and exposure, need not describe early updates or selectors that change target content, and is not guaranteed merely by detaching a changing teacher.

C.1. Proof of Theorem 1 in the two-teacher model

  • The episode’s retained average pulls the shared preference toward its retained teachers’ mean target; the cap and episode size affect exposure, not that conditional mean.The proof averages over the actual random retained count, with zero loss when no corrections remain.Source: §C.1 · p. 23
  • Reducing insensitive corrections’ retention relative to sensitive corrections raises the fixed-teacher equilibrium and its limiting success, independently of episode size and proposal cap.The mean target falls as advice improves because sensitive failures become rarer and the weaker insensitive teacher supplies a larger share of supervision; the flow converges from every finite initialization.Source: §C.1 · p. 24
  • Detaching a feedback-conditioned teacher justifies the conditional gradient calculation but does not alone preserve a finite learning limit when targets evolve.Targets that move partway with the student preserve the distillation-only equilibrium, whereas targets fixed ahead of the student can drive preference toward 1.Source: §C.1 · p. 25

C.2. Proof of Theorem 2 and Corollary 1 in the two-teacher model

  • Preferential retention yields higher limiting success than retaining every proposal under a common reward objective and initialization.The comparison is strict because the gated field has a higher limiting preference, and expected success increases with preference.Source: §C.2 · pp. 25, 27
  • Uniform thinning changes exposure without changing the retained target mixture, yielding at least the no-gating limit with reward learning and the same limit without it.Without reward learning, both flows converge to the same distillation-only equilibrium from any common finite initialization.Source: §C.2 · p. 28
  • In the illustrated case, the composition and exposure terms at the ungated limit are 0.287 and 0.057, respectively; changing exposure alone explains part of the limiting gain, while changing retained targets raises the limit further.Source: §C.2 · p. 28
  • At θ = −2, the gated field is 0.177 versus 0.217 ungated, yet limiting advice-1 probabilities are 0.736, 0.824, and 0.892 for F0, FR, and FG, respectively.Thus the limiting comparison does not imply that every earlier update improves.Source: §C.2 · pp. 28–29

C.3. Stationary random teachers and action-dependent selection

  • With stationary random teachers, the expected gradient is Bp(1 − p)(θ − μ); if ℓ̄1 − ℓ̄2 ≤ 4, every finite initialization converges to a unique fixed point independent of episode size and cap.Episode size and cap affect the positive exposure factor B, and thus flow speed, but not the fixed point.Source: §C.3 · pp. 30–31
  • When classwise retention rates vary with fixed retained means and the stated target orderings hold, decreasing rI/rS strictly increases the limit and expected success; retaining fewer insensitive corrections alone does not guarantee better targets.A new selector may change teacher content within a type, changing retained means as well as retention rates.Source: §C.3 · pp. 30–31
  • Under Assumption 3, selective dynamics converge from a common finite start to strictly higher parameter and expected-success limits when μG(θ) > μ0(θ); trajectories are strictly ordered from starts at or above a0.The comparison also requires the ungated target gap condition; below a0, the result concerns limits rather than necessarily early trajectories.Source: §C.3 · p. 32
  • With equal retained mean targets, lower exposure yields weakly ordered trajectories and limits under reward learning from a common start, while equal exposure gives identical flows; the quota control need not preserve composition.Without reward learning, both selectors converge to the same limit.Source: §C.3 · p. 33

D. Training and implementation details

AdviSD trains a Qwen3-8B advisor while keeping the executor fixed, combining outcome learning with selective feedback-conditioned self-distillation. Selection compares the advisor’s scores for the same recorded executor response with and without its advice.

D. Training and implementation details

  • AdviSD trains Qwen3-8B with Claude Sonnet 4.6 or Gemini 3.7 Flash as the fixed executor, using Gemini 3.7 Flash for reflection.EnvScaler uses one pass over 1,880 training tasks, with 235 updates and 64 episodes per update.Source: D. Training and implementation details · p. 33
  • Selection compares scores for the same recorded executor response with and without issued advice, without estimating the executor’s response law.The response was observed with advice; removing advice changes the scoring context, not the recorded execution.Source: D. Training and implementation details · pp. 33–34
  • Donor contrasts calibrate a run-specific threshold that is frozen during training; the pilot bound does not establish later pass rates or sensitivity-based retention.BFCL pilot checks require at least 200 matched decisions and at least 10% matched retention.Source: D. Training and implementation details · pp. 34–35
  • Training combines an outcome-based GRPO objective with reflection-flagged decisions selected for auxiliary self-distillation.Flagged original abstentions bypass the numeric gate; valid issued-advice decisions must exceed the contrast threshold.Source: D. Training and implementation details · p. 35
  • A feedback-conditioned copy of the pre-update advisor supervises the student using execution evidence, failed checks, episode reward, and reflection feedback.Teacher and student distributions are renormalized over the student’s top 100 tokens; feedback blocks over the context budget are skipped.Source: D. Training and implementation details · p. 35

E. Baselines and evaluation protocol

The evaluation compares advisor training and selection controls with prompt optimization and other advisor methods, using held-out benchmark tests and validation-selected checkpoints. The appendix also reports supervision dynamics for one run and gives the exact prompts and interaction rules.

E. Baselines and evaluation protocol

  • Comparisons include outcome-only advisor-GRPO, executor-prompt GEPA, native SDPO and DistIL, and AdviSD controls for ungated and matched-count random selection.GEPA prompt search uses 8,192 scored task episodes per executor and in-domain benchmark; this is not a compute-matched comparison with advisor training.Source: E. Baselines and evaluation protocol · pp. 35–36
  • BFCL results use a fixed 320-task test set, while EnvScaler uses a fixed 200-task test set; Table 5 summarizes datasets and primary metrics.Each run has separate training and validation partitions, and checkpoints are selected using four validation evaluations.Source: E. Baselines and evaluation protocol · p. 37, Table 5 · p. 37
  • Trained-method scores average four test evaluations of each run’s validation-selected checkpoint; reported run-level SD is not a confidence interval.The Table 3 macro average weights benchmarks equally and has no uncertainty estimate.Source: E. Baselines and evaluation protocol · pp. 37–38
  • The learning analysis assumes fixed teachers and stationary retention, and does not establish convergence for AdviSD’s changing-teacher GRPO–AdamW training.Evaluation covers two executor families, one shared reflector, and three runs per trained method; API updates can constrain exact reproducibility.Source: E. Baselines and evaluation protocol · p. 38

E.1. Training-time supervision dynamics

  • In one Claude Sonnet 4.6 BFCL run, advice and ordinary retention decline over training, supervision reaches fewer episodes, and bypasses account for about one-fifth of selected decisions in middle and late phases.These allocation statistics are compatible with the proposed mechanism but do not identify sensitivity classes or measure gradient magnitudes.Source: §E.1 · p. 39, Table 6 · p. 39

F. Exact prompts

  • The advisor gives concise guidance before every executor response, or abstains when guidance would not improve that response; reflection flags evidence-based, correctable advice decisions.The reflector may use later observed events to identify errors but must judge proposed corrections using information available before the decision.Source: F. Exact prompts · pp. 39–41

G. Paired qualitative evidence

The paired evidence illustrates a booking interaction and reports outcomes across a selected 16-task sample. The extended related work situates AdviSD among learned advising, reflection and prompt optimization, feedback-conditioned distillation, and methods for localizing supervision.

G. Paired qualitative evidence

  • Across 16 sampled tasks, the primary checker found 13 joint passes, two AdviSD-only passes, and one standalone-only pass; requiring both checks gave 10 AdviSD and 11 standalone passes.The illustrated AdviSD trajectory passed both checks with nine tool calls versus 14 for standalone, but was not faster in the recorded comparison; the sample does not estimate overall accuracy.Source: G. Paired qualitative evidence · p. 42

H. Extended Related Work

  • The extended review groups related work around adapting frozen models, turning interaction feedback into supervision, and using predictive comparisons to guide learning.It distinguishes natural-language advising and prompt optimization from AdviSD’s training-time feedback-conditioned supervision.Source: H. Extended Related Work · p. 44, §H.1 · p. 44

H.1. Advising and prompt optimization

  • Prior work learns hints and multi-turn advice [Li et al., 2023; Li et al., 2025] or optimizes reusable prompts from reflection [Pryzant et al., 2023; Agrawal et al., 2026a]; AdviSD trains a context-dependent advisor.Advisor Models uses GRPO on executor outcome rewards [Asawa et al., 2026], whereas AdviSD also targets feedback-selected supervision.Source: §H.1 · p. 44

H.2. Feedback-conditioned distillation

  • Feedback-conditioned methods such as SDPO and DistIL supervise student-generated tokens [Hübotter et al., 2026; Agrawal et al., 2026b]; AdviSD selects advice decisions for an advisor serving a separate executor.Related approaches localize feedback to turns, actions, or spans; AdviSD scores the recorded executor response with and without issued advice to select supervision.Source: §H.2 · pp. 44–45

H.3. Predictive contrasts and selection

AdviSD uses a paired prediction contrast to select advice decisions for self-distillation, rather than estimating the executor’s counterfactual behavior. The analysis relates this allocation choice to teacher mixtures and learning dynamics.

H.3. Predictive contrasts and selection

  • AdviSD scores a separate executor’s recorded response with and without issued advice, then uses the contrast magnitude to select auxiliary self-distillation while leaving GRPO advantages unchanged.The paired contrast is distinct from approaches that reweight outcome-based advantages.Source: §H.3 · p. 45
  • The contrast measures how issued advice changes the advisor’s prediction, not a behavioral effect or improvement in task return.It varies only the advice while holding the advisor snapshot, interaction history, and recorded response fixed.Source: §H.3 · p. 46
  • Unlike behavioral-influence and credit-assignment methods, AdviSD’s rescoring does not estimate counterfactual task returns or replace the policy-gradient advantage.Selection uses an existing response and requires no additional executor rollouts.Source: §H.3 · p. 46
  • The learning analysis links supervision composition and frequency to eventual performance under shared-parameter assumptions, but does not show that AdviSD identifies theoretical sensitivity classes.Its matched-count control and selection ablations evaluate the predictive rule rather than establish those classes.Source: §H.3 · p. 46
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