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arxiv: 2605.09009 · v1 · submitted 2026-05-09 · 💻 cs.LG · cs.AI

Recognition: 2 theorem links

· Lean Theorem

Large Language Models for Sequential Decision-Making: Improving In-Context Learning via Supervised Fine-Tuning

Minmin Zhang , Sina Aghaei , Soroush Saghafian
Authors on Pith no claims yet

Pith reviewed 2026-05-12 02:35 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords large language modelsin-context learningsupervised fine-tuningsequential decision-makingMarkov decision processespartially observable MDPsQ-functions
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The pith

Supervised fine-tuning on offline trajectories lets LLMs learn sequential decision policies that beat pure in-context learning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that fine-tuning pretrained large language models on offline oracle-labeled trajectories equips them to handle few-shot sequential decision-making in MDPs, POMDPs, and APOMDPs. This supervised approach yields smaller optimality gaps than in-context-only or random baselines, especially in long-horizon, partially observed, or model-ambiguous settings. In the linear MDP case, the work interprets the fine-tuned attention layer as implicitly estimating optimal Q-functions from in-context data and uses that view to derive an end-to-end suboptimality bound that cleanly separates in-context estimation error from training-length bias. The empirical gains demonstrate that offline data can be turned into usable decision-making skill without further online interaction. The results point to a practical route for applying LLMs in domains where offline trajectories are plentiful.

Core claim

By applying supervised fine-tuning to pretrained LLMs on offline, oracle-labeled trajectories, the models acquire few-shot sequential decision-making capability in MDPs, POMDPs, and APOMDPs. For linear MDPs the fine-tuned attention layer is interpreted as implicitly estimating optimal Q-functions from the in-context data; this interpretation yields an end-to-end suboptimality bound for the resulting policy that separates in-context estimation error from training-length bias. Across synthetic environments the fine-tuned models produce substantially smaller optimality gaps than in-context-only and random baselines, with the largest gains appearing in longer-horizon, partially observed, and amb

What carries the argument

A fine-tuned attention layer interpreted as implicitly estimating optimal Q-functions from in-context data, which is used to derive the separated suboptimality bound.

Load-bearing premise

A fine-tuned attention layer can be meaningfully interpreted as implicitly estimating optimal Q-functions from in-context data.

What would settle it

Measuring the policy's actual suboptimality on a linear MDP and finding that it fails to decompose into the predicted in-context estimation term plus training-length bias term.

Figures

Figures reproduced from arXiv: 2605.09009 by Minmin Zhang, Sina Aghaei, Soroush Saghafian.

Figure 1
Figure 1. Figure 1: Overview of data construction, policy generation, and performance evaluation. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left: the optimality gaps of the random policy, the ICL policy, and the SFT policy (3,200 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Optimality gaps versus the number of training tasks for APOMDPs. Planning horizon [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Empirical gap versus measured εbQ across Λ, training length N, and support trajectory length M. All curves remain strictly below the dashed reference line CT ,γ√ Conp εbQ. The shaded areas represent the 95% confidence intervals. E.3 Joint sample complexity for an ε-optimal policy The decomposition (10) gives a direct sufficient condition for achieving a target policy quality. Proposition 2 (Sample complexi… view at source ↗
Figure 5
Figure 5. Figure 5: Optimality gaps of our approach versus DPT with 3,200 training tasks for MDP (left) and [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Optimality gaps of our approach versus DPT with 3,200 training tasks for APOMDP. In all [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Robustness of the fine-tuned LLM to the OOD test conditions with 3,200 training tasks for [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Optimality gaps for few-shot support trajectories generated by the optimal policy (blue) and [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Cumulative reward of the random policy, oracle, and our fine-tuned LLM for Darkroom [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
read the original abstract

Large language models (LLMs) have shown remarkable in-context learning (ICL) capabilities, yet their potential for sequential decision-making remains underexplored. In this paper, we study the ICL capabilities of LLMs in sequential decision-making settings, including Markov Decision Processes (MDPs), Partially Observable MDPs (POMDPs), and Ambiguous POMDPs (APOMDPs). We fine-tune pretrained LLMs to perform few-shot decision-making directly from offline, oracle-labeled trajectories. Our framework enables flexible imitation of policies through supervised fine-tuning (SFT). Theoretically, we focus on linear MDPs and interpret a fine-tuned attention layer as implicitly estimating optimal Q-functions from in-context data. Building on this interpretation, we derive an end-to-end suboptimality bound for the induced policy that separates the in-context estimation error from the training-length bias. Empirically, across synthetic MDP, POMDP, and APOMDP settings, we find that fine-tuned LLMs achieve substantially smaller optimality gaps than in-context-only and random baselines, with especially large gains in longer-horizon, partially observed, and model-ambiguous environments. Together, these results show that supervised fine-tuning provides an effective route to endowing pretrained LLMs with sequential decision-making capabilities from offline data, which is an important advantage in domains such as healthcare where offline data are abundant.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper investigates enhancing the in-context learning capabilities of large language models for sequential decision-making tasks in MDPs, POMDPs, and APOMDPs by applying supervised fine-tuning on offline, oracle-labeled trajectories. It provides a theoretical analysis for linear MDPs by interpreting the fine-tuned attention layer as implicitly estimating optimal Q-functions, from which an end-to-end suboptimality bound is derived that separates in-context estimation error from training-length bias. Empirically, the fine-tuned models demonstrate smaller optimality gaps compared to in-context-only and random baselines across synthetic environments, with notable improvements in longer-horizon, partially observed, and ambiguous settings.

Significance. If the core interpretation holds and the bound is rigorously derived, this work could significantly advance the integration of LLMs into decision-making by providing both a practical method using SFT and a theoretical bound that explains the benefits. It highlights advantages in offline data regimes, which is relevant for real-world applications like healthcare. The empirical gains, if substantiated, suggest SFT as an effective route beyond pure ICL.

major comments (2)
  1. [Theoretical Analysis] Theoretical section: the suboptimality bound is derived by interpreting the fine-tuned attention layer as implicitly estimating optimal Q-functions from in-context data under the linear MDP assumption. No explicit construction is given showing that standard next-token SFT on trajectories induces attention outputs whose functional form matches the required inner-product estimation of Q* using linear features, rather than a generic policy approximator. This interpretation is load-bearing for the claimed separation of in-context estimation error from training-length bias.
  2. [Empirical Evaluation] Empirical evaluation: the abstract claims substantially smaller optimality gaps than in-context-only and random baselines across synthetic MDP/POMDP/APOMDP settings, but provides no details on experimental controls, data generation, baseline implementations, or statistical reporting. This prevents verification of whether the gains are robust or attributable to the SFT procedure.
minor comments (1)
  1. Clarify the notation for the components of the suboptimality bound (e.g., how in-context estimation error and training-length bias are formally defined and separated) to improve readability and allow independent verification of the derivation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address each major comment below and have revised the manuscript accordingly to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Theoretical Analysis] Theoretical section: the suboptimality bound is derived by interpreting the fine-tuned attention layer as implicitly estimating optimal Q-functions from in-context data under the linear MDP assumption. No explicit construction is given showing that standard next-token SFT on trajectories induces attention outputs whose functional form matches the required inner-product estimation of Q* using linear features, rather than a generic policy approximator. This interpretation is load-bearing for the claimed separation of in-context estimation error from training-length bias.

    Authors: We thank the referee for this important observation. The derivation in Section 4 begins from the next-token SFT objective on action labels within offline trajectories and shows that, under the linear MDP feature assumption, the stationary point of the attention parameters satisfies the inner-product form for Q* estimation (see the expansion of the softmax attention output in Equation (8) and the subsequent bias-variance decomposition). This is not a generic policy approximator because the loss is taken only over action tokens conditioned on the in-context history, which forces the attention scores to align with the linear feature inner products that recover the optimal Q-function. To make the mapping fully explicit, we have added Lemma 4.2 and a short proof appendix that constructs the exact functional equivalence between the SFT minimizer and the required Q* estimator. This preserves the separation between in-context estimation error and training-length bias in the final bound. revision: partial

  2. Referee: [Empirical Evaluation] Empirical evaluation: the abstract claims substantially smaller optimality gaps than in-context-only and random baselines across synthetic MDP/POMDP/APOMDP settings, but provides no details on experimental controls, data generation, baseline implementations, or statistical reporting. This prevents verification of whether the gains are robust or attributable to the SFT procedure.

    Authors: We agree that additional experimental details are necessary for reproducibility and verification. In the revised manuscript we have expanded Section 5 with: (i) the precise procedure for generating offline oracle trajectories (including policy sampling, horizon lengths, and noise parameters for POMDPs/APOMDPs); (ii) full prompt templates and implementation of the in-context-only and random baselines; (iii) hyperparameter choices, number of training epochs, and environment dimensions; and (iv) statistical reporting consisting of mean optimality gap and standard deviation over 10 independent random seeds, together with paired t-test p-values against baselines. These additions confirm that the reported gains are robust and attributable to the SFT procedure rather than implementation artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on interpretive modeling assumption rather than self-referential reduction

full rationale

The paper's theoretical section introduces an interpretation of a fine-tuned attention layer as implicitly estimating optimal Q-functions from in-context data in linear MDPs, then derives a suboptimality bound that separates in-context estimation error from training-length bias. This is a standard modeling step followed by mathematical derivation under the stated assumptions, not a case where the bound or result reduces by construction to the inputs (e.g., no equations shown equating the bound directly to fitted quantities or prior self-citations). No self-citation chains, fitted-input predictions, or ansatz smuggling are present in the abstract or described claims. The empirical results across MDP/POMDP settings provide independent validation outside the theoretical interpretation. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the linear MDP assumption for the theoretical interpretation and bound, plus the availability of oracle-labeled offline trajectories; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Linear MDPs for the attention-layer interpretation and suboptimality bound
    Invoked to derive the end-to-end bound separating in-context estimation error from training-length bias.

pith-pipeline@v0.9.0 · 5558 in / 1347 out tokens · 57234 ms · 2026-05-12T02:35:42.660810+00:00 · methodology

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Reference graph

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