Selective Critique for Cost-Aware LLM Agents in Long-Horizon Decision Making

Heewon Park; Somin Im; Minhae Kwon

cs.LGOct 5, 2026

Selective Critique for Cost-Aware LLM Agents in Long-Horizon Decision Making

Authors: Heewon Park, Somin Im, Minhae Kwon

Organizations: Department of Electrical and Computer Engineering, Sungkyunkwan University, Republic of Korea. · Soongsil University, Republic of Korea.

Abstract

Improving the reliability of large language model (LLM) agents in long-horizon decision-making remains a key challenge. When deployed as autonomous agents interacting with complex environments, early mistakes can propagate through trajectories and cause cascading failures. Recent approaches improve reliability by incorporating external critique or deliberation, but invoking these mechanisms at every step substantially increases token consumption and latency, limiting practical deployment. We propose SAG (Self-improving Agent with Gated critique), a cost-aware framework that formulates critique invocation as a step-wise decision problem during long-horizon interaction. SAG introduces a lightweight, training-free gating mechanism that estimates the utility of critique using action-level ambiguity signals--global entropy and local top-2 margin--computed over admissible actions. From a decision-theoretic perspective, this mechanism approximates the Value of Information (VoI) of critique, enabling the agent to selectively allocate expensive feedback only when its expected benefit justifies the cost. SAG further incorporates online bootstrapped self-improvement, allowing the actor to internalize critic-assisted behaviors and progressively reduce reliance on critique. Across three long-horizon interactive benchmarks and multiple backbone models, SAG substantially improves the performance-cost trade-off compared with both no-critique and always-on critique agents. On ALFWorld, SAG increases task success from 24.6% to 78.4% while maintaining a token budget comparable to ReAct, yielding a $3.1\times$ improvement in normalized token efficiency. Moreover, a 7B actor with a lightweight 3B critic achieves performance comparable to a 14B actor without critique, showing that selective critique can recover most of the reliability benefits of deliberation while dramatically reducing inference cost.

Figures & tables

Figure 1 : Normalized token efficiency and success rate. Token efficiency measures success rate per token usage and is normalized by ReAct (ReAct = 1.0). Always-on critique (LAC) improves success but can substantially reduce efficiency, whereas SAG achieves both high success and high token efficiency.

Figure 2 : Overview of SAG. At each step, action-level ambiguity decides whether to query a critic; successful trajectories are periodically distilled into the actor via online SFT.

Figure 3 : Performance–cost comparison. Bubble area indicates normalized token efficiency (ReAct = $1.0$ ).

Model	Type	Method	ALFWorld				BabyAI				WebShop
			Succ $\uparrow$	#Horizon $\downarrow$	#Token $\downarrow$	Eff $\uparrow$	Succ $\uparrow$	#Horizon $\downarrow$	#Token $\downarrow$	Eff $\uparrow$	Succ $\uparrow$	#Horizon $\downarrow$	#Token $\downarrow$	Eff $\uparrow$
GPT-4.1	Basic	ReAct	$80.6$	$11.9$	$32$	$1.00$	$74.0$	$15.2$	$27$	$1.00$	$33.5$	$7.9$	$10$	$1.00$
Qwen2.5- 7B-Instruct	Basic	ReAct	$24.6$	$15.8$	$\mathbf{55}$	$1.00$	$36.0$	$7.4$	$55$	$1.00$	$11.0$	$6.3$	$12$	$1.00$
	Deliberation	Reflexion	$40.3$	$16.3$	$150$	$0.60$	$41.0$	$\mathbf{7.0}$	$162$	$0.39$	$11.5$	$6.8$	$15$	$0.81$
	Deliberation	Debate	$31.3$	$14.3$	$389$	$0.18$	$52.0$	$8.9$	$441$	$0.18$	$20.0$	$\mathbf{4.7}$	$90$	$0.24$
	Deliberation	CER	$60.5$	$16.4$	$210$	$0.64$	$45.0$	$8.0$	$239$	$0.29$	$16.0$	$5.1$	$11$	$1.50$

Table 1 : Performance comparison on three benchmarks with three backbones. Succ : success rate (%). #Horizon : average steps per successful episode. #Token : average tokens per episode (k). Eff : normalized token efficiency, computed as

\text{Succ}/\text{\#Token}

and normalized so that ReAct = 1.0 for each backbone and benchmark.

Figure 4 : Success rate over task level. Task difficulty is stratified by the trajectory length of a GPT-4.1 ReAct agent.

Figure 5 : Case Study: SAG effectively corrects the trajectory, avoiding both failure and pervasive critique overhead.

Figure 6 : Actor–critic capacity scaling for SAG. Each cell reports success rate for a given actor–critic size pairing. Marginal bars show mean performance across actor and critic sizes.

Global	Local	Variant	Succ $\uparrow$	#Horizon $\downarrow$	#Token $\downarrow$
✓	✓	Full (SAG)	78.3	11.4	56
✗	✓	w/o $\bar{H}_{t}$	77.6	12.1	51
✓	✗	w/o $m_{t}$	74.6	11.4	52
✗	✗	Always (no gating)	62.0	17.4	282
✗	✗	w/o critic	33.0	19.3	50

Table 2 : Ablation study on ALFWorld. Global indicates using global ambiguity

\bar{H}_{t}

; Local indicates using local ambiguity

m_{t}

. Always removes the gate and invokes critique at every step; w/o critic disables critic invocation.

Method	Critique	Succ. $\uparrow$	#Token $\downarrow$
ReAct + online SFT	None	30.2	57
LAC + online SFT	Always-on	74.2	341
SAG	Gated	78.3	56

Table 3 : Matched online-SFT controls. All methods use the same online update protocol.

Figure 7 : Parameter sensitivity analysis

Panel of Figure 8 — Figure 8 : Learning dynamics of SAG under online self-improvement. Metrics are aggregated into Early/Mid/Late phases over 134 evaluation episodes.

Appendix: Selective Critique for Cost-Aware LLM Agents in Long-Horizon Decision Making

Table 12

Appendix figures & tables27 assets

Supplementary material from the paper’s appendix.

Appendix

Notation	Description
$t$	Time step in an interaction episode
$o_{t}$	Environment observation at step $t$
$x_{t}$	Actor context at step $t$ , including task instruction, observation, and truncated history
$\mathcal{A}_{t}$	Set of admissible actions at step $t$
$a_{t}$	Action executed at step $t$
$r_{t}$	Actor reasoning state generated from $x_{t}$ at step $t$

Appendix

Table 13

[Actor Prompt] You are an agent for household tasks. Your goal is to complete the task described in natural language by reasoning step-by-step and producing an action. Always output in the format: "think: reasoning here" "action: [chosen action]" Actions must come from the admissible set provided. Do not invent new actions. [Critic Prompt] You are a critic for an LLM-based agent. Your GOAL: detect and correct hallucinations, loops, or inconsistent actions. INPUTS: - task: the goal - history: what happened so far - actions: valid moves. INSTRUCTIONS: 1. verify objects: does the object the agent is targeting MATCH the task description? 2. verify history: did the agent already check this empty location or repeat failures? 3. decision: - If the agent is safe and correct, output "next_action": "continue". - If the agent is wrong, provide a specific "next_action" to fix it. 4. reasoning: - Also provide a short explanation in "reasoning". - The reasoning should explain why the proposed action is appropriate. - Keep it concise, one or two sentences.

Appendix

Table 4 : Prompts used for ALFWorld

[Actor Prompt] You are an agent in the Grid world. Your goal is to follow the natural language instruction step-by-step. At each step, reason explicitly before acting. Use the format: "think: reasoning here" "action: [chosen action]" Primitive actions include: go left, go right, go forward, pick up object, drop object, etc. [Critic Prompt] You are a critic helping an actor agent navigate a small grid world. Your GOAL: - Detect when the actor is stuck, uncertain, or moving inefficiently. - Propose a corrective plan that helps the actor make progress toward the goal. INPUTS: - goal: The current task the actor must complete. - observation: The actor’s current state in the grid world. - valid actions: The list of actions the actor can execute now. INSTRUCTIONS: 1. check progress: - Determine whether the actor is making progress toward the goal. - If the actor seems stuck in a loop, suggest actions that break the loop. 2. check validity: - Only use actions from the valid actions list. - Do not invent new actions. 3. proposed plan: - Propose a SHORT sequence of 1 to 3 actions. - The plan should be directly executable in the current state. 4. reasoning: - Provide a brief reason explaining why the plan is helpful. - Keep the reasoning concise, at most one sentence.

Appendix

Table 5 : Prompts used for BabyAI-Text

[Actor Prompt] You are a shopping assistant. Your task is to satisfy the given shopping goal. At each step, reason aloud and then select one action. Use search[query] for the initial query; after search results are shown, choose from the web actions available in the current observation, such as click[item], click[option], navigation, or click[Buy Now]. Use format: "think: reasoning here" "action: [web action]" [Critic Prompt] You are a critic for a WebShop shopping agent. GOAL: - Help the actor choose the best next action for completing the shopping task. - Detect inefficient actions, loops, or choices that do not satisfy the user instruction. INPUTS: - user instruction: the shopping request, including constraints such as product type, size, flavor, count, price, rating, or other preferences. - recent history: The recent actions and observations from the shopping trajectory. - candidate actions: The list of actions currently available to the actor. INSTRUCTIONS: 1. check constraints: - Identify the important constraints in the user instruction. - Prefer actions that move toward satisfying all constraints. 2. check progress: - Avoid repeating unhelpful actions. - Avoid going back unless it clearly helps recover from a mistake. - Prefer clicking the most relevant product, option, or navigation action. 3. choose action: - Choose exactly ONE best next action. - The action must be one of the candidate actions. - If no candidate action is clearly useful, choose the safest progress-making action. - Use "none" only when no valid progress-making action exists. 4. rationale: - Provide a very short reason explaining why the chosen action is appropriate. - Keep the rationale concise, one sentence at most.

Appendix

Table 6 : Prompts used for WebShop

Figure 9 : Overall online self-improvement process

Component	Value	Component	Value
Uncertainty-based critique gate
Gate threshold $\tau$	0.4	Margin threshold $\delta$	0.2
Online SFT (self-improvement)
History window	8 steps	Max obs. length	800 chars
Buffer capacity	50,000	Successes per update	10
Train batch size	2	Grad. accumulation	8

Appendix

Table 7: SAG hyperparameters and online SFT configuration (shared across benchmarks unless otherwise noted).

Dimension	RL-based agent post-training	SAG
Primary goal	Improve the underlying policy before deployment	Decide when to use critique during deployment
Typical methods	PPO, GRPO, GiGPO	Gated critique + online SFT
Training signal	Rewards, preferences, or advantage estimates	Successful trajectories from online interaction
Rollout structure	Multiple sampled trajectories/completions per task	One interaction stream with selective critique
Models during training	Actor, often reference policy, optimizer states	Actor update; critic fixed and queried selectively
Cost focus	Training-time rollout and optimization budget	Inference-time token, critic-call, and latency cost

Appendix

Table 8: Scope comparison between RL-based agent post-training and SAG.

Benchmark	Backbone	w/o critic			always-on critic			SAG
Benchmark	Backbone	Succ.	Token	Call	Succ.	Token	Call	Succ.	Token	Call
ALFWorld	3B	21.6	57	–	59.0	271	15.1	69.4	58	3.2
	7B	25.4	55	–	74.8	273	14.7	78.3	56	2.6
	14B	77.2	49	–	80.5	292	13.3	82.1	53	2.3
	32B	79.1	48	–	86.2	308	13.2	87.2	54	2.1
BabyAI	3B	34.0	59	–	52.3	356	10.3	61.8	79	3.3

Appendix

Table 9: Extended scaling results with no critic, always-on critic, and SAG. Token usage includes actor and critic tokens.

Actor / Critic	Succ. $\uparrow$
7B / No critic	25.4
7B / 3B critic	76.9
7B / 7B critic	78.3
7B / 14B critic	82.1

Appendix

Table 10: Effect of critic capacity with a fixed 7B actor on ALFWorld.

Method	ALFWorld		BabyAI-Text		WebShop
Method	Succ. $\uparrow$	#Token $\downarrow$	Succ. $\uparrow$	#Token $\downarrow$	Succ. $\uparrow$	#Token $\downarrow$
ReAct + online SFT	30.2	57	40.8	56	15.3	12
LAC + online SFT	74.2	341	67.2	438	32.1	84
SAG	78.3	56	70.0	78	37.0	9

Appendix

Table 11: Matched online-SFT controls across all benchmarks. All methods use the same online update protocol. Token usage includes both actor and critic tokens.

Order Setting	Seed / Order	Success (%)	Token (k)
Default benchmark order	default	$78.3$	$56$
Shuffled order	1	$78.7$	$56$
Shuffled order	2	$78.2$	$58$
Mean $\pm$ std over shuffled orders	default/1/2	78.3 $\pm$ 0.3	56.7 $\pm$ 1.2

Appendix

Table 12 : Robustness of online-SFT across different episode orders

$\tau$	Succ. $\uparrow$	#Token $\downarrow$	$\delta$	Succ. $\uparrow$	#Token $\downarrow$
0.2	79.0	74	0.1	77.1	53
0.3	78.9	63	0.2	78.3	56
0.4	78.3	56	0.4	78.1	61
0.5	75.1	49	0.5	77.8	64
0.7	66.1	45	1.0	75.3	60

Appendix

Table 13: Sensitivity to

\tau

and

\delta

on ALFWorld.

Figure 10 : Parameter sensitivity analysis on BabyAI-Text benchmark

Panel of Figure 11 — Figure 11 : Learning dynamics of SAG under online self-improvement. Metrics are aggregated into Early/Mid/Late phases over 100 evaluation episodes on BabyAI-Text benchmark.

Figure 12 : Parameter sensitivity analysis on WebShop benchmark

Panel of Figure 13 — Figure 13 : Learning dynamics of SAG under online self-improvement. Metrics are aggregated into Early/Mid/Late phases over 200 evaluation episodes on WebShop benchmark.

Method	ALFWorld		BabyAI-Text		WebShop
Method	Succ. $\uparrow$	#Token $\downarrow$	Succ. $\uparrow$	#Token $\downarrow$	Succ. $\uparrow$	#Token $\downarrow$
One-shot SFT	72.8	63	66.9	82	34.8	10
Online SFT (SAG)	78.3	56	70.0	78	37.0	9

Appendix

Table 14: Comparison between one-shot SFT and online-SFT.

Successes / Update	Succ. $\uparrow$	Critic Calls / Ep. $\downarrow$	#Token $\downarrow$
5	76.9	2.52	58
10	78.3	2.10	56
20	78.1	2.28	57
30	77.7	2.42	58

Appendix

Table 15: Sensitivity to the number of successful episodes per update on ALFWorld.

Prompt variant	Step	Rationale by critic
Full prompt	5	Search shelves for both bowl and desklamp
w/o expected JSON example	5	Search shelves as likely bowl location
w/o goal	5	Bowl may be on an unchecked shelf
Full prompt	9	Check whether bowl is near the found desklamp
w/o expected JSON example	9	Re-examine shelf for missed items
w/o goal	9	Bowl may be near the desklamp

Appendix

Table 16 : Qualitative examples of how critic prompts affect the generated rationales

	ID			OOD
SFT target	Actor SR	SAG SR	Calls	Actor SR	SAG SR	Calls
No SFT	24.6	72.3	3.00	25.7	70.7	2.85
Matched reasoning	43.2	76.0	1.35	42.9	77.8	1.67
Action-only	45.7	80.3	1.18	43.4	80.9	1.41

Appendix

Table 17: Comparison of SFT targets. Actor denotes execution without critique; Calls denotes critic calls per episode.

Score quartile	Q1	Q2	Q3	Q4
Number of states	45	45	44	44
Disagreements	8	10	14	20
Disagreement rate (%)	17.8	22.2	31.8	45.5

Appendix

Table 18: Reference-action disagreement across gating-score quartiles, ordered from lowest to highest

S_{t}

You are in the middle of a room. Looking quickly around you, you see an armchair 1, a cabinet 4, a cabinet 3, a cabinet 2, a cabinet 1, a drawer 5, a drawer 4, a drawer 3, a drawer 2, a drawer 1, a dresser 1, a garbagecan 1, a safe 1, a shelf 12, a shelf 11, a shelf 10, a shelf 9, a shelf 8, a shelf 7, a shelf 6, a shelf 5, a shelf 4, a shelf 3, a shelf 2, a shelf 1, a sidetable 1, and a sofa 1. Your task is to: put two pillow in sofa. > [Agent] Act 1: think: To solve the task, I need to find and take the first pillow, then put it in sofa, then find and take the second pillow, then put it in sofa. OK. > [Agent] Act 2: think: First I need to find the first pillow. A pillow is more likely to appear in armchair (1), cabinet (1-4), drawer (1-5), dresser (1), sidetable (1), sofa (1). I can check one by one, starting with armchair 1. OK. > [Agent] Act 3: go to armchair 1 You arrive at armchair 1. On the armchair 1, you see a cellphone 2, a pillow 2, and a pillow 1. > [Agent] Act 4: take pillow 1 from armchair 1 You pick up the pillow 1 from the armchair 1. > [Agent] Act 5: think: Now I find the first pillow (1). Next, I need to put it in sofa 1. OK. > [Agent] Act 6: go to sofa 1 You arrive at sofa 1. On the sofa 1, you see a newspaper 3. > [Gate] global ambiguity

\bar{H}_{t}=0.20

, local margin

m_{t}=0.06<\delta

. > [Gate] score

S_{t}=\bar{H}_{t}+\mathbb{I}[m_{t}<\delta]=1.20>\tau

(VoI proxy

>

cost)

\Rightarrow

critic invoked. > [Critic] Suggested action: move pillow 1 to sofa 1. > [Critic] Rationale: You are close, but you forgot to put the first pillow in the sofa before searching for the second one. Putting the first pillow in the sofa now reduces the risk of forgetting it later. > [Agent] Act 7: move pillow 1 to sofa 1 On the sofa 1, you see a newspaper 3, and a pillow 1. > [Agent] Act 8: go to armchair 1 You arrive at armchair 1. On the armchair 1, you see a cellphone 2, and a pillow 2. > [Agent] Act 9: take pillow 2 from armchair 1 You pick up the pillow 2 from the armchair 1. > [Agent] Act 10: think: Now I find the second pillow (2). Next, I need to put it in sofa 1. OK. > [Agent] Act 11: go to sofa 1 You arrive at sofa 1. On the sofa 1, you see a newspaper 3, and a pillow 1. > [Agent] Act 12: move pillow 2 to sofa 1 You move the pillow 2 to the sofa 1. Outcome: success > [SAG] Successful episode. Trajectory is added to the self-improvement buffer.

Appendix

Table 19 : An example trajectory from ALFWorld for pick_two_obj_and_place . SAG selectively invokes the critic based on ambiguity (global entropy and local margin) and stores successful trajectories for online self-improvement.

You are in the middle of a room. Looking quickly around you, you see a cabinet 4, a cabinet 3, a cabinet 2, a cabinet 1, a countertop 1, a garbagecan 1, a handtowelholder 2, a handtowelholder 1, a sinkbasin 2, a sinkbasin 1, a toilet 1, a toiletpaperhanger 1, and a towelholder 1. Your task is to: put a clean cloth in countertop. > [Agent] Act 1: think: To solve the task, I need to find and take a cloth, clean it with a sinkbasin, then place it on the countertop. OK. > [Agent] Act 2: think: First I need to find a cloth. I will check the cabinets starting from cabinet 4. OK. > [Agent] Act 3: go to cabinet 4 You arrive at cabinet 4. The cabinet 4 is closed. > [Agent] Act 4: open cabinet 4 You open the cabinet 4. The cabinet 4 is open. In it, you see a soapbottle 2. > [Agent] Act 5: go to cabinet 3 You arrive at cabinet 3. The cabinet 3 is closed. > [Agent] Act 6: open cabinet 3 You open the cabinet 3. The cabinet 3 is open. In it, you see a cloth 2. > [Agent] Act 7: take cloth 2 from cabinet 3 You pick up the cloth 2 from the cabinet 3. > [Agent] Act 8: go to sinkbasin 1 You arrive at sinkbasin 1. On the sinkbasin 1, you see a soapbar 1. > [Agent] Act 9: clean cloth 2 with sinkbasin 1 You clean the cloth 2 using the sinkbasin 1. > [Agent] Act 10: go to countertop 1 You arrive at countertop 1. On the countertop 1, you see a candle 1, a cloth 3, and a spraybottle 1. > [Agent] Act 11: think: I might need to fetch soap again before placing the cloth. I should go back to cabinet 4. OK. > [Gate] global ambiguity

\bar{H}_{t}=0.55

, local margin

m_{t}=0.78

. > [Gate] score

S_{t}=\bar{H}_{t}+\mathbb{I}[m_{t}<\delta]=0.55>\tau

(VoI proxy

>

cost)

\Rightarrow

critic invoked. > [Critic] Suggested action: move cloth 2 to countertop 1. > [Critic] Rationale: The cloth you are holding is already clean. The task only requires placing a clean cloth on the countertop. Fetching soap again is unnecessary and risks delaying completion. > [Agent] Act 12: move cloth 2 to countertop 1 On the countertop 1, you see a candle 1, a cloth 3, and a spraybottle 1. > [Agent] Act 13: move cloth 2 to countertop 1 You move the cloth 2 to the countertop 1. Outcome: success > [SAG] Successful episode. The trajectory is added to the self-improvement buffer

\mathcal{D}

Appendix

Table 20 : Example trajectory on ALFWorld pick_clean_then_place_in_recep . SAG invokes critique when ambiguity indicates high error risk, preventing unnecessary detours.

You are in the middle of a room. Looking quickly around you, you see a cabinet 6, a cabinet 5, a cabinet 4, a cabinet 3, a cabinet 2, a cabinet 1, a coffeemachine 1, a countertop 3, a countertop 2, a countertop 1, a drawer 3, a drawer 2, a drawer 1, a fridge 1, a garbagecan 1, a microwave 1, a shelf 3, a shelf 2, a shelf 1, a sinkbasin 1, a stoveburner 4, a stoveburner 3, a stoveburner 2, a stoveburner 1, and a toaster 1. Your task is to: put a hot apple in fridge. > [Agent] Act 1: think: First I need to find an apple. I will start by checking the fridge. OK. > [Agent] Act 2: go to fridge 1 You arrive at fridge 1. The fridge 1 is closed. > [Agent] Act 3: open fridge 1 You open the fridge 1. In it, you see a bowl 1, a cup 2, a cup 1, a lettuce 1, a mug 2, a potato 1, and a tomato 1. > [Agent] Act 4: think: No apple here. I might need to search cabinets one by one. OK. > [Gate] global ambiguity

\bar{H}_{t}=0.21

, local margin

m_{t}=0.09<\delta

. > [Gate] score

S_{t}=\bar{H}_{t}+\mathbb{I}[m_{t}<\delta]=1.21>\tau

(VoI proxy

>

cost)

\Rightarrow

critic invoked. > [Critic] Suggested action: go to countertop 1. > [Critic] Rationale: Apples are more likely to be placed on open surfaces such as countertops. Searching cabinets first is less efficient. > [Agent] Act 5: go to countertop 1 You arrive at countertop 1. On the countertop 1, you see an apple 1, an apple 2, and a mug 3. > [Agent] Act 6: take apple 1 from countertop 1 You pick up the apple 1 from the countertop 1. > [Agent] Act 7: go to microwave 1 You arrive at microwave 1. The microwave 1 is closed. > [Agent] Act 8: heat apple 1 with microwave 1 You heat the apple 1 using the microwave 1. > [Agent] Act 9: think: The apple is now hot. I should place it in the fridge. OK. > [Agent] Act 10: go to fridge 1 You arrive at fridge 1. The fridge 1 is open. > [Agent] Act 11: move apple 1 to fridge 1 You move the apple 1 to the fridge 1. Outcome: success > [SAG] Successful trajectory is added to the self-improvement buffer

\mathcal{D}

Appendix

Table 21 : Example trajectory on ALFWorld pick_heat_then_place_in_recep . SAG corrects inefficient exploration by invoking critique under high global ambiguity.

Your mission: pick up the green key. You start in a corridor with a blue key on the floor and a closed door in front. > [Agent] Act 1: think: The green key is not visible. I should move toward the door. OK. > [Agent] Act 2: go forward You are now standing directly in front of the door. > [Gate] global ambiguity

\bar{H}_{t}=0.28

, local margin

m_{t}=0.08<\delta

. > [Gate] score

S_{t}=1.28>\tau\Rightarrow

critic invoked. > [Critic] Suggested action: open the door. > [Critic] Rationale: Progress requires entering the next room; waiting in front of the door adds no information. > [Agent] Act 3: open door The door opens. Inside you see a red ball in front, a green key on the right, and a yellow box. > [Agent] Act 4: go forward > [Agent] Act 5: turn left > [Agent] Act 6: turn right > [Gate] global ambiguity

\bar{H}_{t}=0.34

, local margin

m_{t}=0.07<\delta

. > [Gate] score

S_{t}=1.34>\tau\Rightarrow

critic invoked. > [Critic] Suggested action: turn right toward the green key. > [Critic] Rationale: The goal object is already identified; reorientation loops are unnecessary. > [Agent] Act 7: turn right > [Agent] Act 8: go forward > [Agent] Act 9: pick up green key > [Agent] Act 10: stop Outcome: success > [SAG] Successful trajectory with two gated interventions is added to the self-improvement buffer

\mathcal{D}

Appendix

Table 22 : Example trajectory on BabyAI-Text pick_up_green_key . SAG intervenes selectively to prevent looping behavior.

Your task: purchase a red T-shirt under

20. The homepage lists categories: shirts, shoes, bags. > [Agent] Act 1: click "shirts" The page shows 5 items: blue T-shirt (

15), red T-shirt (

25), red T-shirt (

18), green hoodie (

22), white T-shirt (

10). > [Agent] Act 2: think: There are two red T-shirts. I might choose the

25 one. > [Gate] global ambiguity

\bar{H}{t}=0.33 $, local margin$ m{t}=0.04<\delta

. > [Gate] score

S_{t}=1.33>\tau\Rightarrow

critic invoked. > [Critic] Suggested action: add the

18 red T-shirt to the cart. > [Critic] Rationale: The

25 option violates the budget constraint. > [Agent] Act 3: add red T-shirt (

18) to cart > [Agent] Act 4: buy Outcome: Reward 1.0, success > [SAG] Successful trajectory is added to self-improvement buffer.

Appendix

Table 23 : Example trajectory on WebShop buy_red_tshirt_under_20 . SAG resolves constraint ambiguity via targeted critique.

Your task: purchase a cheap black backpack. > [Agent] Act 1: click "bags" The bags page shows: black backpack (

55), black backpack (

25), red backpack (

20). > [Agent] Act 2: think: The

55 one might be better quality. > [Gate] global ambiguity

\bar{H}_{t}=0.24

, local margin

m_{t}=0.07<\delta

. > [Gate] score

S_{t}=1.24>\tau\Rightarrow

critic invoked. > [Critic] Suggested action: add the

25 black backpack to the cart. > [Critic] Rationale: The task requires a cheap black backpack;

55 violates this constraint. > [Agent] Act 3: add black backpack (

25) to cart > [Agent] Act 4: view cart > [Agent] Act 5: think: The cart satisfies color and price. > [Agent] Act 6: go to checkout > [Gate] global ambiguity

\bar{H}{t}=0.31 $, local margin$ m{t}=0.06<\delta

. > [Gate] score

S_{t}=1.31>\tau\Rightarrow$ critic invoked. > [Critic] Suggested action: place the order. > [Critic] Rationale: No further browsing is required once all constraints are satisfied. > [Agent] Act 7: buy Outcome: Reward 1.0, success

Appendix

Table 24 : Example trajectory on WebShop buy_black_backpack . SAG intervenes twice to enforce constraints and finalize execution.

Explore similar work

CAST: Critique-Aware Supervision for Training Reliable Long-Horizon Tool-Calling Agents
Aug 31, 2026Amir Saeidi, Zehua Zhang, Rishitosh Singh +6Large Language Model Agents Critic-Free Reinforcement Learning
Arizona State University · Cisco Research
Act More, Decide Less: Skill-Guided Adaptive Action Chunking for Long-Horizon LLM Agents
Sep 2, 2026Yanting Yang, Can Jin, Jinman Zhao +6Action Chunks
Rutgers University · University of Toronto · The Hong Kong Polytechnic University +2
Multi $^2$ : Hierarchical Multi-Agent Decision-Making with LLM-Based Agents in Interactive Environments
Jun 2, 2026Sangeun Park, Minhae KwonLong-Horizon Agents Single-Agent Baselines
Department of Electrical and Computer Engineering, Sungkyunkwan University, Republic of Korea.

Aug 31, 2026, cs.CLJ/K move · Enter open · S save

CAST: Critique-Aware Supervision for Training Reliable Long-Horizon Tool-Calling Agents

Amir Saeidi, Zehua Zhang, Rishitosh Singh, Naman Ahuja+5

Arizona State University · Cisco Research

Large Language Model Agents Critic-Free Reinforcement Learning Long-Horizon Agents

Open paper AskPDF arXiv

Large language model (LLM) agents are increasingly deployed in long-horizon, interactive, and stateful environments. In these settings, a single wrong action, such as refunding the wrong purchase, can cause irreversible task failure and must be intercepted before execution. Such failures may not appear in every single run, but can emerge across repeated trials, making reliability across steps and trials critical. However, ensuring agentic reliability is challenging: even frontier LLMs struggle to explain why an action may be wrong, especially in long, intertwined trajectories governed by domain-specific policies. Much recent work relies on prompt-based critique agents, while optimization-based methods lack a systematic way to produce rich verification rationales for training. We address this gap with CAST, a critique-aware training framework that converts sparse task outcomes into action-level supervision for critique learning and policy optimization. CAST analyzes agent trajectories to synthesize structured rationales explaining action validity under partial observability. The resulting critique model is used to construct critique-aware training data for optimizing the policy model. Fine-tuning Qwen3-family models on dynamic tool-calling benchmarks, CAST improves reliability across domains, outperforming GPT-OSS-120B by over 10% pass^4 on Retail tasks and yielding an additional 9% improvement on Telehealth in an out-of-domain setting. These results demonstrate that critique-aware training improves the robustness of LLM agents in realistic dynamic environments.

Abstract

Explore similar work

CAST: Critique-Aware Supervision for Training Reliable Long-Horizon Tool-Calling Agents

Act More, Decide Less: Skill-Guided Adaptive Action Chunking for Long-Horizon LLM Agents

Multi2^22: Hierarchical Multi-Agent Decision-Making with LLM-Based Agents in Interactive Environments

Multi $^2$ : Hierarchical Multi-Agent Decision-Making with LLM-Based Agents in Interactive Environments