Cognitive Friction: A Decision-Theoretic Framework for Bounded Deliberation in Tool-Using Agents

Davide Di Gioia

cs.AIMar 31, 2026

Cognitive Friction: A Decision-Theoretic Framework for Bounded Deliberation in Tool-Using Agents

Authors: Davide Di Gioia

Abstract

Autonomous tool-using agents in networked environments must decide which information source to query and when to stop querying and act. Without principled bounds on information-acquisition costs, unconstrained agents exhibit systematic failure modes: excessive tool use under congestion, prolonged deliberation under time decay, and brittle behavior under ambiguous evidence. We propose the Triadic Cognitive Architecture (TCA), a decision-theoretic framework that formalizes these failure modes via cognitive friction. By combining nonlinear filtering, congestion-dependent cost dynamics, and HJB optimal stopping, TCA models deliberation as stochastic control over a joint belief-congestion state, explicitly pricing information by tool signal quality and live network load. TCA yields an HJB-inspired stopping boundary and a computable rollout-based approximation of belief-dependent value-of-information with a net-utility halting condition. We validate TCA in two controlled environments (EMDG and NSTG) designed to isolate stopping quality, action selection under congestion, and temporal urgency. TCA improves resource outcomes while reducing time-to-action without degrading accuracy, gaining 36 viability points in EMDG and 33 integrity points in NSTG over greedy baselines. Ablations show that selection and stopping must be optimized jointly, as stopping rules alone recover at most 4 viability points. Sensitivity sweeps over alpha, beta, and lambda_S yield stable accuracy and interpretable trade-offs, and a continuation-value sweep over eta values 0, 0.1, 0.3, and 0.5 finds eta equal to zero is optimal under high temporal urgency. Finally, we demonstrate an illustrative instantiation around a black-box LLM on a memorisation-free corpus, where the same stopping principle executes using empirically computable uncertainty and value-of-information proxies.

Figures & tables

Symbol	Meaning
$b_{t}\in\Delta^{\|\Theta\|-1}$	Categorical belief over hypotheses at step $t$
$H(b_{t})$	Shannon entropy of belief $b_{t}$ [ 13 ]
$\widehat{\Delta H}(a\mid b_{t})$	Rollout-estimated VOI (expected entropy reduction)
$\alpha$	Cost-to-utility scaling ( cost_scale )
$\beta$	Per-step temporal decay/latency penalty ( beta )
$\lambda_{S}$	Spatial cost weight ( lambda_s )

Table 1: Notation summary for the discrete EMDG instantiation.

Panel of Figure 1 — Figure 1: EMDG Monte Carlo (N=200): mean entropy and patient viability trajectories over a fixed horizon. Step corresponds to discrete tool-query iterations; trajectories are padded after stopping by carrying forward the terminal state, ensuring step-wise consistency (e.g., time cannot decrease).

Agent	Time	Viability	Entropy	Accuracy	$p_{\mathrm{true}}$	Total information gain
ReAct (Greedy)	114.5 $\pm$ 3.1	56.76 $\pm$ 0.89	0.0386 $\pm$ 0.0038	1.00 $\pm$ 0.00	0.9941 $\pm$ 0.0007	1.5708 $\pm$ 0.0038
Triadic Control	14.5 $\pm$ 0.4	93.03 $\pm$ 0.19	0.1714 $\pm$ 0.0119	1.00 $\pm$ 0.00	0.9643 $\pm$ 0.0032	1.4380 $\pm$ 0.0119

Table 2: EMDG results (N=200). Terminal values are taken from the last logged row per seed. Total information gain is the per-episode sum of info_gain ; in this setup it equals entropy reduction

H(b_{0})-H(b_{T})

(a telescoping sum). At step 0, ReAct selects MRI_Network in 100% of seeds while TCA selects Hematology_Lab in 100% of seeds. Bold marks the best value for the two primary objectives (Time and Viability); lower entropy and higher information gain in ReAct reflect expensive over-querying, not better performance.

Panel of Figure 2 — Figure 2: EMDG ablations (N=200): terminal patient viability and terminal deliberation time across controller variants. Bars show means and error bars denote $\pm 1\sigma$ over seeds. The full triadic controller achieves the highest viability while minimizing deliberation time, illustrating the necessity of jointly pricing space, time, and enforcing an explicit stopping boundary.

Agent	Time	Viability	Entropy	Accuracy
ReAct (Greedy)	114.5 $\pm$ 3.1	56.76 $\pm$ 0.89	0.0386 $\pm$ 0.0038	1.00 $\pm$ 0.00
Entropy-Threshold ( $\tau_{H}{=}0.17$ )	102.6 $\pm$ 2.8	60.17 $\pm$ 0.80	0.0687 $\pm$ 0.0060	1.00 $\pm$ 0.00
Fixed-K ( $K{=}3$ )	135.0 $\pm$ 0.0	50.92 $\pm$ 0.00	0.0152 $\pm$ 0.0021	1.00 $\pm$ 0.00
Triadic Control (TCA)	14.5 $\pm$ 0.4	93.03 $\pm$ 0.19	0.1714 $\pm$ 0.0119	1.00 $\pm$ 0.00

Table 3: Extended comparison: TCA vs. purposive stopping baselines (N=200). Entropy-Threshold uses

\tau_{H}{=}0.17

(TCA mean terminal entropy); Fixed-K uses

K{=}3

(TCA mean query count before Stop ). Both baselines use greedy (cost-blind) query selection identical to ReAct. TCA values reproduced from Table 2 for convenience. Bold marks the best per metric.

Panel of Figure 3 — Figure 3: Univariate parameter sensitivity: terminal patient viability (mean $\pm$ 95% CI, $N{=}200$ seeds per setting). Each panel varies one parameter while holding the others at default ( $\alpha{=}0.01$ , $\beta{=}0.50$ , $\lambda_{S}{=}0.80$ ); the middle bar in each panel corresponds to the default. Dashed line in the $\alpha$ panel marks ReAct viability (56.8) for reference. Accuracy remains 1.0 across all 7 configurations.

Agent	Time	Integrity	Entropy	Accuracy	$p_{\mathrm{true}}$	Total information gain
ReAct (Greedy)	149.7 $\pm$ 4.2	64.08 $\pm$ 0.80	0.0376 $\pm$ 0.0037	1.00 $\pm$ 0.00	0.9943 $\pm$ 0.0006	1.5718 $\pm$ 0.0037
Triadic Control	9.5 $\pm$ 0.3	97.18 $\pm$ 0.08	0.3230 $\pm$ 0.0213	1.00 $\pm$ 0.00	0.9180 $\pm$ 0.0083	1.2864 $\pm$ 0.0213

Table 4: NSTG results (N=200). Resource metric is system integrity (same exponential decay formula as EMDG patient viability, with

\beta{=}0.30

). At step 0, ReAct selects FullForensics in 100% of seeds while TCA selects QuickScan in 100% of seeds. Bold marks the best per metric.

Environment	Agent	Time	Resource	Entropy	Accuracy
EMDG ( $\beta{=}0.50$ )	ReAct (Greedy)	114.5 $\pm$ 3.1	56.76 $\pm$ 0.89	0.0386 $\pm$ 0.0038	1.00
	Triadic Control	14.5 $\pm$ 0.4	93.03 $\pm$ 0.19	0.1714 $\pm$ 0.0119	1.00
NSTG ( $\beta{=}0.30$ )	ReAct (Greedy)	149.7 $\pm$ 4.2	64.08 $\pm$ 0.80	0.0376 $\pm$ 0.0037	1.00
	Triadic Control	9.5 $\pm$ 0.3	97.18 $\pm$ 0.08	0.3230 $\pm$ 0.0213	1.00

Table 5: Cross-environment summary: TCA vs. ReAct (Greedy),

N{=}200

seeds per environment. Resource metric

=

patient viability (EMDG) / system integrity (NSTG); both decay exponentially with elapsed time. Bold marks the best per row.

$\kappa$	Agent	Time	Viability	Accuracy
$0.00$	ReAct (Greedy)	$114.5\pm 3.1$	$56.76\pm 0.89$	$1.00$
$0.00$	Triadic Control	$\mathbf{14.5\pm 0.4}$	$\mathbf{93.03\pm 0.19}$	$1.00$
$0.05$	ReAct (Greedy)	$114.5\pm 3.1$	$56.76\pm 0.89$	$1.00$
$0.05$	Triadic Control	$\mathbf{14.8\pm 0.5}$	$\mathbf{92.89\pm 0.21}$	$1.00$
$0.10$	ReAct (Greedy)	$114.5\pm 3.1$	$56.76\pm 0.89$	$1.00$
$0.10$	Triadic Control	$\mathbf{15.2\pm 0.5}$	$\mathbf{92.72\pm 0.22}$	$1.00$

Table 6: Congestion-decay robustness: TCA vs. ReAct (Greedy) for

\kappa\in\{0.00,0.05,0.10\}

(

N{=}200

seeds).

\kappa{=}0.00

replicates Table 2 exactly. Bold marks best viability per

\kappa

level.

Panel of Figure 4 — Figure 4: Triadic Cognitive Architecture (TCA): a coupled loop between Space (state), Time (dynamics), and Epistemic Truth (belief revision).

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

$\|\mathcal{A}\|$	Non-trivial step-0	TCA Viability	ReAct Viability	Gap	Accuracy
$5$	$76\%$	$91.78\pm 0.50$	$81.94\pm 1.52$	$+9.8$	$1.00$
$10$	$85\%$	$92.62\pm 0.49$	$82.89\pm 1.35$	$+9.7$	$1.00$
$20$	$90\%$	$93.85\pm 0.38$	$78.84\pm 1.61$	$+15.0$	$1.00$

Appendix

Table 7: Action-space scaling (

N_{\text{cfg}}{=}30

random tool configurations per

|\mathcal{A}|

N_{\text{seed}}{=}10

seeds per configuration). Non-trivial step-0 : fraction of (config, seed) pairs where TCA selects a tool with

\tau>\min_{a}\tau(a)

. Viability: mean

\pm

95% CI. For

|\mathcal{A}|{=}2

, see Table 1.

Policy	$U$	EM	F1	$n_{r}$	%ACT	%DEFER
NeverRetrieve	$-10.00$	$0.000$	$0.054$	$0.00$	$100\%$	$0\%$
AlwaysRetrieve	$+5.33$	$0.817$	$0.927$	$1.00$	$100\%$	$0\%$
TCA (ours)	$+2.20$	$0.500$	$0.580$	$0.63$	$72\%$	$28\%$

Appendix

Table 9: Real-LLM instantiation on fictional corpus (

N{=}60

questions, GPT-4.1).

U

= expected utility; EM = exact match;

n_{r}

= avg retrieval calls; %ACT, %DEFER = terminal rates. NeverRetrieve scores EM = 0.00 confirming zero memorisation contamination. TCA uses 63% of AlwaysRetrieve’s retrieval budget while exhibiting both terminal outcomes ( Act / Defer ) under the same net-utility stopping rule.

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