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

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.

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

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.

Paper Structure

This paper contains 67 sections, 25 equations, 4 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Novelty and contributions.
  3. Related Work
  4. Tool-Using Autonomous Agents
  5. Bounded Rationality and Meta-Reasoning
  6. Active Inference and Stochastic Control
  7. Formalizing Cognitive Friction: The Coupled Stochastic Control Objective
  8. Problem setup.
  9. Intuition (for ML practitioners).
  10. The observation model and belief dynamics
  11. The triadic value function
  12. The HJB variational inequality and optimal stopping
  13. Discrete-time instantiation used in EMDG (rollout VOI + myopic stopping)
  14. Notation.
  15. On the discretization gap.
  16. ...and 52 more sections

Figures (4)

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