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Autonomy-Aware Clustering: When Local Decisions Supersede Global Prescriptions

Amber Srivastava, Salar Basiri, Srinivasa Salapaka

TL;DR

The paper addresses clustering when data points exhibit local autonomy that can override policy-prescribed cluster assignments. It couples a maximum-entropy, deterministic annealing (DA) framework with a reinforcement-learning (RL) approach to jointly learn assignment policies and cluster representatives under known or unknown autonomy models, respectively. A key innovation is the Adaptive Distance Estimation Network (ADEN), a transformer-based architecture that predicts autonomy-aware distances $d_{\text{avg}}(x_i,y_j)$ and enables knowledge transfer across problem instances and online operation. Empirically, the autonomy-aware framework achieves ground-truth-aligned solutions with a small gap ($\sim$3–4%) and substantially outperforms autonomy-ignoring baselines (often by tens of percent), with real-world applicability demonstrated via UAV placement in decentralized sensing. The combination of DA phase-transition insights, RL-based learning, and the ADEN model provides a scalable and flexible toolkit for autonomy-aware clustering in dynamic, uncertain environments.

Abstract

Clustering arises in a wide range of problem formulations, yet most existing approaches assume that the entities under clustering are passive and strictly conform to their assigned groups. In reality, entities often exhibit local autonomy, overriding prescribed associations in ways not fully captured by feature representations. Such autonomy can substantially reshape clustering outcomes -- altering cluster compositions, geometry, and cardinality -- with significant downstream effects on inference and decision-making. We introduce autonomy-aware clustering, a reinforcement learning (RL) framework that learns and accounts for the influence of local autonomy without requiring prior knowledge of its form. Our approach integrates RL with a Deterministic Annealing (DA) procedure, where, to determine underlying clusters, DA naturally promotes exploration in early stages of annealing and transitions to exploitation later. We also show that the annealing procedure exhibits phase transitions that enable design of efficient annealing schedules. To further enhance adaptability, we propose the Adaptive Distance Estimation Network (ADEN), a transformer-based attention model that learns dependencies between entities and cluster representatives within the RL loop, accommodates variable-sized inputs and outputs, and enables knowledge transfer across diverse problem instances. Empirical results show that our framework closely aligns with underlying data dynamics: even without explicit autonomy models, it achieves solutions close to the ground truth (gap ~3-4%), whereas ignoring autonomy leads to substantially larger gaps (~35-40%). The code and data are publicly available at https://github.com/salar96/AutonomyAwareClustering.

Autonomy-Aware Clustering: When Local Decisions Supersede Global Prescriptions

TL;DR

The paper addresses clustering when data points exhibit local autonomy that can override policy-prescribed cluster assignments. It couples a maximum-entropy, deterministic annealing (DA) framework with a reinforcement-learning (RL) approach to jointly learn assignment policies and cluster representatives under known or unknown autonomy models, respectively. A key innovation is the Adaptive Distance Estimation Network (ADEN), a transformer-based architecture that predicts autonomy-aware distances and enables knowledge transfer across problem instances and online operation. Empirically, the autonomy-aware framework achieves ground-truth-aligned solutions with a small gap (3–4%) and substantially outperforms autonomy-ignoring baselines (often by tens of percent), with real-world applicability demonstrated via UAV placement in decentralized sensing. The combination of DA phase-transition insights, RL-based learning, and the ADEN model provides a scalable and flexible toolkit for autonomy-aware clustering in dynamic, uncertain environments.

Abstract

Clustering arises in a wide range of problem formulations, yet most existing approaches assume that the entities under clustering are passive and strictly conform to their assigned groups. In reality, entities often exhibit local autonomy, overriding prescribed associations in ways not fully captured by feature representations. Such autonomy can substantially reshape clustering outcomes -- altering cluster compositions, geometry, and cardinality -- with significant downstream effects on inference and decision-making. We introduce autonomy-aware clustering, a reinforcement learning (RL) framework that learns and accounts for the influence of local autonomy without requiring prior knowledge of its form. Our approach integrates RL with a Deterministic Annealing (DA) procedure, where, to determine underlying clusters, DA naturally promotes exploration in early stages of annealing and transitions to exploitation later. We also show that the annealing procedure exhibits phase transitions that enable design of efficient annealing schedules. To further enhance adaptability, we propose the Adaptive Distance Estimation Network (ADEN), a transformer-based attention model that learns dependencies between entities and cluster representatives within the RL loop, accommodates variable-sized inputs and outputs, and enables knowledge transfer across diverse problem instances. Empirical results show that our framework closely aligns with underlying data dynamics: even without explicit autonomy models, it achieves solutions close to the ground truth (gap ~3-4%), whereas ignoring autonomy leads to substantially larger gaps (~35-40%). The code and data are publicly available at https://github.com/salar96/AutonomyAwareClustering.

Paper Structure

This paper contains 18 sections, 3 theorems, 54 equations, 5 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation and Solution Methodology
  4. Reinforcement-based method for Autonomy-aware clustering
  5. Simulations
  6. Convergence Proof
  7. Case A: When the assumptions in Theorem \ref{['thm: fixedPointItr']} hold true
  8. Case B: When the assumptions in Theorem \ref{['thm: fixedPointItr']} do not hold
  9. Phase Transition and Critical annealing parameter
  10. Hessian Computation
  11. $\beta_{\text{cr}}$ - Critical annealing parameter value
  12. Sensitivity of $Y$ to the annealing parameter $\beta$
  13. Change in $Y$ versus $\beta$ and Critical Temperatures
  14. Reinforcement-based learning for Case (C1)
  15. ADEN Architecture
  16. ...and 3 more sections

Key Result

Theorem 1

The fixed-point iteration defined by (eq: GibbsDistribution) and (eq: ClusterLoc) is equivalent to gradient descent iteration of the form where $\hat{P}_{\pi_\rho}^{Y(t)} = P_{\pi_\rho}^{Y(t)} \otimes \mathbb{I}_d$, $\mathbb{I}_d$ is the $d \times d$ identity, $\otimes$ is the Kronecker product, and $P_{\pi_\rho}^{Y(t)} \in \mathbb{R}^{K \times K}$ is diagonal with $[P_{\pi_\rho}^{Y(t)}]_{\ell\el

Figures (5)

  • Figure 1: (a) Dataset, (b) No local autonomy - $y_j$'s at cluster centroid, (c) $p(k|j,i) = 0.25$, all $y_j$'s at the centroid of the dataset, and (d) $p(k|j,i) = 0.083$ if $k\neq j$ and $p(k|j,i) = 0.75$, $y_j$'s shifted towards the centroid of the dataset
  • Figure 2: Clustering of the UDT19 dataset under parameterized autonomy for varying $\kappa$. UAVs are indicated by colored stars, and sensor (denoted by $*$) colors denote their associated UAV.
  • Figure 3: (a)Dataset, (b) Change in $Y$ versus $\beta$ demonstrates phenomenon of phase transitions
  • Figure 4: Overall Deep Architecture to predict autonomy-aware distances.
  • Figure 5: 4$\times$4 grid of benchmark images. Each subcaption shows the tuple {$\kappa,\gamma,\zeta,T$} in that order.

Theorems & Definitions (3)

  • Theorem 1: Inner-Loop Convergence
  • Theorem 2: Phase Transitions
  • Theorem 3: Insensitivity in-between phase transitions