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Optimal Information Combining for Multi-Agent Systems Using Adaptive Bias Learning

Siavash M. Alamouti, Fay Arjomandi

TL;DR

The paper tackles systematic covariate-dependent biases in multi-agent information fusion and asks when learning such biases yields tangible gains. It introduces a framework that decomposes each agent's bias as $b_i(X)=f_i(X)+\nu_i$ with learnability ratio $\lambda_i=\|f_i\|^2/(\|f_i\|^2+\tau_i^2)$ and derives a fundamental bound on achievable improvement. It then develops the ABLOC algorithm, which alternates learning bias corrections with scalar-weight combining to converge toward the theoretical limits, using closed-form weight updates. Experiments on synthetic data show ABLOC achieves typically 40-70% of the theoretical maximum improvement, with higher gains under favorable learnability and signal-to-noise conditions, providing a practical diagnostic for deployment decisions. The framework and ABLOC thus enable principled, efficient bias correction in Hybrid Edge Cloud and Device-First Continuum AI, with broad applicability to sensor networks, distributed estimation, and crowdsourcing ensembles.

Abstract

Modern multi-agent systems ranging from sensor networks monitoring critical infrastructure to crowdsourcing platforms aggregating human intelligence can suffer significant performance degradation due to systematic biases that vary with environmental conditions. Current approaches either ignore these biases, leading to suboptimal decisions, or require expensive calibration procedures that are often infeasible in practice. This performance gap has real consequences: inaccurate environmental monitoring, unreliable financial predictions, and flawed aggregation of human judgments. This paper addresses the fundamental question: when can we learn and correct for these unknown biases to recover near-optimal performance, and when is such learning futile? We develop a theoretical framework that decomposes biases into learnable systematic components and irreducible stochastic components, introducing the concept of learnability ratio as the fraction of bias variance predictable from observable covariates. This ratio determines whether bias learning is worthwhile for a given system. We prove that the achievable performance improvement is fundamentally bounded by this learnability ratio, providing system designers with quantitative guidance on when to invest in bias learning versus simpler approaches. We present the Adaptive Bias Learning and Optimal Combining (ABLOC) algorithm, which iteratively learns bias-correcting transformations while optimizing combination weights through closedform solutions, guaranteeing convergence to these theoretical bounds. Experimental validation demonstrates that systems with high learnability ratios can recover significant performance (we achieved 40%-70% of theoretical maximum improvement in our examples), while those with low learnability show minimal benefit, validating our diagnostic criteria for practical deployment decisions.

Optimal Information Combining for Multi-Agent Systems Using Adaptive Bias Learning

TL;DR

The paper tackles systematic covariate-dependent biases in multi-agent information fusion and asks when learning such biases yields tangible gains. It introduces a framework that decomposes each agent's bias as with learnability ratio and derives a fundamental bound on achievable improvement. It then develops the ABLOC algorithm, which alternates learning bias corrections with scalar-weight combining to converge toward the theoretical limits, using closed-form weight updates. Experiments on synthetic data show ABLOC achieves typically 40-70% of the theoretical maximum improvement, with higher gains under favorable learnability and signal-to-noise conditions, providing a practical diagnostic for deployment decisions. The framework and ABLOC thus enable principled, efficient bias correction in Hybrid Edge Cloud and Device-First Continuum AI, with broad applicability to sensor networks, distributed estimation, and crowdsourcing ensembles.

Abstract

Modern multi-agent systems ranging from sensor networks monitoring critical infrastructure to crowdsourcing platforms aggregating human intelligence can suffer significant performance degradation due to systematic biases that vary with environmental conditions. Current approaches either ignore these biases, leading to suboptimal decisions, or require expensive calibration procedures that are often infeasible in practice. This performance gap has real consequences: inaccurate environmental monitoring, unreliable financial predictions, and flawed aggregation of human judgments. This paper addresses the fundamental question: when can we learn and correct for these unknown biases to recover near-optimal performance, and when is such learning futile? We develop a theoretical framework that decomposes biases into learnable systematic components and irreducible stochastic components, introducing the concept of learnability ratio as the fraction of bias variance predictable from observable covariates. This ratio determines whether bias learning is worthwhile for a given system. We prove that the achievable performance improvement is fundamentally bounded by this learnability ratio, providing system designers with quantitative guidance on when to invest in bias learning versus simpler approaches. We present the Adaptive Bias Learning and Optimal Combining (ABLOC) algorithm, which iteratively learns bias-correcting transformations while optimizing combination weights through closedform solutions, guaranteeing convergence to these theoretical bounds. Experimental validation demonstrates that systems with high learnability ratios can recover significant performance (we achieved 40%-70% of theoretical maximum improvement in our examples), while those with low learnability show minimal benefit, validating our diagnostic criteria for practical deployment decisions.

Paper Structure

This paper contains 41 sections, 4 theorems, 46 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multi-Source Information Fusion
  4. Bias Correction and Calibration
  5. Theoretical Foundations
  6. Theoretical Framework
  7. Bias Decomposition and Learnability
  8. Weight Formulation
  9. Performance Bounds
  10. Algorithm
  11. Adaptive Bias Learning and Optimal Combining (ABLOC)
  12. Implementation Details
  13. Function Class Selection
  14. Regularization and Stability
  15. Iteration Control
  16. ...and 26 more sections

Key Result

Theorem 1

Consider $K$ agents with learnability ratios $\{\lambda_i\}$, measurement noise variances $\{\sigma_i^2\}$, and total bias variances $\{\beta_i^2\}$ where $\beta_i^2 = \|f_i\|^2 + \tau_i^2$. For any bias learning algorithm using $N$ samples, the relative improvement in mean squared error is bounded where $w_i^*$ are the optimal weights and the $O(N^{-1/2})$ term represents finite-sample effects.

Figures (2)

  • Figure 1: ABLOC performance analysis: (a) Mean squared error comparison across methods, (b) Learned weights versus oracle weights for each agent, (c) Relationship between learnability ratio and weight assignment. Marker size indicates bias magnitude $\beta_i$, color indicates noise level $\sigma_i$.
  • Figure 2: Detailed performance metrics: (a) Component-wise MSE comparison between baseline and ABLOC, (b) Relative improvement percentage for each parameter component, (c) Achieved efficiency compared to theoretical bound, showing 49.2% achievement ratio.

Theorems & Definitions (10)

  • Definition 1: Bias Decomposition
  • Definition 2: Learnability Ratio
  • Definition 3: Weighted Combination
  • Theorem 1: Achievable Performance Bound
  • proof
  • Corollary 1: Simplified Bound
  • Theorem 2: Sample Requirements
  • proof
  • Theorem 3: Convergence of ABLOC
  • proof : Proof Sketch