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Algorithm Design for Continual Learning in IoT Networks

Shugang Hao, Lingjie Duan

TL;DR

This work tackles continual learning in IoT networks where a mobile agent can route data collection to alter the training task sequence. It derives closed-form expressions for forgetting loss under both underparameterized and overparameterized regimes, proves the problem is NP-hard via a shortest Hamiltonian path reduction, and proposes a polynomial-time approximation achieving ratios $\frac{3}{2}$ (underparameterized) and $\frac{3}{2} + r^{1-T}$ (overparameterized) with $r = 1 - \frac{n}{m}$. The authors design a two-layer algorithm that first selects a task order and then learns region predictors, with a Christofides-based SHP step to guarantee performance bounds, and they validate the approach through simulations showing close-to-optimal performance and substantial improvements over baselines. The results enable practical deployment of CL in dynamic IoT scenarios by balancing forgetting across tasks with travel costs, offering provable guarantees and insights into regime-dependent behavior as the feature-to-sample ratio changes. The work also highlights how problem structure—route planning combined with model updating—drives new approximation techniques in continual learning contexts.

Abstract

Continual learning (CL) is a new online learning technique over sequentially generated streaming data from different tasks, aiming to maintain a small forgetting loss on previously-learned tasks. Existing work focuses on reducing the forgetting loss under a given task sequence. However, if similar tasks continuously appear to the end time, the forgetting loss is still huge on prior distinct tasks. In practical IoT networks, an autonomous vehicle to sample data and learn different tasks can route and alter the order of task pattern at increased travelling cost. To our best knowledge, we are the first to study how to opportunistically route the testing object and alter the task sequence in CL. We formulate a new optimization problem and prove it NP-hard. We propose a polynomial-time algorithm to achieve approximation ratios of $\frac{3}{2}$ for underparameterized case and $\frac{3}{2} + r^{1-T}$ for overparameterized case, respectively, where $r:=1-\frac{n}{m}$ is a parameter of feature number $m$ and sample number $n$ and $T$ is the task number. Simulation results verify our algorithm's close-to-optimum performance.

Algorithm Design for Continual Learning in IoT Networks

TL;DR

This work tackles continual learning in IoT networks where a mobile agent can route data collection to alter the training task sequence. It derives closed-form expressions for forgetting loss under both underparameterized and overparameterized regimes, proves the problem is NP-hard via a shortest Hamiltonian path reduction, and proposes a polynomial-time approximation achieving ratios (underparameterized) and (overparameterized) with . The authors design a two-layer algorithm that first selects a task order and then learns region predictors, with a Christofides-based SHP step to guarantee performance bounds, and they validate the approach through simulations showing close-to-optimal performance and substantial improvements over baselines. The results enable practical deployment of CL in dynamic IoT scenarios by balancing forgetting across tasks with travel costs, offering provable guarantees and insights into regime-dependent behavior as the feature-to-sample ratio changes. The work also highlights how problem structure—route planning combined with model updating—drives new approximation techniques in continual learning contexts.

Abstract

Continual learning (CL) is a new online learning technique over sequentially generated streaming data from different tasks, aiming to maintain a small forgetting loss on previously-learned tasks. Existing work focuses on reducing the forgetting loss under a given task sequence. However, if similar tasks continuously appear to the end time, the forgetting loss is still huge on prior distinct tasks. In practical IoT networks, an autonomous vehicle to sample data and learn different tasks can route and alter the order of task pattern at increased travelling cost. To our best knowledge, we are the first to study how to opportunistically route the testing object and alter the task sequence in CL. We formulate a new optimization problem and prove it NP-hard. We propose a polynomial-time algorithm to achieve approximation ratios of for underparameterized case and for overparameterized case, respectively, where is a parameter of feature number and sample number and is the task number. Simulation results verify our algorithm's close-to-optimum performance.

Paper Structure

This paper contains 17 sections, 7 theorems, 22 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model of Continual Learning in the IoT Network
  4. Problem Formulation
  5. The Agent's Expected Forgetting Loss in Closed Form and NP-Hardness
  6. Analysis of the Underparameterized Case
  7. Analysis of the Overparameterized Case
  8. NP-Hardness
  9. An Efficient Approximation Algorithm Design, Analysis and Simulation
  10. Algorithm Design for the Underparameterized Case
  11. Algorithm Design for the Overparameterized Case
  12. Simulation Results for Verification
  13. Conclusion
  14. Proof of Lemma \ref{['L1']}
  15. Proof of Lemma \ref{['L2']}
  16. ...and 2 more sections

Key Result

Lemma 1

In the underparameterized case of $n \geq m+2$, the agent's expected forgetting loss $\mathbb{E}[F_T^u]$ is in closed form:

Figures (2)

  • Figure 1: The ratio $R$ between the agent's expected overall loss $\mathbb{E}[\bar{\pi}^*]$ of our Algorithm \ref{['Al1']} and the optimum $\mathbb{E}[\bar{\pi}^{**}]$ versus the feature number $m$.
  • Figure 2: The ratios between the agent's expected overall loss $\mathbb{E}[\bar{\pi}^*]$ of our Algorithm \ref{['Al1']} and the CL baseline to the optimum $\mathbb{E}[\bar{\pi}^{**}]$ versus the region number $T$, respectively. Here we choose feature number $m$=80 for the underparameterized case and $m$=120 for the overparameterized case.

Theorems & Definitions (7)

  • Lemma 1
  • Lemma 2
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Corollary 1
  • Lemma 3