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Learning to Help in Multi-Class Settings

Yu Wu, Yansong Li, Zeyu Dong, Nitya Sathyavageeswaran, Anand D. Sarwate

TL;DR

The paper tackles resource-constrained edge deployment by coupling a fixed local model with a learnable server model and a client rejector in a hybrid client-server framework. It extends Learning to Help (L2H) to multi-class problems and introduces a stage-switching surrogate loss that is differentiable and Bayes-consistent, enabling asynchronous training under Pay-Per-Request, Intermittent Availability, and Bounded Reject Rate constraints. The work provides a generalized multi-class loss, derives Bayes-optimal predictors, and develops scalable algorithms (PPR, IA, BRR) with theoretical guarantees and practical performance on CIFAR/SVHN/CIFAR-100, demonstrating improved accuracy with controlled server usage. The approach offers a robust path for deploying server-assisted inference in systems with legacy local models and limited retraining, productive for the current era of hybrid ML and large-scale models.

Abstract

Deploying complex machine learning models on resource-constrained devices is challenging due to limited computational power, memory, and model retrainability. To address these limitations, a hybrid system can be established by augmenting the local model with a server-side model, where samples are selectively deferred by a rejector and then sent to the server for processing. The hybrid system enables efficient use of computational resources while minimizing the overhead associated with server usage. The recently proposed Learning to Help (L2H) model trains a server model given a fixed local (client) model, differing from the Learning to Defer (L2D) framework, which trains the client for a fixed (expert) server. In both L2D and L2H, the training includes learning a rejector at the client to determine when to query the server. In this work, we extend the L2H model from binary to multi-class classification problems and demonstrate its applicability in a number of different scenarios of practical interest in which access to the server may be limited by cost, availability, or policy. We derive a stage-switching surrogate loss function that is differentiable, convex, and consistent with the Bayes rule corresponding to the 0-1 loss for the L2H model. Experiments show that our proposed methods offer an efficient and practical solution for multi-class classification in resource-constrained environments.

Learning to Help in Multi-Class Settings

TL;DR

The paper tackles resource-constrained edge deployment by coupling a fixed local model with a learnable server model and a client rejector in a hybrid client-server framework. It extends Learning to Help (L2H) to multi-class problems and introduces a stage-switching surrogate loss that is differentiable and Bayes-consistent, enabling asynchronous training under Pay-Per-Request, Intermittent Availability, and Bounded Reject Rate constraints. The work provides a generalized multi-class loss, derives Bayes-optimal predictors, and develops scalable algorithms (PPR, IA, BRR) with theoretical guarantees and practical performance on CIFAR/SVHN/CIFAR-100, demonstrating improved accuracy with controlled server usage. The approach offers a robust path for deploying server-assisted inference in systems with legacy local models and limited retraining, productive for the current era of hybrid ML and large-scale models.

Abstract

Deploying complex machine learning models on resource-constrained devices is challenging due to limited computational power, memory, and model retrainability. To address these limitations, a hybrid system can be established by augmenting the local model with a server-side model, where samples are selectively deferred by a rejector and then sent to the server for processing. The hybrid system enables efficient use of computational resources while minimizing the overhead associated with server usage. The recently proposed Learning to Help (L2H) model trains a server model given a fixed local (client) model, differing from the Learning to Defer (L2D) framework, which trains the client for a fixed (expert) server. In both L2D and L2H, the training includes learning a rejector at the client to determine when to query the server. In this work, we extend the L2H model from binary to multi-class classification problems and demonstrate its applicability in a number of different scenarios of practical interest in which access to the server may be limited by cost, availability, or policy. We derive a stage-switching surrogate loss function that is differentiable, convex, and consistent with the Bayes rule corresponding to the 0-1 loss for the L2H model. Experiments show that our proposed methods offer an efficient and practical solution for multi-class classification in resource-constrained environments.
Paper Structure (34 sections, 3 theorems, 44 equations, 7 figures, 7 tables, 5 algorithms)

This paper contains 34 sections, 3 theorems, 44 equations, 7 figures, 7 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Hybrid ML systems.
  3. Learning with Abstention (LWA).
  4. Learning to Defer (L2D).
  5. Learning to Help (L2H).
  6. Problem formulation
  7. generalized 0-1 loss for multi-class classification
  8. Bayes optimal rejector and server classifier
  9. Stage-switching surrogate loss function
  10. Convexity and monotonicity of the surrogate loss function
  11. Consistency of surrogate loss function
  12. Computationally feasible algorithms for learning to help
  13. Pay-Per-Request (PPR)
  14. Intermittent Availability (IA)
  15. Bounded-Reject-Rate (BRR)
  16. ...and 19 more sections

Key Result

Theorem 2.1

Given a client classifier $m(x)$, the solutions of Bayes classifiers (defined in equation eq: Bayes) for generalized $0$-$1$ loss under the space of all measurable functions are: where $\eta_{i}(x)$ is defined in equation equ: regression function and where $j^{*}(x)\triangleq\arg \max_j m_j (x)$.

Figures (7)

  • Figure 1: Diagram of learning to help framework.
  • Figure 2: Impact of $c_e$ and $c_1$ on accuracy and reject rate. First row: change of accuracy as reject rate changes; Second row: change of reject rate as reject cost $c_e$ changes.
  • Figure 3: Comparison of the training loss for different synchronized settings.
  • Figure 4: Comparison of synchronization and synchronization with different parameters
  • Figure 5: Samples from SVHN with $r(x)=\textsc{local}$
  • ...and 2 more figures

Theorems & Definitions (3)

  • Theorem 2.1
  • Proposition 3.1
  • Theorem 3.2