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Learning to Partially Defer for Sequences

Sahana Rayan, Ambuj Tewari

TL;DR

This work extends Learning to Defer to sequential outputs by introducing token-level and one-time partial deferral, enabling interleaved collaboration between a predictor and an expert. It develops convex surrogate losses with Bayes consistency guarantees for both granularities and derives generalization bounds to support finite-sample performance. Empirically, partial deferral yields better cost-accuracy tradeoffs than full-sequence deferral on tasks like TSP, XSUM, and MWP, with token-level deferral often providing the strongest gains. The results highlight the practical value of granularity in deferral and lay groundwork for future extensions to multiple experts and broader sequence domains.

Abstract

In the Learning to Defer (L2D) framework, a prediction model can either make a prediction or defer it to an expert, as determined by a rejector. Current L2D methods train the rejector to decide whether to reject the {\em entire prediction}, which is not desirable when the model predicts long sequences. We present an L2D setting for sequence outputs where the system can defer \textit{specific outputs} of the whole model prediction to an expert in an effort to interleave the expert and machine throughout the prediction. We propose two types of model-based post-hoc rejectors for pre-trained predictors: a token-level rejector, which defers specific token predictions to experts with next token prediction capabilities, and a one-time rejector for experts without such abilities, which defers the remaining sequence from a specific point onward. In the experiments, we also empirically demonstrate that such granular deferrals achieve better cost-accuracy tradeoffs than whole deferrals on Traveling salesman solvers, News summarization, and Weather prediction.

Learning to Partially Defer for Sequences

TL;DR

This work extends Learning to Defer to sequential outputs by introducing token-level and one-time partial deferral, enabling interleaved collaboration between a predictor and an expert. It develops convex surrogate losses with Bayes consistency guarantees for both granularities and derives generalization bounds to support finite-sample performance. Empirically, partial deferral yields better cost-accuracy tradeoffs than full-sequence deferral on tasks like TSP, XSUM, and MWP, with token-level deferral often providing the strongest gains. The results highlight the practical value of granularity in deferral and lay groundwork for future extensions to multiple experts and broader sequence domains.

Abstract

In the Learning to Defer (L2D) framework, a prediction model can either make a prediction or defer it to an expert, as determined by a rejector. Current L2D methods train the rejector to decide whether to reject the {\em entire prediction}, which is not desirable when the model predicts long sequences. We present an L2D setting for sequence outputs where the system can defer \textit{specific outputs} of the whole model prediction to an expert in an effort to interleave the expert and machine throughout the prediction. We propose two types of model-based post-hoc rejectors for pre-trained predictors: a token-level rejector, which defers specific token predictions to experts with next token prediction capabilities, and a one-time rejector for experts without such abilities, which defers the remaining sequence from a specific point onward. In the experiments, we also empirically demonstrate that such granular deferrals achieve better cost-accuracy tradeoffs than whole deferrals on Traveling salesman solvers, News summarization, and Weather prediction.

Paper Structure

This paper contains 37 sections, 17 theorems, 56 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Learning to Defer
  4. Consistent Losses
  5. Token-level partial deferral
  6. Surrogate Loss
  7. Generalization Bounds
  8. One-time partial deferral
  9. Influence of large $L$
  10. Surrogate loss
  11. Generalization Bounds
  12. Related Works
  13. Experiments
  14. Tasks
  15. Baselines
  16. ...and 22 more sections

Key Result

Lemma 3.1

Let $0 < \bar{c} \leq c_j(x, \widehat{y}_{<j}, y) \leq \bar{C} < \infty$ for all $j$, $0 \leq l(y, \widehat{y}^h_j) \leq \bar{l} < \infty$, and $\phi$ be a binary surrogate loss that satisfies the following inequality for any distribution over ${\cal X} \times \{-1, 1\}$ and any measurable function where ${\cal R}_{\text{binary }0-1}$ is the binary 0-1 risk and $\Gamma : \mathbb{R}^+ \to \mathbb{

Figures (5)

  • Figure 1: Deferral Curve for XSUM (closer to the lower left corner is better). See \ref{['sec:morecostlossplot']} for deferral curves of other tasks.
  • Figure 2: Plots of Size of ${\cal J}$ against percentage improvement in AUDC relative to the random baseline for TSP (on the left) and XSUM (on the right). See \ref{['sec:numexperts']} for exact AUDC values.
  • Figure 3: Cost-Loss plots for TSP (on the left) and MWP (on the right).
  • Figure 4: Plots of Size of ${\cal J}$ against AUDC and percentage improvement in AUDC relative to the random baseline for TSP (on the left) and XSUM (on the right) for models trained with different $\alpha_1$ value. The costs displayed in the legend refer to the deferral cost per token or $\alpha_L$
  • Figure 5: Cost-Loss plots for XSUM for various model architectures and training strategies.

Theorems & Definitions (30)

  • Definition 2.1: Consistency
  • Lemma 3.1
  • Theorem 3.2: Consistency
  • Theorem 3.3
  • Corollary 3.4
  • Theorem 4.1: Consistency
  • Theorem 4.2
  • Proposition A.1
  • proof
  • Lemma A.2
  • ...and 20 more