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Solving Few-Shot Multiobjective Multitask Optimization via Iterative Sequential Transfer

Tingyang Wei, Haofeng Wu, Ananda Phan Iman, Zhao Wei, Jiao Liu, Yew-Soon Ong

arXiv:2609.11228v1cs.LGcs.AIcs.NE

TL;DR

Few-shot MOMTO makes beneficial knowledge transfer difficult because limited evaluations hinder identification of elite solution distributions across tasks. The paper introduces IST, which models MTO as sequential transfer with selective target evaluation and likelihood-informed prioritization, and reports effectiveness on benchmark and real-world problems under tight budgets.

  • Problem

    Few-shot MOMTO limits the evaluations available for identifying elite solution distributions needed for beneficial transfer across tasks.

  • Method

    IST models MTO as sequential transfer problems, selecting one target task per iteration through likelihood-informed prioritization.

  • Results

    IST is reported effective on benchmark and real-world few-shot MOMTO problems, including implementations based on F-invTrEMO and AMTEA.

  • Takeaways & Limitations

    Selective evaluation and controlled transfer provide a framework that accommodates existing sequential transfer optimization algorithms.

Abstract

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Applying knowledge transfer across multiple optimization tasks, multitask optimization (MTO) emerges as a promising approach to solving synergistic optimization tasks simultaneously. However, the development of effective knowledge transfer mechanisms in MTO fundamentally relies on aligning elite solution distributions across tasks. This dependency creates a critical bottleneck in few-shot optimization regimes, as restricted evaluation budgets impede the identification of elite solution distributions required for beneficial transfer. This challenge is exacerbated in multiobjective multitask problems, where each optimizer must approximate a continuous Pareto manifold rather than a single optimal point. This paper introduces Iterative Sequential Transfer (IST) to circumvent this bottleneck. We model MTO as a sequence of sequential transfer optimization problems, concentrating evaluations on a single target per iteration. We propose a likelihood-informed task prioritization mechanism to maximize transfer utility by identifying the task most likely ready for knowledge integration. Empirical results on benchmark and real-world problems verify the effectiveness of the proposed method under tight budgets.

I. INTRODUCTION

MTO exploits inter-task relationships to solve multiple optimization problems, but few-shot budgets make beneficial transfer difficult, especially when approximating multiobjective Pareto manifolds.

  • I. INTRODUCTION: MTO solves multiple optimization tasks simultaneously by sharing solution components or mapping relationships between task pairs.Each task has its own decision space and objective function.
  • I. INTRODUCTION: Few-shot evaluation budgets can prevent any task from identifying high-quality solutions, causing stagnant search or negative transfer.Transfer effectiveness depends on aligned elite solution distributions across tasks.
  • I. INTRODUCTION: IST converts MTO into sequential transfer problems and applies knowledge transfer only when it is most beneficial.A likelihood-informed prioritization mechanism selects the target task for each iteration.
  • I. INTRODUCTION: The study evaluates IST with F-invTrEMO on few-shot MOMTO benchmarks and real-world problems, and also extends AMTEA to test generality.The experiments focus on stringent computational budgets.

II. RELATED WORKS

The paper frames few-shot MOMTO as a low-budget extension of multitask optimization and motivates IST through sequential transfer optimization and existing transfer-based solvers.

  • II. RELATED WORKS: Few-shot MOMTO limits each task to O(10^2) evaluations instead of the O(10^5) evaluations common in standard MTO benchmarks.The setting extends scalar task objectives to vector-valued functions with multiple objectives.
  • II. RELATED WORKS: Sequential transfer optimization uses source-task data or models to accelerate search in a target task, including methods based on surrogate stacking, transfer Gaussian processes, inverse modeling, and optimal transport.AMTEA is identified as a pioneering transfer-stacking method for target multiobjective problems.
  • II. RELATED WORKS: The proposed framework models multitask optimization as a sequence of iterative sequential transfer optimization problems.The framework description covers its workflow, base optimizer, and likelihood-informed task prioritization.
  • II. RELATED WORKS: IST is implemented through an algorithm that initializes task evaluations, repeatedly prioritizes a task, and solves the corresponding transfer problem.The supplied algorithm specifies task size, initial budgets, total budgets, objective functions, and a prioritization function.

A. General Framework

IST retains the MTO objective while replacing evenly distributed evaluations with selective, single-target sequential transfer guided by current task histories.

  • A. General Framework: IST preserves the goal of generating optimal solution sets for all tasks while converting the overall problem into sequential transfer optimization tasks.The framework therefore maintains the original multitask objective while changing evaluation allocation.
  • A. General Framework: IST selects one target task per iteration to receive an evaluation, using a likelihood-informed utility function based on all tasks’ optimization histories.The target is chosen while respecting each task’s total evaluation limit.
  • A. General Framework: Unlike standard MTO, IST uses single-directional knowledge transfer and selectively evaluates the task most ready for knowledge integration.This design creates an explicit budget designation process for controlled transfer.
  • A. General Framework: The general workflow initializes every task, prioritizes a target to maximize transfer utility, and optimizes that target using the remaining tasks as sources.Established sequential transfer solvers perform the target-task optimization.

B. Base Sequential Transfer Optimizer

IST instantiates F-invTrEMO as its base sequential transfer optimizer, combining hybrid forward-inverse mappings with scalarization for multiobjective search.

  • B. Base Sequential Transfer Optimizer: F-invTrEMO leverages inter-task relationships through a hybrid forward-inverse mapping approach for few-shot multiobjective multitask optimization.It serves as the sequential transfer optimizer integrated into IST.
  • B. Base Sequential Transfer Optimizer: Within each task, the vector-valued objective is scalarized with augmented Tchebycheff scalarization using weight vectors from an (m−1)-dimensional simplex.The formulation supports handling multiple objectives during transfer optimization.
  • B. Base Sequential Transfer Optimizer: The scalarization uses an ideal point, a utopia point offset by ϵ, and a small constant ρ to maintain Pareto optimality.These quantities define the reference structure used by the scalarized objective.

2) Multitask Gaussian Process:

MTGP models scalarized objectives across tasks by combining task similarity with solution similarity, then estimates posterior distributions for queried task-solution pairs from noisy evaluations.

  • Multitask Gaussian Process: MTGP models evaluated task-solution pairs with noisy scalarized objectives using task and solution inputs.Each observation includes a task index, solution, and noisy objective value with additive Gaussian noise.
  • Multitask Gaussian Process: The multitask kernel is the product of a task-similarity kernel and a solution-similarity kernel.This factorization captures both inter-task relationships and similarities among candidate solutions.
  • Multitask Gaussian Process: Using the kernel and evaluation history, MTGP estimates a posterior mean and variance for each queried task-solution pair.The posterior is represented as a Gaussian distribution over the query prediction.

3) MTGP-based Forward-Inverse Transfer:

The forward-inverse transfer procedure models objective values and inverse mappings between preference weights and solutions, then uses these models to generate target-task candidates from source-task experience.

  • MTGP-based Forward-Inverse Transfer: F-invTrEMO constructs forward and inverse MTGP models from task, solution, objective, and weight records before sequential transfer.The workflow includes forward modeling, inverse modeling for each solution dimension, and target-task solution sampling.
  • MTGP-based Forward-Inverse Transfer: Inverse modeling maps preference-weight vectors from the simplex to the target task’s solution space through separate single-output models.Predictions from the individual dimensions are aggregated into multidimensional solutions.
  • MTGP-based Forward-Inverse Transfer: Algorithm 2 takes target and source tasks, evaluation records, dimension size, a predefined weight vector, and a sample size to produce target-task solutions.The workflow is specified as a single pass of F-invTrEMO.

10 Evaluate solution ˜x in the target task TK

During target-task solution selection, F-invTrEMO uses the available forward and inverse MTGP models and maximizes the lower confidence bound for minimization.

  • 10 Evaluate solution ˜x in the target task TK: For minimization, F-invTrEMO selects target-task solutions by maximizing the lower confidence bound.The forward and inverse MTGP models are built from per-iteration datasets and used during sequential transfer.
  • 10 Evaluate solution ˜x in the target task TK: The algorithm’s sequential-transfer stage directly uses the constructed forward and inverse MTGP models to guide target-task optimization.This stage appears in the workflow’s transfer lines after model construction.

4) Factorized MTGP-based Forward-Inverse Transfer:

The factorized approach replaces joint MTGP training across all tasks with pairwise source-target formulations, while prioritizing the next target through inter-task relationships captured during modeling.

  • Factorized MTGP-based Forward-Inverse Transfer: Pairwise MTGP formulations replace joint training across all tasks to reduce bias toward a source task with substantially more data than the target.The formulation uses one source task together with the target task rather than training one model over every task jointly.
  • Factorized MTGP-based Forward-Inverse Transfer: The factorized formulation combines source-target MTGP posterior quantities with a single-task target model for practical sequential transfer.The cited formulation distinguishes posterior mean and variance from source-target modeling and target-only modeling.
  • Factorized MTGP-based Forward-Inverse Transfer: IST prioritizes the next target task using inter-task relationships captured during MTGP modeling.The prioritization function is intended to identify the task that should receive the next evaluation budget.

1) Task Prioritization Function:

The task prioritization mechanism estimates source-target synergy and uses it to select targets compatible with the full source pool while retaining stochastic exploration.

  • 1) Task Prioritization Function:: Task-pair search synergy is estimated online and interpreted as the likelihood that tasks should serve as source and target.Higher synergy indicates a lower optimization regret bound for the target under Gaussian-process optimization with an LCB component.
  • 1) Task Prioritization Function:: The prioritization function takes the minimum synergy between candidate target t and every other task, ensuring compatibility across the entire source pool.Maximizing this lower bound favors targets with consistently high synergy rather than strong compatibility with only one source.
  • 1) Task Prioritization Function:: A softmax replaces argmax target selection because deterministic selection could leave some tasks static and undermine high-quality source distributions.The target task is sampled from a multinomial distribution whose probabilities are defined by the softmax.
  • 1) Task Prioritization Function:: The softmax pressure parameter S controls selection concentration, while threshold θ boosts tasks above it and gives lower-scoring tasks a common baseline weight.Tasks below θ remain selectable with e0 = 1, preserving search vitality.

IV. EXPERIMENTAL STUDIES

Experiments evaluate IST on benchmark and hyperparameter-optimization problems using IGD+ and repeated trials. Results show gains over single-task and plain transfer baselines, including across heterogeneous real-world tasks.

  • A. Test Problems: The benchmark study covers nine two-task MOMTO problem classes formed from optima intersection and search-space similarity, excluding NIMS and NILS because the optimizer cannot handle distinct objective sizes.The excluded classes are identified as a stated limitation and future direction.
  • A. Test Problems: Performance is quantified with IGD+, statistical significance is tested using the Wilcoxon signed-rank test, and benchmark and hyperparameter studies use 20 and 10 independent trials, respectively.The experiments compare ParEGO, F-invTrEMO, and F-invTrEMO-IST in the benchmark setting.
  • B. Results: F-invTrEMO-IST outperforms ParEGO and plain F-invTrEMO on benchmark problems except the least-similar CILS and PILS sets.The reported exceptions are attributed to biased solution distributions and limited usefulness of transfer between dissimilar search spaces.
  • C. A Case Study on Real-world Application: Multiobjective Multitask Hyperparameter Optimization: F-invTrEMO-IST outperforms F-invTrEMO across all reported hyperparameter-optimization tasks, producing better model sets trading off precision, size, and interpretability.The comparison is reported in Table II for multitask hyperparameter-tuning problems.

D. A Case Study on Generality of the Framework: IST based on AMTEA

IST generalizes beyond its original optimizer by integrating with AMTEA for few-shot multiobjective multitask optimization, using single-objective transformations and Gaussian-process evaluation. AMTEA-IST generally improves over AMTEA, especially when task similarity is lower.

  • D. A Case Study on Generality of the Framework: IST based on AMTEA: AMTEA-IST transforms each multiobjective problem into a single-objective problem at every iteration and evaluates it with a Gaussian-process surrogate.Solutions are sampled from the solution distribution managed by AMTEA, following the approach used in ParEGO and Algorithm 2.
  • D. A Case Study on Generality of the Framework: IST based on AMTEA: AMTEA-IST outperforms AMTEA in 11 of 14 multiobjective tasks with carefully configured transfer directions.The improvements are generally strongest on problem sets with lower search-space similarity.
  • D. A Case Study on Generality of the Framework: IST based on AMTEA: Both AMTEA and AMTEA-IST outperform ParEGO in 13 of 14 tasks, demonstrating effective knowledge transfer under few-shot MOMTO budgets.The comparison is reported in supplementary Table S-I.
  • D. A Case Study on Generality of the Framework: IST based on AMTEA: Improvements over AMTEA are not significant for CIHS and CIMS because their high-quality solutions are similar and task prioritization cannot precisely capture their relationship.For lower-similarity problem sets, filtering out the least likely task pair generally yields significant improvements.
  • D. A Case Study on Generality of the Framework: IST based on AMTEA: IST is designed to accommodate existing sequential transfer optimizers, extending the framework beyond its original optimizer.AMTEA-IST provides the reported generality case study under stringent evaluation budgets.
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