Research map / Learning theory and algorithms / Combinatorial and search optimization
Efficient First-Order Optimization on the Pareto Set for Multi-Objective Learning under Preference Guidance
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Casts preference-guided multi-objective learning as optimization on the Pareto set (semivectorial bilevel), converts the vector lower level into a smoothed log-sum-exp merit function, and solves the penalty reformulation with a first-order method (FOOPS) with convergence guarantees.
Problem
Multi-objective learning with user-specified preferences: optimize a preference function over the weakly Pareto set of a vector-valued objective, which is hard due to nonsmooth max-min merit structure and nonconvex objectives.
Approach
Replace the Pareto-set constraint with a smoothed, regularized log-sum-exp merit function v_{l,tau} that has an easy-to-evaluate gradient, use a polynomial penalty of it, and prove error-bound (HEB/KL) properties under subanalyticity to get relations between penalty and constrained solutions and first-order convergence.
Key results
- On multi-patch image classification, FOOPS achieves the highest hypervolume on all six reported metrics, e.g., 0.72 vs 0.53 for FERERO on Mt-F+M accuracy.
- On multi-lingual speech recognition, FOOPS-FT reaches 4.7% Chinese WER and 5.1% average WER, matching FERERO-FT's average.
- Theory establishes that the smoothed merit function has HEB and KL properties on bounded sets under subanalyticity, yielding relations between penalty and constrained solutions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FOOPS instead of FERERO | Multi-patch image classification · Mt-M loss | hypervolume (×10⁻²): 1.95 ±0.21 -> 2.62 ±0.21 | Helped |
| Use FOOPS instead of FERERO | Multi-patch image classification · Mt-F loss | hypervolume (×10⁻²): 7.76 ±0.18 -> 8.32 ±0.37 | Helped |
| Use FOOPS instead of FERERO | Multi-patch image classification · Mt-F+M loss | hypervolume (×10⁻²): 3.82 ±0.21 -> 4.80 ±0.45 | Helped |
| Use FOOPS instead of FERERO | Multi-patch image classification · Mt-M accuracy | hypervolume (×10⁻²): 0.25 ±0.04 -> 0.33 ±0.02 | Helped |
| Use FOOPS instead of FERERO | Multi-patch image classification · Mt-F accuracy | hypervolume (×10⁻²): 1.13 ±0.07 -> 1.22 ±0.07 | Helped |
| Use FOOPS instead of FERERO | Multi-patch image classification · Mt-F+M accuracy | hypervolume (×10⁻²): 0.53 ±0.04 -> 0.72 ±0.06 | Helped |
| Use FOOPS-FT instead of FERERO-FT | Multilingual speech recognition fine-tuning · Speech recognition, English | WER (%): 5.4 -> 5.7 | Hurt |
| Use FOOPS-FT instead of FERERO-FT | Multilingual speech recognition fine-tuning · Speech recognition, Chinese | WER (%): 4.9 -> 4.7 | Helped |
| Use FOOPS-FT instead of FERERO-FT | Multilingual speech recognition fine-tuning · Speech recognition, average | WER (%): 5.1 -> 5.1 | No clear effect |
| Use FOOPS instead of preference-constrained methods | Preference-guided multi-objective optimization · Multi-patch image classification | preference alignment | Hurt |
| Use FOOPS instead of preference-constrained methods | Preference-guided multi-objective optimization · Multilingual speech recognition | preference function optimization | Hurt |
Surprising findings
- Linear scalarization cannot reach preferred Pareto optimal solutions for certain initializations regardless of weights.
- FOOPS is worse at aligning with user preferences than baselines even though it achieves larger hypervolume.
Limitations
- Stochastic variants and convergence analysis are left for future work.
- Nonsmooth case (theta<1) convergence not established.
- Preference alignment is weaker than baselines in experiments.
Experimental setup
Datasets: Multi-MNIST Multi-Fashion Multi-Fashion+MNIST Librispeech AISHELL v1
Benchmarks: Multi-MNIST Multi-Fashion Multi-Fashion+MNIST
Metrics: hypervolume objective loss accuracy word error rate
Baselines: LS PMTL EPO XWC-MGDA FERERO
Builds on: PB-PDO FERERO EPO PMTL
Closest papers by meaning
- Preference Optimization on Pareto Sets: On a Theory of Multi-Objective Optimization (NeurIPS 2025 · similarity 0.86)
- FERERO: A Flexible Framework for Preference-Guided Multi-Objective Learning (NeurIPS 2024 · similarity 0.85)
- Generalized Smooth Bilevel Optimization with Nonconvex Lower-Level (ICML 2025 · similarity 0.85)
- Tuning-Free Bilevel Optimization: New Algorithms and Convergence Analysis (ICLR 2025 · similarity 0.85)
- TSP: A Two-Sided Smoothed Primal-Dual Method for Nonconvex Bilevel Optimization (ICML 2025 · similarity 0.84)
- On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximation (ICLR 2024 · similarity 0.84)
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