Controllable Pareto Multi-Task Learning

1. Introduction

• Fixed-capacity MTL tasks can conflict, so practitioners must balance task performance and may need to group tasks carefully.Existing approaches for different trade-offs can require training and storing multiple models.Source: §1 · p. 1
• Real-world MTL applications may require real-time trade-off adjustments, while storing multiple models for different preferences is costly and unsuitable for those adjustments.Source: §1 · pp. 1–2
• The proposed controllable Pareto MTL framework learns the whole trade-off curve for all tasks with a single model and allows inference-time preference control.Source: Figure 1 · p. 1, §1 · p. 2
• The framework formulates MTL as preference-conditioned multiobjective optimization and uses a solution generator to learn the trade-off curve.Source: §1 · p. 2
• A hypernetwork-based multi-task network and end-to-end algorithm optimize different trade-off preferences through a single model.Source: §1 · p. 2
• Experiments on different MTL problems report that the method learns trade-off curves and supports real-time trade-off control.Source: §1 · p. 2

2. Related Work

• Deep MTL research has explored shared representations and adaptive task weights, while combining tasks remains challenging and linear scalarization remains a common default.Source: §2 · p. 2
• Multiobjective MTL methods seek one or multiple Pareto solutions, but covering a trade-off curve with separate models can be costly.Recent methods pursue diverse or dense Pareto solutions, while the paper proposes learning the curve with one model.Source: §2 · p. 2
• A concurrent work also learns an entire MTL trade-off curve with a hypernetwork, while this paper emphasizes inference-time preference control and large-scale MTL.Source: §2 · p. 2
• MOEA/D decomposes a multiobjective problem into finite preference-based subproblems, whereas this paper aims to learn the trade-off curve, potentially containing infinitely many solutions, with one model.Source: §2 · p. 2
• Other multiobjective methods often find one or finitely many solutions without real-time control, while this paper uses a hypernetwork to generate the main network's parameters from preferences.Source: §2 · p. 2
• Hypernetworks have been applied to model compression, hyperparameter optimization, Bayesian inference, and transfer learning.Source: §2 · p. 2

3. MTL as Multi-Objective Optimization

• An MTL network has parameters θ and an empirical loss L_i(θ) for each task, and aims to minimize all task losses together.Source: §3 · p. 3
• A single solution may not optimize every task loss simultaneously, motivating trade-offs among tasks.Source: §3 · p. 3
• A Pareto-optimal solution is not dominated by another solution, and the set of such solutions is the Pareto set whose objective-space image is the Pareto front.Source: §3 · p. 3
• The Pareto set and front can be infinite, so traditional methods approximate them using a finite set of solutions and corresponding objective vectors.Source: §3 · p. 3
• Covering a trade-off curve may require a number of large neural-network solutions that grows exponentially with task count, increasing training and storage costs.Source: §3 · p. 3

4. Preference-Based Solution Generator

• A preference vector maps through a solution generator to a corresponding solution, and sweeping valid preferences reconstructs the approximate Pareto set and front.The generator is not guaranteed to recover the ground-truth Pareto front.Source: §4 · p. 3
• Linear scalarization treats each preference-vector component as a task weight and defines the corresponding solution by minimizing the weighted task losses.The paper assumes a one-to-one mapping from preferences to solutions for simplicity.Source: §4 · p. 4
• Linear scalarization cannot find Pareto solutions on non-convex portions of the front, so it cannot cover the whole Pareto set unless the front is convex.Source: §4 · p. 4
• The preference-based approach selects a Pareto solution in the region closest to the preference vector, using the solution whose loss vector has the smallest angle to it.Valid preference vectors are unit vectors in the task-loss space.Source: §4 · p. 4

5.1. Hypernetwork-based Deep Multi-Task Network

• A fixed-structure MTL network uses a shared encoder and task-specific heads, while a hypernetwork generates its parameters conditioned on the preference vector.The shared encoder is regularized across tasks through the generated encoder parameters.Source: §5.1 · pp. 4–5, Figure 5 · p. 5
• Chunking lets the hypernetwork generate separate parts of a large MTL network using chunk embeddings, keeping the hypernetwork reasonably sized.Reusable fully connected layers and shared parameter tensors compress generation; the model is kept comparable in size to its MTL counterpart, with acceptable inference-latency overhead for real-time control.Source: §5.1 · p. 5

5.2. Optimization: Learning the Generator

• Training samples preference vectors with Monte Carlo and updates hypernetwork parameters by stochastic gradient descent using a valid descent direction.For the multiobjective case, the direction combines task losses and activated constraints with dynamic weights.Source: §5.2 · pp. 5–6
• The algorithm optimizes the generator across valid preferences and can generate a solution for any preference, reconstructing the approximate trade-off curve.The paper samples preferences and reference vectors uniformly; its training curves continually learn the trade-off curve during optimization.Source: §5.2 · p. 6, Figure 6 · p. 6

6. Synthetic Multi-Objective Problem

• The authors first test algorithm behavior and convergence on a low-dimensional multiobjective problem because the MTL decision space is high-dimensional and its Pareto front is unknown.Source: §6 · p. 6
• The method successfully reconstructs the whole Pareto set and front for a synthetic problem with a sine-like solution-space set and a concave objective-space front.Traditional methods find only finite solutions, and preference-based linear scalarization performs poorly on the totally concave front.Source: §6 · p. 6

• With one model, the proposed method learns trade-off curves on MultiMNIST, CityScapes, and NYUv2 that dominate the curves found by linear scalarization.The compared methods require multiple models to cover the entire curve.Source: Figure 8 · p. 7, §7 · p. 7
• The model is described as more parameter-efficient than methods that train and store multiple MTL models, while learning the whole trade-off curve.Its inference latency is described as having affordable overhead for real-time preference adjustment.Source: §7 · pp. 7–8
• On CIFAR-100 with 20 tasks, real-time preference adjustment achieves the best overall performance and outperforms the balanced hypernet approach.The balanced hypernet uses the same hypernetwork-based model but optimizes tasks with equal preference.Source: §7 · p. 7, Figure 9 · p. 8
• With a pretrained ResNet-50 backbone, the model learns a good trade-off curve between the two NYUv2 tasks.The hypernetwork generates the encoder’s last few layers and all task-specific heads; task balancing and decoder design could further improve performance.Source: Figure 10 · p. 8, §7 · p. 8

8. Conclusion

• A preference-based hypernetwork learns the whole trade-off curve with one model and lets practitioners adjust task trade-offs at inference time.Experiments on various MTL applications are reported to demonstrate the method’s usefulness and efficiency.Source: §8 · p. 8

Appendix

• The appendix summarizes discussion of convergence, comparisons with a concurrent hypernetwork method, experimental settings, and planned public code.It also points to a detailed derivation of preference-based multiobjective gradient descent.Source: Appendix · p. 12

A. Preference-based Multiobjective Gradient Descent

• The appendix section derives the preference-based multiobjective gradient direction and a batched-preference optimization variant for training the hypernetwork-based MTL model.Source: A. Preference-based Multiobjective… · p. 12

A.1. Preference-based Gradient Direction

• For each sampled preference, the algorithm updates generator parameters φ rather than a single solution’s parameters, seeking a direction that reduces all losses and activated constraints.If no nonzero valid direction exists, the current solution is locally restricted Pareto optimal within Ω(p, U).Source: §A.1 · pp. 12–13

A.2. Adaptive Linear Scalarization

• The valid descent direction is expressed as a dynamic linear combination of task-loss gradients, with coefficients obtained by solving the dual problem.The dual uses the Frank-Wolfe algorithm, and experiments use three reference vectors.Source: §A.2 · p. 13

A.3. Batched Preferences Update

• Batched updates sample multiple preferences together, with adaptive weights depending on their losses and activated constraints.Using the other sampled preferences as references yields K(K −1) constraints, though some may be inactive during training.Source: §A.3 · pp. 13–14

Convergence Analysis

• Convergence is difficult to analyze for deep MTL with complicated optimization landscapes and infinite preferences.With proper assumptions, the authors expect fixed preferences to share the single-preference convergence guarantee.Source: B. Convergence Analysis · pp. 14–15

Single Preference

• For a single fixed preference, optimization follows prior single-model MTL methods with an added hypernetwork, and converges to a local Pareto stationary point if no valid descent direction exists.That point need not be Pareto optimal for a general problem.Source: B. Convergence Analysis · pp. 14–15

Fixed and Finite Multiple Preferences

• For fixed finite preferences, batched-preference updates optimize the generator for all preferences at each iteration.Each preference-specific objective reduces to the single-preference case.Source: B. Convergence Analysis · p. 15

Infinite Preferences

• For infinitely many preferences, the method samples a finite set at each iteration to approximate the expected objective, then iteratively improves the generator across preferences.This is described as Monte Carlo approximation, analogous to stochastic or batched SGD versus full gradient descent.Source: B. Convergence Analysis · p. 15
• The method cannot guarantee the ground-truth Pareto front for a general problem, nor that generated solutions cover even a local Pareto set.Under mild assumptions the Pareto set is an (m −1)-dimensional manifold, but the learned manifold may not cover it.Source: B. Convergence Analysis · pp. 14–15

Conclusion

• The authors position their approach as a single-model method for large-scale trade-off curves with real-time control and minimal inference overhead.They describe it as, to their knowledge, the first approach to learn such curves for large-scale MTL problems.Source: C. More Experimental Results · p. 15

Result Analysis

• The comparison evaluates trade-off curves on MultiMNIST, MultiFashion, and MultiFashionMNIST, and reports hypervolume as a measure of approximated-front quality.The experiments use reference point (0.5, 0.5); larger hypervolume indicates a better-approximated front with a fixed reference point.Source: C. More Experimental Results · pp. 15–16

Models

• Continuous Pareto Exploration generates 20 solutions from each of five seed solutions, requiring 105 full MTL models to approximate the front.Seeds use linear scalarization or Pareto multitask learning.Source: C. More Experimental Results · p. 16
• The authors could not tune PHN to match their method’s performance and suggest its 3.2M-parameter hypernetwork may be difficult to optimize.They point to hypernetwork initialization and optimization dynamics as possible avenues for improvement.Source: C. More Experimental Results · p. 16

Result Analysis

• 1.1% of the compared methods’ model size yields better or comparable trade-off curves across all problems.Table 2 reports performance and model sizes for MultiMNIST and its variants.Source: C. More Experimental Results · p. 16, Table 2 · p. 16
• Sharing parameters across preference-conditioned solutions supports scaling to large MTL models without decreasing their performance.The authors relate this sharing to similarities among solutions for different preferences.Source: C. More Experimental Results · p. 16

Synthetic Example

• The synthetic example uses n = 10 and a two-layer MLP with 50 hidden units per layer to generate Pareto solutions from preferences.Source: D. Experimental Setting · p. 16

MultiMNIST and Two Variants

• MultiMNIST classifies two overlapped digits, while its variants classify two fashion items or one fashion item and one digit.The experiments use a LeNet-based MTL model with two task-specific fully connected layers; the hypernetwork has a similar parameter count to a single MTL model.Source: D. Experimental Setting · pp. 16–17

CityScapes

• CityScapes pairs pixel-wise segmentation of seven coarser labels with depth estimation on resized street-view images.The model uses a SegNet shared encoder and two task-specific lightweight convolution layers; depth uses L1 loss.Source: D. Experimental Setting · p. 17

NYUv2

• NYUv2 evaluates 13-class indoor semantic segmentation and depth estimation, using images resized to 288 × 384.The study includes training-from-scratch and pretrained-encoder settings; the latter uses an ImageNet-pretrained ResNet-50 backbone.Source: D. Experimental Setting · p. 17

CIFAR100 with 20 Tasks

• CIFAR-100 is split into 20 five-class tasks, evaluated with a four-convolution-layer shared network and 20 task-specific fully connected layers.The hypernetwork is an MLP; the preference and chunking embeddings are 32-dimensional, and test accuracy is reported for all 20 tasks.Source: D. Experimental Setting · p. 17