Multi-objective learning (MOL) aims to optimize multiple objectives simultaneously. The multi-gradient descent algorithm (MGDA) is a workhorse that iteratively updates along a common descent or conflict-avoidant (CA) direction across objectives. In stochastic settings, however, the vanilla stochastic MGDA method, SMG, lacks a fast convergence rate because mini-batch sampling introduces noise in the gradients. This causes bias in the update direction, which is controlled by the CA direction continuity. In this paper, we show that the CA direction is $1/2$-Holder continuous with respect to the Jacobian matrix, and the exponent $1/2$ cannot be improved in the worst case. This leads to a suboptimal convergence rate for vanilla stochastic MGDA in prior works. Nevertheless, under additional regularity conditions, we show this can be improved to Lipschitz continuity. Based on this insight, we propose a stochastic multi-objective regularity-aware (MoRe) method that exploits the Lipschitz continuity of the CA direction when the subproblem is regular, and switches to a fixed scalarization weight otherwise. Intuitively, the proposed algorithm employs CA direction update when the gradient conflict is large, and linear scalarization update otherwise. Theoretically, our method improves the convergence rate of SMG in the nonconvex setting from $\widetilde{\mathcal O}(T^{-1/4})$ to $\widetilde{\mathcal O}(T^{-1/2})$, where $\widetilde{\mathcal O}(\cdot)$ hides logarithmic factors. Meanwhile, we also establish the per-iterate conflict-avoidance guarantees. Empirically, experiments demonstrate its effectiveness in multi-task performance and verify convergence behavior consistent with the established theoretical rate.
Cross-subject generalization remains a fundamental challenge in surface electromyography (sEMG)-based gesture recognition. Although deep learning methods have improved within-subject performance, they often rely on subject-specific data and struggle to balance invariance and discriminability. In this work, we propose a conservative multi-objective learning framework for subject-invariant sEMG gesture recognition. The proposed model adopts a multi-head architecture that jointly optimizes gesture classification, adversarial subject confusion through gradient reversal, and triplet-based metric learning to encourage discriminative and subject-invariant representations. To improve optimization stability, a Lipschitz-inspired adaptive weighting mechanism is introduced to dynamically balance the auxiliary objectives according to their relative magnitudes during training. The proposed method is evaluated on two benchmark datasets: UCI EMG (36 subjects, 6 gestures) and NinaPro DB5 (10 subjects, 10 gestures). On the UCI EMG dataset, the method achieves 84.48\% accuracy compared to 78.2\% reported by state-of-the-art methods. On NinaPro DB5, it achieves 61.44\% accuracy versus 41.30\%, corresponding to a 49\% relative improvement. In addition, the proposed framework reduces cross-subject prediction variance and produces more structured latent representations. These results indicate that jointly enforcing invariance and discriminability through adaptive multi-objective optimization leads to more stable training and improved cross-subject generalization in sEMG-based gesture recognition systems.
Multi-objective masked image modeling (MIM) combines complementary learning signals (token distillation, CLS alignment, and pixel reconstruction) but existing methods weight these objectives with global scalars, ignoring spatial heterogeneity across patches. We present ExPLoRe (Expert Patch-Level Loss Routing), which repurposes Soft Mixture of Experts (MoE) dispatch weights as learned, per-patch loss coefficients. The key mechanism is loss-coupling: allowing loss gradients to flow through dispatch weights to the router enables content-dependent specialization, where different patches receive different emphases across objectives. A detach ablation confirms loss-coupling as the core mechanism, degrading performance by 1.6% when gradients are blocked. On ImageNet-1K with ViT-Base, ExPLoRe improves over non-MoE baselines on two objective combinations (Token+CLS: +0.5% k-NN, +4.4% linear probe; Token+Pixel: +2.2% k-NN), achieving 80.6% linear probe and 85.3% finetuning accuracy, competitive with published methods. For downstream transfer, we develop adaptation recipes (Freeze Routing, Expert Dropout, and Freeze Attention) that improve MoE finetuning by +1.5% over the vanilla MoE, and close a 2.5--2.9 mIoU segmentation gap so that MoE models match or exceed non-MoE baselines on ADE20K.
Learning to bid in repeated multi-unit auctions with bandit feedback poses a fundamental challenge. Existing methods often rely on rigid explore-then-exploit schedules, assume stationary adversaries, and optimize solely for bidder utility, thereby limiting adaptability and strategic robustness. To address these limitations, we introduce the A3M framework, which integrates adaptive deep reinforcement learning (DRL), explicit adversarial reasoning, and principled multi-objective reward design for online auction strategy optimization. A3M employs an actor-critic DRL backbone to dynamically balance exploration and exploitation, an opponent model for fictitious play against non-stationary adversaries, and a composite reward function to jointly maximize utility, auctioneer revenue, and fairness. We provide the first comprehensive empirical evaluation of this integrated approach against established baselines in both discriminatory and uniform price auctions. Results show that A3M reduces final regret by 30--40\% in standard settings, maintains robust performance against adversarial strategy shifts, scales favorably with the number of units $K$, and enables tunable multi-objective trade-offs. An extensive ablation study confirms the necessity of each core component. Our work establishes A3M as a powerful and flexible framework for learning in complex auction environments.
Dialogue systems in e-commerce scenarios often need to satisfy multiple objectives: accurately reasoning over user profiles (e.g., eligibility, credit limit) to ensure correct decision-making and user state interpretation, while also generating natural and faithful responses. These goals are complementary but not identical. In this work, we propose MORE, an adaptive Multi-Objective REinforcement learning framework that jointly optimizes reasoning accuracy and linguistic naturalness. Our preliminary experiments show that directly mixing rewards with diverging optimization dynamics can cause oscillations and unstable learning. Thus, instead of optimizing a single mixed reward, we treat reasoning functions as constraints that guide policy optimization. At inference time, the system directly generates responses without explicit reasoning steps, while still benefiting from reasoning-enhanced scaffold and avoiding additional inference overhead. To better balance linguistic objectives during response generation, we introduce an adaptive multi-reward mechanism that aggregates signals such as fluency and naturalness and dynamically reweighs them via gradient feedback. We evaluate MORE on two real-world dialogue systems at ByteDance and the MultiWOZ 2.2 benchmark, where it consistently outperforms strong baselines. In 14-day online experiments on ByteDance production traffic, MORE improves overall and reached conversion by 16.53% and 30.09%, while increasing user satisfaction and reducing handoff rates. Notably, in a human-machine comparison, MORE recovers about 60% of the incremental conversion lift achieved by human agents.