Fenchel
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Related Articles from SNS
Neural Legendre-Fenchel transform with Hessian Preconditioning
Announce Type: new Abstract: The Legendre-Fenchel (LF) transform is a fundamental tool in convex analysis and machine learning that maps lower semi-continuous functions to their convex conjugates. In practice, when closed-form formula are not available for expressing convex conjugates of given functions, one must approximate them using various techniques. One recent such versatile numerical method is the deep Legendre transform method which relies on neural networks although it remains...
Cross-Epoch Adaptive Rollout Optimization for RL Post-Training
arXiv:2606.05606v1 Announce Type: new Abstract: LLM post-training often relies on reinforcement learning methods that sample multiple rollouts per prompt, yet most existing approaches use a fixed rollout budget for every prompt, despite large differences in the training signal different prompts provide. In this paper, we study adaptive rollout allocation under a fixed global budget and formulate the problem as online resource allocation with prompt-level diminishing returns. Our method,...
Learning to Optimize by Differentiable Programming
arXiv:2601.16510v3 Announce Type: replace Abstract: Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn how to design them. Modern frameworks such as PyTorch, TensorFlow, and JAX enable this paradigm through efficient automatic differentiation.
Regularized Large Neighborhood Search
Announce Type: new Abstract: Operations research practitioners typically tackle NP-hard combinatorial problems using large neighborhood search (LNS), a scalable heuristic that iteratively refines a current solution by locally re-optimizing subsets of its variables. In contrast, most existing approaches for integrating combinatorial optimization layers into neural networks still assume access to an exact global solution, which is computationally intractable. We bridge this gap by introducing...
Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling
Announce Type: new Abstract: Sign-based and LMO-inspired optimizers have recently attracted substantial attention in deep learning due to their strong performance and low memory footprint. However, their fixed-magnitude updates can hurt terminal convergence: they decouple update mechanisms from gradient magnitudes and fail to account for parameter heterogeneity, often leading to oscillation rather than convergence. We propose SoftSignum, a smooth relaxation of sign-based optimization that...
A Unified Variational Design of Predictive Mirror Descent in Convex Games under Stochastic Feedback
Announce Type: cross Abstract: Mirror descent provides a geometric framework for learning in games, but its last-iterate behavior can fail in weakly stable regimes, where the dynamics may exhibit rotational or recurrent transients. Predictive mirror methods mitigate this issue by modifying the feedback entering the mirror update, yet standard predictive variants are typically introduced algorithmically and analyzed one at a time. This letter gives a variational route to predictive feedback...