Residual-Controlled Multiplier Learning for Stochastic Constrained Decision-Making

• URL: http://arxiv.org/abs/2606.07088v2
• Date: Tue, 09 Jun 2026 09:03:36 GMT
• Title: Residual-Controlled Multiplier Learning for Stochastic Constrained Decision-Making
• Abstract summary: CML addresses the problem of tracking the noise of primal feedback multipliers under mini-batch conditions.<n>We decompose the multiplier into an effective pressure signal for primal descent and a finite-gain multiplier.
• Score: 12.04727482907937
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic constrained decision-making requires optimizing performance objectives while enforcing statistical requirements such as safety or fairness. However, standard primal--dual methods struggle to update multipliers robustly under stochastic mini-batch feedback, as the noise of mini-batch gradients and constraint estimates can be directly accumulated into the multiplier memory. To address this issue, we propose Residual-Controlled Multiplier Learning (RCML), which reformulates multiplier updating as projected-pressure feedback. The central idea is to decompose the projected multiplier into an effective pressure signal for primal descent and a pressure-memory residual for finite-gain multiplier tracking. To handle heterogeneous and noisy observations, we further augment this residual-integral backbone with modular stochastic stabilization components. For the convex-affine backbone, we establish finite-gain convergence, derive a stochastic residual bound under mini-batch feedback, and show that the residual feedback law admits a local KKT-residual interpretation near regular KKT points of nonconvex problems. Experiments across optimization, allocation, and fair-ranking tasks show that RCML improves feasibility control and multiplier stability while maintaining competitive objective performance. Code is released at https://anonymous.4open.science/r/RCML-3114/.

Related papers

• Scalable Lindblad Noise Learning via Stochastic Tensor-Network Simulation [48.887627688666974]
  Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies.<n>Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a simulation method, the Jump Method (TJM)<n>We demonstrate the approach on two noise models in the Ising model, in which independent dissipation rates are learned for each site up to $N_mathrmsite=16$.<n>This combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices.
  arXiv  Detail & Related papers  (2026-08-25T15:07:11Z)
• RBE-Flow: Recurrent Bayesian Estimation on Feature Manifolds for Cross-Modal Registration [14.194086645453767]
  Cross-pixel image registration is challenging due to severe non-linear radiometric and uncertainty.<n>In this paper we propose a novel framework that reformulates dense-modal flow estimation.
  arXiv  Detail & Related papers  (2026-06-29T15:58:25Z)
• Precise: SDE-Consistent Stochastic Sampling for RL Post-Training of Flow-Matching Models [56.67321805551389]
  Reinforcement learning (RL) has become an effective way to improve prompt alignment and perceptual quality in diffusion and flow-matching generators.<n>The sampler, controlling the exploration behavior and denoising dynamics, is thus part of the policy.<n>We propose a new sampler that balances effective exploration with stability.
  arXiv  Detail & Related papers  (2026-05-22T11:37:22Z)
• Clipping Bottleneck: Stabilizing RLVR via Stochastic Recovery of Near-Boundary Signals [83.0127582612634]
  Near-boundary Rescue (NSR) is a minimal, plug-and-play modification that retains out-of-bound tokens to recover lost signals.<n>NSR substantially improves training stability and delivers consistent gains over strong baselines such as DAPO and GSPO.
  arXiv  Detail & Related papers  (2026-05-21T16:45:31Z)
• MARR: Module-Adaptive Residual Reconstruction for Low-Bit Post-Training Quantization [42.904834974723535]
  We propose Module-Adaptive Residual Reconstruction (MARR)<n>MARR assigns a module-specific scaling coefficient to adaptively balance accumulated-error correction and residual-related HA bias for each module.<n>Experiments on several typical large language models (LLMs) and vision transformers (ViTs) demonstrate the effectiveness of MARR under low-bit quantization.
  arXiv  Detail & Related papers  (2026-05-18T07:51:49Z)
• SAGE: Shaping Anchors for Guided Exploration in RLVR of LLMs [55.46289074417954]
  reinforcement learning with verifiable rewards (RLVR) reliably improves pass@1 on reasoning tasks, yet often fails to yield comparable gains in pass@k.<n>We argue that a central structural constraint arises from reverse-KL regularization, which stabilizes training but inherently anchors the policy to the reference distribution.<n>We propose SAGE, a principled framework that enables controllable empirical support expansion by reshaping the reverse-KL anchor distribution itself.
  arXiv  Detail & Related papers  (2026-05-15T07:42:21Z)
• Too Correct to Learn: Reinforcement Learning on Saturated Reasoning Data [55.84428098924793]
  We propose Constrained Uniform Top-K Sampling (CUTS), a parameter-free decoding strategy enforcing structure-preserving exploration.<n>We integrate this into Mixed-CUTS, a training framework synergizing exploitative and exploratory rollouts to amplify intra-group advantage variance.<n> Notably, Mixed-CUTS improves Pass@1 accuracy on the challenging AIME25 benchmark by up to 15.1% over standard GRPO.
  arXiv  Detail & Related papers  (2026-04-20T16:43:28Z)
• Diffusion Controller: Framework, Algorithms and Parameterization [54.82539154511621]
  We present a unified control-theoretic view that casts reverse diffusion sampling as state-only control within (generalized) linearly-solvable Markov Decision Processes.<n>Under this framework, control acts by reweighting the pretrained reverse-time transition kernels, balancing terminal objectives against an $f$-divergence cost.<n>Experiments on Stable Diffusion v1.4 show consistent gains in preference-alignment win rates and improved quality-efficiency trade-offs.
  arXiv  Detail & Related papers  (2026-03-07T01:49:59Z)
• Rethinking the Trust Region in LLM Reinforcement Learning [72.25890308541334]
  Proximal Policy Optimization (PPO) serves as the de facto standard algorithm for Large Language Models (LLMs)<n>We propose Divergence Proximal Policy Optimization (DPPO), which substitutes clipping with a more principled constraint.<n>DPPO achieves superior training and efficiency compared to existing methods, offering a more robust foundation for RL-based fine-tuning.
  arXiv  Detail & Related papers  (2026-02-04T18:59:04Z)
• Breaking the Stochasticity Barrier: An Adaptive Variance-Reduced Method for Variational Inequalities [0.0]
  We propose VR-A-A (VarianceReduced-Ascent with Armijo) as a novel algorithm for non-con optimization tasks.<n>We show that our method effectively suppresses limit cycles and accelerates convergence with reduced dependence on manual learning scheduling.
  arXiv  Detail & Related papers  (2026-01-30T14:43:07Z)
• Stability and Generalization for Bellman Residuals [8.250374560598493]
  Bellman residual minimization (BRM) has emerged as an attractive remedy for offline reinforcement learning.<n>This paper introduces a single Lyapunov potential that couples SGDA runs on neighbouring datasets and yields an O (1/n) on-average argument-stability bound.<n>The results hold for standard neural-network parameterizations and minibatch SGD.
  arXiv  Detail & Related papers  (2025-08-26T07:15:36Z)
• Convergence and Generalization of Anti-Regularization for Parametric Models [0.0]
  Anti-regularization introduces a reward term with a reversed sign into the loss function.<n>We formalize spectral safety conditions and trust-region constraints.<n>We design a lightweight safeguard that combines a projection operator with gradient clipping to guarantee stable intervention.
  arXiv  Detail & Related papers  (2025-08-24T15:34:17Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.