Optimal Control

Follow this topic Ask about this topic

Momentum

4 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

Jul 13Week of Sep 28

Latest papers 96

All topics

A statistical physics framework for optimal learning
Jul 10, 2025Francesca Mignacco, Francesco MoriStatistical Physics of Learning Neural Network Training Dynamics
1Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ 08544, USA · 2Graduate Center, City University of New York, New York, NY 10016, USA · Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA
Continuous Policy and Value Iteration for Stochastic Control Problems and Its Convergence
Jun 9, 2025Qi Feng, Gu WangStochastic Optimal Control Policy Iteration
Department of Mathematics, Florida State University, Tallahassee, 32306 · Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609
BR-MPPI: Barrier-Rate Guided MPPI for Enforcing Multiple Inequality Constraints with Learned Signed Distance Fields
Jun 8, 2025Hardik Parwana, Taekyung Kim, Kehan Long +4Constrained Motion Planning Control Barrier Functions
Robotics Department, University of Michigan, Ann Arbor, MI 48109, USA · Contextual Robotics Institute, University of California San Diego, La Jolla, CA 92093, USA. · Toyota Motor North America, Research & Development, Ann Arbor, MI 48105, USA.
Rough Stochastic Pontryagin Maximum Principle and an Indirect Shooting Method
Feb 10, 2025Thomas LewStochastic Differential Equations Stochastic Optimal Control
Toyota Research Institute
Safe Learning Control with Optimality and Stability Guarantees
Jan 26, 2025Xinyang Wang, Hongwei Zhang, Shimin Wang +2Control Barrier Functions Robust Control
Shenzhen Key Lab for Advanced Motion Control and Modern Automation Equipments, School of Intelligence Science and Engineering, Harbin Institute of Technology, Shenzhen, Guangdong 518055, China · School of Data Science, Lingnan University, Hong Kong · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, with M3S, SMART, and with MIT CSAIL +1
Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations
Date pendingMinseok Kim, Yeongjong Kim, Namkyeong Cho +1Neural PDE Solvers Stochastic Optimal Control
Department of Applied Artificial Intelligence, Seoul National University of Science and Technology, Seoul, Republic of Korea. · Department of Mathematics, Pohang University of Science and Technology, Pohang, Republic of Korea. · Department of Mathematical Finance and Big Data, Gachon University, Seongnam, Republic of Korea +1

Jul 10, 2025, cond-mat.dis-nnJ/K move · Enter open · S save

A statistical physics framework for optimal learning

Francesca Mignacco, Francesco Mori

1Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ 08544, USA · 2Graduate Center, City University of New York, New York, NY 10016, USA · Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA

Statistical Physics of Learning Neural Network Training Dynamics Statistical Learning Theory Optimal Control Hyperparameter Optimization

Open paper AskPDF arXiv

Learning is a complex dynamical process shaped by a range of interconnected decisions. Careful design of hyperparameter schedules for artificial neural networks or efficient allocation of cognitive resources by biological learners can dramatically affect performance. Yet, theoretical understanding of optimal learning strategies remains sparse, especially due to the intricate interplay between evolving metaparameters and nonlinear learning dynamics. The search for optimal protocols is further hindered by the high dimensionality of the learning space, often resulting in predominantly heuristic, difficult to interpret, and computationally demanding solutions. Here, we combine statistical physics with control theory in a unified theoretical framework to identify optimal learning protocols in prototypical neural network models. In the high-dimensional limit, we derive closed-form ordinary differential equations that track online stochastic gradient descent through low-dimensional order parameters. We formulate the design of learning protocols as an optimal control problem directly on the dynamics of the order parameters with the goal of minimizing the generalization error. This formulation encompasses a variety of learning scenarios, optimization constraints, and control budgets. We apply it to representative cases, including optimal curricula, adaptive dropout regularization and noise schedules in denoising autoencoders. We find nontrivial yet interpretable strategies highlighting how optimal protocols mediate learning trade-offs. Our results establish a principled foundation for understanding and designing optimal protocols and suggest a path toward a theory of meta-learning grounded in statistical physics.

Momentum

Related topics

Latest papers 96

A statistical physics framework for optimal learning

Continuous Policy and Value Iteration for Stochastic Control Problems and Its Convergence

BR-MPPI: Barrier-Rate Guided MPPI for Enforcing Multiple Inequality Constraints with Learned Signed Distance Fields

Rough Stochastic Pontryagin Maximum Principle and an Indirect Shooting Method

Safe Learning Control with Optimality and Stability Guarantees

Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations