The BAR-SOT Method: Long-term Average Cost Control as Stochastic Optimal Self-Transport

arXiv:2609.17966 · math.OC, cs.SY, eess.SY, math.PR · Submitted 2026-09-16 · Read on arXiv

math.OC, cs.SY, eess.SY, math.PR

Submitted: 2026-09-16

Updated: 2026-09-16

Terminology

• Regularization — 20× in this paper · explained in 3 episodes
• Consistency — 12× in this paper · explained in 3 episodes
• Benchmark — 11× in this paper · explained in 2 episodes
• Optimal Transport — 11× in this paper · explained in 5 episodes
• Embeddings — 5× in this paper · explained in 2 episodes
• Lyapunov function — 5× in this paper · explained in 2 episodes
• Core — 4× in this paper · explained in 2 episodes
• Reinforcement Learning — 4× in this paper · explained in 4 episodes
• Admissibility — 3× in this paper · explained in 2 episodes
• Action Space — 2× in this paper · explained in 1 episode
• Aggregation — 2× in this paper · explained in 1 episode
• Self-consistency — 2× in this paper · explained in 2 episodes
• Steering — 2× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Action Flow — 1× in this paper · explained in 1 episode
• Actor — 1× in this paper · explained in 3 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Alternation — 1× in this paper · explained in 1 episode
• Attention Mechanism — 1× in this paper · explained in 3 episodes
• Benchmarking — 1× in this paper · explained in 3 episodes
• Deep Reinforcement Learning — 1× in this paper · explained in 2 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Markov Decision Process (MDP) — 1× in this paper · explained in 11 episodes
• Physics-Informed Neural Network (PINN) — 1× in this paper · explained in 3 episodes
• Proximal Policy Optimization (PPO) — 1× in this paper · explained in 5 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Weak Basic Adjoint Relationship — 1× in this paper

Sources

• QGym: Scalable Simulation and Benchmarking of Queuing Network Controllers
• A Generalized Sinkhorn Algorithm for Mean-Field Schr\"odinger Bridge
• Optimal Weighted-Delay Scheduling in $2\times 2$ Input-Queued Switches
• A unified view of entropy-regularized Markov decision processes
• Steering Large Agent Populations using Mean-Field Schrodinger Bridges with Gaussian Mixture Models

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