CAM is an unsupervised training method for discrete diffusion models on combinatorial optimization problems that uses discrete adjoint dynamics to supply low-variance trajectory-level signals.
Sethi.Optimal control theory
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Lecture notes present the first-order theory for optimal control with box constraints, including modified Pontryagin principle, projection/clamping formulas for quadratic Hamiltonians, and forward-backward sweep methods based on an existing book.
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Unsupervised Diffusion Solver for Combinatorial Optimization via Combinatorial Adjoint Matching
CAM is an unsupervised training method for discrete diffusion models on combinatorial optimization problems that uses discrete adjoint dynamics to supply low-variance trajectory-level signals.
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Lecture Note for Bounded Controls in Continuous-Time and Control of Several Variables
Lecture notes present the first-order theory for optimal control with box constraints, including modified Pontryagin principle, projection/clamping formulas for quadratic Hamiltonians, and forward-backward sweep methods based on an existing book.