Log-concave Sampling from a Convex Body with a Barrier: a Robust and Unified Dikin Walk

We consider the problem of sampling from a d-dimensional log-concave distribution π(θ) exp( f(θ)) for L-Lipschitz f, constrained to a convex body with an efficiently computable self-concordant barrier function, contained in a ball of radius R with a w-warm start. We propose a robust sampling framework that computes spectral approximations to the Hessian of the barrier functions in each iteration.