| [ | |
| "The Sequential Optimization via SMC (SOSMC) framework replaces expensive inner MCMC sampling loops with a sequential Monte Carlo particle population that is reused and reweighted across optimization iterations, as formalized in Algorithm 1 (Section 3.1, Algorithm 1).", | |
| "Proposition 2 establishes a linear convergence rate for the idealized SOSMC iteration under mu-Polyak-Lojasiewicz and L-smooth loss assumptions, showing l(theta_k) - inf(l) <= (1-gamma*mu)^k * (l(theta_0) - inf(l)) for step size gamma <= 1/L (Proposition 2).", | |
| "Propositions 3 and 4 show the effective sample size of the SMC weights decays exponentially in the squared gradient norm and step size, ESS_infinity(gamma) = N*exp(-gamma^2*||grad l||^2) for Gaussian targets, motivating an adaptive step-size/resampling scheme (Section 4.2, Propositions 3-4).", | |
| "On Langevin reward-tuning of energy-based models with non-differentiable reward functions, SOSMC-ULA outperforms the ImpDiff baseline and achieves reduced variance compared to single-chain SOUL (Section 5.1).", | |
| "On 2D EBM benchmark datasets, SOSMC achieves higher objective values than ImpDiff for small regularization strengths, with particle-based reward estimates that track true expectations throughout optimization (Section 5.2).", | |
| "On MNIST, SOSMC remains robust in high dimensions even under mismatch between the pretraining and tuning kernels, without exhibiting reward hacking (Section 5.3)." | |
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