repsmin

Repsmin, short for Representative Minimization, is a term used in optimization and machine learning to denote a class of methods that seek to minimize an objective by solving a reduced problem built from a set of representative samples or scenarios. The central idea is to replace the full problem with a smaller surrogate that preserves essential structure, enabling faster iterations with controlled approximation error. In practice, the representative set is updated during optimization and may be selected through random sampling, clustering, importance reweighting, or active selection.

Most implementations formulate a weighted loss over the representative set and incorporate a divergence-based constraint to keep the sampling distribution aligned with the original problem, often via a relative-entropy (KL) term or entropy regularization. The resulting algorithm alternates between updating model parameters to minimize the weighted surrogate and regenerating the representative set to reflect progress.

Theoretical properties depend on the specifics, but common results assume smoothness and bounded gradients; under those conditions, convergence to a stationary point can be established for suitable step sizes, with error bounds tied to how well the representative set approximates the full data.

Applications include large-scale empirical risk minimization, stochastic optimization in engineering, and reinforcement learning when simulating all scenarios is impractical. Repsmin is particularly useful when data or demand scenarios are abundant but expensive to process, and when a principled way to maintain distributional fidelity is desirable.

Relation to related methods: conceptually linked to stochastic gradient methods with mini-batches, importance sampling, and subset selection, as well as to entropy-regularized approaches such as REPS in reinforcement learning. In published literature, the exact meaning of repsmin has varied, and the term is not universally standardized.