# AS-BOX: Additional Sampling Method for Weighted Sum Problems with Box Constraints

## TL;DR

The paper introduces AS-BOX, a new stochastic optimization method for weighted sum problems with box constraints, combining adaptive sampling, projected gradients, and line search to improve efficiency and convergence.

## Contribution

It presents a novel adaptive sampling algorithm for constrained stochastic optimization that guarantees convergence and demonstrates practical effectiveness.

## Key findings

- AS-BOX outperforms existing algorithms in numerical tests.
- The method adapts sample size dynamically based on progress.
- Theoretical convergence and complexity bounds are established.

## Abstract

A class of optimization problems characterized by a weighted finite-sum objective function subject to box constraints is considered. We propose a novel stochastic optimization method, named AS-BOX (\text{A}ddi\-ti\-onal \text{S}ampling for \text{BOX} constraints), that combines projected gradient directions with adaptive variable sample size strategies and nonmonotone line search. The method dynamically adjusts the batch size based on progress with respect to the additional sampling function and on structural consistency of the projected direction, enabling practical adaptivity of AS-BOX, while ensuring theoretical support. We establish almost sure convergence under standard assumptions and provide complexity bounds. Numerical experiments demonstrate the efficiency and competitiveness of the proposed method compared to state-of-the-art algorithms.